For an arbitrary tensor(multi-index array) with linear constraints at each direction,it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for t...For an arbitrary tensor(multi-index array) with linear constraints at each direction,it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for the corresponding directions.展开更多
A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programming problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent ...A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programming problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.展开更多
An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace def...An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace defined by the active constraints,which is solved using the quasi-Newton method.The major update formula is similar to the one given by Dennis,Gay and Welsch (1981).In this paper,we state the detailed implement of the algorithm,such as the choice of active set,the solution of subproblem and the avoidance of zigzagging.We also prove the globally convergent property of the algorithm.展开更多
This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted av...This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted average and the cosine simplex algorithm. The first approach identifies binding constraints by using the weighted average of each constraint, whereas the second algorithm is based on the cosine similarity between the vector of the objective function and the constraints. These two approaches are complementary, and when used together, they locate the essential subset of initial constraints required for solving medium and large-scale linear programming problems. After reducing the dimension of the linear programming problem using the subset of the essential constraints, the solution method can be chosen from any suitable method for linear programming. The proposed approach was applied to a set of well-known benchmarks as well as more than 2000 random medium and large-scale linear programming problems. The results are promising, indicating that the new approach contributes to the reduction of both the size of the problems and the total number of iterations required. A tree-based classification model also confirmed the need for combining the two approaches. A detailed numerical example, the general numerical results, and the statistical analysis for the decision tree procedure are presented.展开更多
This paper considers the concave minimization problem with linear constrailits,proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker poiats,then combines this technique with nank-Wolfe method and simp...This paper considers the concave minimization problem with linear constrailits,proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker poiats,then combines this technique with nank-Wolfe method and simplex method to form a pivoting method which can determine a strictly local minimizer of the problem in a finite number of iterations. Basing on strictly local minimizers, a new cutting plane method is proposed. Under some mild conditions, the new cutting plane method is proved to be finitely terminated at an θ-global minimizer of the problem.展开更多
A parametric variational principle and the corresponding numerical algorithm are proposed to solve a linear-quadratic(LQ)optimal control problem with control inequality constraints.Based on the parametric variational ...A parametric variational principle and the corresponding numerical algorithm are proposed to solve a linear-quadratic(LQ)optimal control problem with control inequality constraints.Based on the parametric variational principle,this control problem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations,which are solved by a linear complementarity solver in the discrete-time domain.The costate variable information is also evaluated by the proposed method.The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems.Two numerical examples are used to test the validity of the proposed method.The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust.The numerical simulations show that the parametric variational algorithm is effective for LQ optimal control problems with control inequality constraints.展开更多
This paper investigates the robust tracking control problem for a class of nonlinear networked control systems (NCSs) using the Takagi-Sugeno (T-S) fuzzy model approach.Based on a time-varying delay system transformed...This paper investigates the robust tracking control problem for a class of nonlinear networked control systems (NCSs) using the Takagi-Sugeno (T-S) fuzzy model approach.Based on a time-varying delay system transformed from the NCSs,an augmented Lyapunov function containing more useful information is constructed.A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints (IQCs) are satisfied while both time-varying networkinduced delays and packet losses are taken into account.The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities (LMIs) and parallel distributed compensation (PDC).Furthermore,robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result.Finally,numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.展开更多
Network virtualization is known as a promising technology to tackle the ossification of current Internet and will play an important role in the future network area. Virtual network embedding(VNE) is a key issue in net...Network virtualization is known as a promising technology to tackle the ossification of current Internet and will play an important role in the future network area. Virtual network embedding(VNE) is a key issue in network virtualization. VNE is NP-hard and former VNE algorithms are mostly heuristic in the literature.VNE exact algorithms have been developed in recent years. However, the constraints of exact VNE are only node capacity and link bandwidth.Based on these, this paper presents an exact VNE algorithm, ILP-LC, which is based on Integer Linear Programming(ILP), for embedding virtual network request with location constraints. This novel algorithm is aiming at mapping virtual network request(VNR) successfully as many as possible and consuming less substrate resources.The topology of each VNR is randomly generated by Waxman model. Simulation results show that the proposed ILP-LC algorithm outperforms the typical heuristic algorithms in terms of the VNR acceptance ratio, at least 15%.展开更多
