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 this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex n...In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.展开更多
Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algor...Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton (AHO) directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O(rln(εo/ε)) is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.展开更多
This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists...This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists of a feasibility step and several centrality steps. At last,we prove that the algorithm has O(nlog n/ε) polynomial complexity,which coincides with the best known one for the infeasible interior-point algorithm at present.展开更多
On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear pro...On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear programming, we propose a new framework of primal-dual infeasible interiorpoint method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results: (a) if the homotopy parameterμcan not reach to zero,then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x, we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x, we can obtain a (?)-solution; and(d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve x(μ), which towards to the generalized solutions.展开更多
This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the fea...This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.展开更多
A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not con...A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size, so providing the potential to dramatically improve the practical computation effectiveness.展开更多
In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps....In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasible interior-point methods.展开更多
The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real applications.In the cases where subproblems do not have closed-for...The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real applications.In the cases where subproblems do not have closed-form solutions,e.g.,due to complex constraints,infeasible subsolvers are indispensable,giving rise to an infeasible inexact PALM(PALM-I).Numerous efforts have been devoted to analyzing the feasible PALM,while little attention has been paid to the PALM-I.The usage of the PALM-I thus lacks a theoretical guarantee.The essential difficulty of analysis consists in the objective value nonmonotonicity induced by the infeasibility.We study in the present work the convergence properties of the PALM-I.In particular,we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact criterion.Based upon these,we manage to establish the stationarity of any accumulation point,and moreover,show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz property.The prominent advantages of the PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3-dimensional anisotropic frictional contact.展开更多
When the allocated fixed cost is treated as the complement of other costs, conventional data envelopment analysis(DEA) researches have ignored the effect of the return to scale(RTS) in fixed cost allocation problems. ...When the allocated fixed cost is treated as the complement of other costs, conventional data envelopment analysis(DEA) researches have ignored the effect of the return to scale(RTS) in fixed cost allocation problems. This paper first demonstrates why the RTS should be considered in fixed cost allocation problems. Then treating the fixed cost as a complementary input, the authors investigate the relationship between the allocated cost and the variable return to scale(VRS) efficiency based on the super BCC DEA model. However, the infeasibility problem may exist in this situation.To deal with it, the authors propose an algorithm. The authors find that the super BCC efficiency is a monotone non-increasing function of the allocated cost. Based on the relationship, the authors finally propose a fixed cost allocation approach in terms of principles as:(i) The fixed cost proportion allocated to inelastic DMUs should be consistent with their consumed cost proportion, and(ii) the same efficiency satisfaction degree to the rest DMUs. The optimal allocation scheme is unique. A numerical example and a real example of allocating fixed costs among 13 subsidiaries are employed to illustrate the proposed approach.展开更多
ORTHOGONAL arrays (OAs) have important applications to many fields. A lot of OAs and their construction methods have been introduced in the experimental design literature (for example, Box, Hunter and Dey). These OAs ...ORTHOGONAL arrays (OAs) have important applications to many fields. A lot of OAs and their construction methods have been introduced in the experimental design literature (for example, Box, Hunter and Dey). These OAs are used for an experimenter to choose in practice.展开更多
Orthogonal arrays (OAs) are used in many fields such as industry, agriculture, medi-cine, quality control of products and other scientific experiments. There are a lot of OAsin the existing experimental design literat...Orthogonal arrays (OAs) are used in many fields such as industry, agriculture, medi-cine, quality control of products and other scientific experiments. There are a lot of OAsin the existing experimental design literature. But when an experimenter wants to choosean OA in practice, it still often happens tha any existing OA contains someunsuitable factor-level combinations. For example, in a chemical experiment withtemperature and pressure as its two factors, high temperature and high pressure展开更多
This paper proposes an infeasible interior-point algorithm for linear complementarity problem with full-Newton steps.The main iteration consists of a feasibility step and several centrality steps.No more than O(n log...This paper proposes an infeasible interior-point algorithm for linear complementarity problem with full-Newton steps.The main iteration consists of a feasibility step and several centrality steps.No more than O(n log(n /ε))iterations are required for getting ε-solution of the problem at hand,which coincides with the best-known bound for infeasible interior-point algorithms.展开更多
We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iterat...We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iteration consisted of one socalled feasibility step and a few centering steps.Here,each iteration consists of only a feasibility step.Thus,the new algorithm improves the number of iterations and the improvement is due to a lemma which gives an upper bound for the proximity after the feasibility step.The complexity result coincides with the best-known iteration bound for infeasible interior-point methods.展开更多
In this paper,we present a path-following infeasible interior-point method for P∗(κ)horizontal linear complementarity problems(P∗(κ)-HLCPs).The algorithm is based on a simple kernel function for finding the search d...In this paper,we present a path-following infeasible interior-point method for P∗(κ)horizontal linear complementarity problems(P∗(κ)-HLCPs).The algorithm is based on a simple kernel function for finding the search directions and defining the neighborhood of the central path.The algorithm follows the central path related to some perturbations of the original problem,using the so-called feasibility and centering steps,along with only full such steps.Therefore,it has the advantage that the calculation of the step sizes at each iteration is avoided.The complexity result shows that the full-Newton step infeasible interior-point algorithm based on the simple kernel function enjoys the best-known iteration complexity for P∗(κ)-HLCPs.展开更多
In this paper, the structure of infeasible solutions to Job Shop Scheduling Problem (JSSP) is quantitatively analyzed, and a necessary and sufficient condition of the deadlock for JSSP is also given. For a simple JSSP...In this paper, the structure of infeasible solutions to Job Shop Scheduling Problem (JSSP) is quantitatively analyzed, and a necessary and sufficient condition of the deadlock for JSSP is also given. For a simple JSSP with 2 machines and N jobs, a formula for calculating the infeasible solutions is proposed, which shows that the infeasible solution possesses the majority of search space and only those heuristic algorithms which do not produce infeasible solutions are valid.展开更多
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 this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.
基金supported by the National Natural Science Foundation of China (Nos. 71061002 and 11071158)the Natural Science Foundation of Guangxi Province of China (Nos. 0832052 and 2010GXNSFB013047)
文摘Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton (AHO) directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O(rln(εo/ε)) is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.
基金Supported by the National Natural Science Fund Finances Projects(71071119)
文摘This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists of a feasibility step and several centrality steps. At last,we prove that the algorithm has O(nlog n/ε) polynomial complexity,which coincides with the best known one for the infeasible interior-point algorithm at present.
文摘On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear programming, we propose a new framework of primal-dual infeasible interiorpoint method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results: (a) if the homotopy parameterμcan not reach to zero,then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x, we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x, we can obtain a (?)-solution; and(d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve x(μ), which towards to the generalized solutions.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11461021)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2017JM1014)Scientific Research Project of Hezhou University(Grant Nos.2014YBZK06 and 2016HZXYSX03)
文摘This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.
基金Supported by the Doctoral Educational Foundation of China of the Ministry of Education(20020486035)
文摘A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size, so providing the potential to dramatically improve the practical computation effectiveness.
文摘In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasible interior-point methods.
基