The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched(gai...The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched(gain-scheduled) state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.展开更多
The Lagrange-I equations and measure differential equations for multibody systems with unilateral and bilateral constraints are constructed.For bilateral constraints,frictional forces and their impulses contain the pr...The Lagrange-I equations and measure differential equations for multibody systems with unilateral and bilateral constraints are constructed.For bilateral constraints,frictional forces and their impulses contain the products of the filled-in relay function induced by Coulomb friction and the absolute values of normal constraint reactions.With the time-stepping impulse-velocity scheme,the measure differential equations are discretized.The equations of horizontal linear complementarity problems(HLCPs),which are used to compute the impulses,are constructed by decomposing the absolute function and the filled-in relay function.These HLCP equations degenerate into equations of LCPs for frictional unilateral constraints,or HLCPs for frictional bilateral constraints.Finally,a numerical simulation for multibody systems with both unilateral and bilateral constraints is presented.展开更多
The dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coorfinates, and Mishirskiiequalions are regarded as the fundamental equations of...The dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coorfinates, and Mishirskiiequalions are regarded as the fundamental equations of dynamics with non-linear andnon-holononlic constraints in one order for the system of the variable mass. From thesethe variant ddferential-equations of dynamics expressed by quasi-coordinates arederived. The fundamental equations of dynamics are compatible with the principle ofJourdain. A case is cited.展开更多
In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary ...In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC.展开更多
In this paper we discuss about infeasibility diagnosis and infeasibility resolution, when the constraint method is used for solving multi objective linear programming problems. We propose an algorithm for resolution o...In this paper we discuss about infeasibility diagnosis and infeasibility resolution, when the constraint method is used for solving multi objective linear programming problems. We propose an algorithm for resolution of infeasibility, which is a combination of interactive, weighting and constraint methods.Numerical examples are provided to illustrate the techniques developed.展开更多
In Linear Programming (LP) applications, unexpected non binding constraints are among the “why” questions that can cause a great deal of debate. That is, those constraints that are expected to have been active based...In Linear Programming (LP) applications, unexpected non binding constraints are among the “why” questions that can cause a great deal of debate. That is, those constraints that are expected to have been active based on price signals, market drivers or manager’s experiences. In such situations, users have to solve many auxiliary LP problems in order to grasp the underlying technical reasons. This practice, however, is cumbersome and time-consuming in large scale industrial models. This paper suggests a simple solution-assisted methodology, based on known concepts in LP, to detect a sub set of active constraints that have the most preventing impact on any non binding constraint at the optimal solution. The approach is based on the marginal rate of substitutions that are available in the final simplex tableau. A numerical example followed by a real-type case study is provided for illustration.展开更多
Traditional linear program (LP) models are deterministic. The way that constraint limit uncertainty is handled is to compute the range of feasibility. After the optimal solution is obtained, typically by the simplex m...Traditional linear program (LP) models are deterministic. The way that constraint limit uncertainty is handled is to compute the range of feasibility. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each constraint limit, one at a time. This yields the range of feasibility within which the solution remains feasible. This sensitivity analysis is useful for helping the analyst get a feel for the problem. However, it is unrealistic because some constraint limits can vary randomly. These are typically constraint limits based on expected inventory. Inventory may fall short if there are overdue deliveries, unplanned machine failure, spoilage, etc. A realistic LP is created for simultaneously randomizing the constraint limits from any probability distribution. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendencies, spread, skewness and extreme values for the purpose of risk analysis. The spreadsheet design presented is ideal for teaching Monte Carlo simulation and risk analysis to graduate students in business analytics with no specialized programming language requirement.展开更多
AbstractAn interior trust-region-based algorithm for linearly constrained minimization problems is proposed and analyzed. This algorithm is similar to trust region algorithms for unconstrained minimization: a trust re...AbstractAn interior trust-region-based algorithm for linearly constrained minimization problems is proposed and analyzed. This algorithm is similar to trust region algorithms for unconstrained minimization: a trust region subproblem on a subspace is solved in each iteration. We establish that the proposed algorithm has convergence properties analogous to those of the trust region algorithms for unconstrained minimization. Namely, every limit point of the generated sequence satisfies the Krush-Kuhn-Tucker (KKT) conditions and at least one limit point satisfies second order necessary optimality conditions. In addition, if one limit point is a strong local minimizer and the Hessian is Lipschitz continuous in a neighborhood of that point, then the generated sequence converges globally to that point in the rate of at least 2-step quadratic. We are mainly concerned with the theoretical properties of the algorithm in this paper. Implementation issues and adaptation to large-scale problems will be addressed in展开更多
Linear programming is a method for solving linear optimization problems with constraints, widely met in real-world applications. In the vast majority of these applications, the number of constraints is significantly l...Linear programming is a method for solving linear optimization problems with constraints, widely met in real-world applications. In the vast majority of these applications, the number of constraints is significantly larger than the number of variables. Since the crucial subject of these problems is to detect the constraints that will be verified as equality in an optimal solution, there are methods for investigating such constraints to accelerate the whole process. In this paper, a technique named proximity technique is addressed, which under a proposed theoretical framework gives an ascending order to the constraints in such a way that those with low ranking are characterized of high priority to be binding. Under this framework, two new Linear programming optimization algorithms are introduced, based on a proposed Utility matrix and a utility vector accordingly. For testing the addressed algorithms firstly a generator of 10,000 random linear programming problems of dimension n with m constraints, where , is introduced in order to simulate as many as possible real-world problems, and secondly, real-life linear programming examples from the NETLIB repository are tested. A discussion of the numerical results is given. Furthermore, already known methods for solving linear programming problems are suggested to be fitted under the proposed framework.展开更多
We describe a new active-set, cutting-plane Constraint Optimal Selection Technique (COST) for solving general linear programming problems. We describe strategies to bound the initial problem and simultaneously add mul...We describe a new active-set, cutting-plane Constraint Optimal Selection Technique (COST) for solving general linear programming problems. We describe strategies to bound the initial problem and simultaneously add multiple constraints. We give an interpretation of the new COST’s selection rule, which considers both the depth of constraints as well as their angles from the objective function. We provide computational comparisons of the COST with existing linear programming algorithms, including other COSTs in the literature, for some large-scale problems. Finally, we discuss conclusions and future research.展开更多
In development of baroclinic disturbances, baroclinity of basic temperature field varies with conversion of available potential energy. The growth rate which depends on the baroclinity varies as well. However, in prev...In development of baroclinic disturbances, baroclinity of basic temperature field varies with conversion of available potential energy. The growth rate which depends on the baroclinity varies as well. However, in previous linear theories, the growth rate was considered constant, so development of disturbances was not constrained by energy sources in the linear theories. In terms of energy conservation and conversion in an isolated atmosphere, we may study the variations in the baroclinity and growth rate and draw the corresponding pictures of perturbation developments in the varying environments. The amplification for the most unstable Eady wave is discussed as an example. It will be found that growth of baroclinic perturbations constrained by energy conservation is significantly different from the growth at the initial constant rate after mature stage.展开更多
基金supported by the Russian Fund for Basic Research (RFBR grant 08-01-00115,RFBR/DFG grant 09-01-91332,RFBR grant 09-01-12058)Priority Research Programme of Department of Mathematical Sciences of Russian Academy of Sciences
文摘For an arbitrary tensor(multi-index array) with linear constraints at each direction,it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for the corresponding directions.
文摘A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programming problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.
基金Supported by The Natural Science Fundations of China and Jiangsu
文摘An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace defined by the active constraints,which is solved using the quasi-Newton method.The major update formula is similar to the one given by Dennis,Gay and Welsch (1981).In this paper,we state the detailed implement of the algorithm,such as the choice of active set,the solution of subproblem and the avoidance of zigzagging.We also prove the globally convergent property of the algorithm.
文摘This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted average and the cosine simplex algorithm. The first approach identifies binding constraints by using the weighted average of each constraint, whereas the second algorithm is based on the cosine similarity between the vector of the objective function and the constraints. These two approaches are complementary, and when used together, they locate the essential subset of initial constraints required for solving medium and large-scale linear programming problems. After reducing the dimension of the linear programming problem using the subset of the essential constraints, the solution method can be chosen from any suitable method for linear programming. The proposed approach was applied to a set of well-known benchmarks as well as more than 2000 random medium and large-scale linear programming problems. The results are promising, indicating that the new approach contributes to the reduction of both the size of the problems and the total number of iterations required. A tree-based classification model also confirmed the need for combining the two approaches. A detailed numerical example, the general numerical results, and the statistical analysis for the decision tree procedure are presented.
文摘This paper considers the concave minimization problem with linear constrailits,proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker poiats,then combines this technique with nank-Wolfe method and simplex method to form a pivoting method which can determine a strictly local minimizer of the problem in a finite number of iterations. Basing on strictly local minimizers, a new cutting plane method is proposed. Under some mild conditions, the new cutting plane method is proved to be finitely terminated at an θ-global minimizer of the problem.
基金supported by the National Natural Science Foundation of China(Nos.11102031 and 11272076)the Fundamental Research Funds for Central Universities(No.DUT13LK25)+2 种基金the Key Laboratory Fund of Liaoning Province(No.L2013015)the China Postdoctoral Science Foundation(No.2014M550155)the State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(No.MCMS-0114G02)
文摘A parametric variational principle and the corresponding numerical algorithm are proposed to solve a linear-quadratic(LQ)optimal control problem with control inequality constraints.Based on the parametric variational principle,this control problem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations,which are solved by a linear complementarity solver in the discrete-time domain.The costate variable information is also evaluated by the proposed method.The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems.Two numerical examples are used to test the validity of the proposed method.The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust.The numerical simulations show that the parametric variational algorithm is effective for LQ optimal control problems with control inequality constraints.
基金supported by National Natural Science Foundation of China (No. 60574014, No. 60425310)Doctor Subject Foundation of China (No. 200805330004)+2 种基金Program for New Century Excellent Talents in University (No. NCET-06-0679)Natural Science Foundation of Hunan Province of China (No. 08JJ1010)Science Foundation of Education Department of Hunan Province (No. 08C106)
文摘This paper investigates the robust tracking control problem for a class of nonlinear networked control systems (NCSs) using the Takagi-Sugeno (T-S) fuzzy model approach.Based on a time-varying delay system transformed from the NCSs,an augmented Lyapunov function containing more useful information is constructed.A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints (IQCs) are satisfied while both time-varying networkinduced delays and packet losses are taken into account.The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities (LMIs) and parallel distributed compensation (PDC).Furthermore,robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result.Finally,numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.
基金supported by the National Basic Research Program of China(973 Program)under Grant 2013CB329005
文摘Network virtualization is known as a promising technology to tackle the ossification of current Internet and will play an important role in the future network area. Virtual network embedding(VNE) is a key issue in network virtualization. VNE is NP-hard and former VNE algorithms are mostly heuristic in the literature.VNE exact algorithms have been developed in recent years. However, the constraints of exact VNE are only node capacity and link bandwidth.Based on these, this paper presents an exact VNE algorithm, ILP-LC, which is based on Integer Linear Programming(ILP), for embedding virtual network request with location constraints. This novel algorithm is aiming at mapping virtual network request(VNR) successfully as many as possible and consuming less substrate resources.The topology of each VNR is randomly generated by Waxman model. Simulation results show that the proposed ILP-LC algorithm outperforms the typical heuristic algorithms in terms of the VNR acceptance ratio, at least 15%.
基金supported by the National Natural Science Foundation of China(6132106261503100)the China Postdoctoral Science Foundation(2014M550189)
文摘The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched(gain-scheduled) state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.
基金supported by the National Natural Science Foundation of China (10672007)
文摘The Lagrange-I equations and measure differential equations for multibody systems with unilateral and bilateral constraints are constructed.For bilateral constraints,frictional forces and their impulses contain the products of the filled-in relay function induced by Coulomb friction and the absolute values of normal constraint reactions.With the time-stepping impulse-velocity scheme,the measure differential equations are discretized.The equations of horizontal linear complementarity problems(HLCPs),which are used to compute the impulses,are constructed by decomposing the absolute function and the filled-in relay function.These HLCP equations degenerate into equations of LCPs for frictional unilateral constraints,or HLCPs for frictional bilateral constraints.Finally,a numerical simulation for multibody systems with both unilateral and bilateral constraints is presented.
文摘The dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coorfinates, and Mishirskiiequalions are regarded as the fundamental equations of dynamics with non-linear andnon-holononlic constraints in one order for the system of the variable mass. From thesethe variant ddferential-equations of dynamics expressed by quasi-coordinates arederived. The fundamental equations of dynamics are compatible with the principle ofJourdain. A case is cited.
文摘In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC.
基金Supported by the Natural Science Foundation of Henan Province(0511012000 0511013600) Supported by the Science Foundation for Pure Research of Natural Science of the Education Department of Henan Province(200512950001)
文摘In this paper we discuss about infeasibility diagnosis and infeasibility resolution, when the constraint method is used for solving multi objective linear programming problems. We propose an algorithm for resolution of infeasibility, which is a combination of interactive, weighting and constraint methods.Numerical examples are provided to illustrate the techniques developed.
文摘In Linear Programming (LP) applications, unexpected non binding constraints are among the “why” questions that can cause a great deal of debate. That is, those constraints that are expected to have been active based on price signals, market drivers or manager’s experiences. In such situations, users have to solve many auxiliary LP problems in order to grasp the underlying technical reasons. This practice, however, is cumbersome and time-consuming in large scale industrial models. This paper suggests a simple solution-assisted methodology, based on known concepts in LP, to detect a sub set of active constraints that have the most preventing impact on any non binding constraint at the optimal solution. The approach is based on the marginal rate of substitutions that are available in the final simplex tableau. A numerical example followed by a real-type case study is provided for illustration.
文摘Traditional linear program (LP) models are deterministic. The way that constraint limit uncertainty is handled is to compute the range of feasibility. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each constraint limit, one at a time. This yields the range of feasibility within which the solution remains feasible. This sensitivity analysis is useful for helping the analyst get a feel for the problem. However, it is unrealistic because some constraint limits can vary randomly. These are typically constraint limits based on expected inventory. Inventory may fall short if there are overdue deliveries, unplanned machine failure, spoilage, etc. A realistic LP is created for simultaneously randomizing the constraint limits from any probability distribution. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendencies, spread, skewness and extreme values for the purpose of risk analysis. The spreadsheet design presented is ideal for teaching Monte Carlo simulation and risk analysis to graduate students in business analytics with no specialized programming language requirement.
基金Research partially supported by the Faculty Research Grant RIG-35547 and ROG-34628 of the University of North Texas and in part by the Cornell Theory Center which receives major funding from the National Science Foundation and IBM Corporation with ad
文摘AbstractAn interior trust-region-based algorithm for linearly constrained minimization problems is proposed and analyzed. This algorithm is similar to trust region algorithms for unconstrained minimization: a trust region subproblem on a subspace is solved in each iteration. We establish that the proposed algorithm has convergence properties analogous to those of the trust region algorithms for unconstrained minimization. Namely, every limit point of the generated sequence satisfies the Krush-Kuhn-Tucker (KKT) conditions and at least one limit point satisfies second order necessary optimality conditions. In addition, if one limit point is a strong local minimizer and the Hessian is Lipschitz continuous in a neighborhood of that point, then the generated sequence converges globally to that point in the rate of at least 2-step quadratic. We are mainly concerned with the theoretical properties of the algorithm in this paper. Implementation issues and adaptation to large-scale problems will be addressed in
文摘Linear programming is a method for solving linear optimization problems with constraints, widely met in real-world applications. In the vast majority of these applications, the number of constraints is significantly larger than the number of variables. Since the crucial subject of these problems is to detect the constraints that will be verified as equality in an optimal solution, there are methods for investigating such constraints to accelerate the whole process. In this paper, a technique named proximity technique is addressed, which under a proposed theoretical framework gives an ascending order to the constraints in such a way that those with low ranking are characterized of high priority to be binding. Under this framework, two new Linear programming optimization algorithms are introduced, based on a proposed Utility matrix and a utility vector accordingly. For testing the addressed algorithms firstly a generator of 10,000 random linear programming problems of dimension n with m constraints, where , is introduced in order to simulate as many as possible real-world problems, and secondly, real-life linear programming examples from the NETLIB repository are tested. A discussion of the numerical results is given. Furthermore, already known methods for solving linear programming problems are suggested to be fitted under the proposed framework.
文摘We describe a new active-set, cutting-plane Constraint Optimal Selection Technique (COST) for solving general linear programming problems. We describe strategies to bound the initial problem and simultaneously add multiple constraints. We give an interpretation of the new COST’s selection rule, which considers both the depth of constraints as well as their angles from the objective function. We provide computational comparisons of the COST with existing linear programming algorithms, including other COSTs in the literature, for some large-scale problems. Finally, we discuss conclusions and future research.
文摘In development of baroclinic disturbances, baroclinity of basic temperature field varies with conversion of available potential energy. The growth rate which depends on the baroclinity varies as well. However, in previous linear theories, the growth rate was considered constant, so development of disturbances was not constrained by energy sources in the linear theories. In terms of energy conservation and conversion in an isolated atmosphere, we may study the variations in the baroclinity and growth rate and draw the corresponding pictures of perturbation developments in the varying environments. The amplification for the most unstable Eady wave is discussed as an example. It will be found that growth of baroclinic perturbations constrained by energy conservation is significantly different from the growth at the initial constant rate after mature stage.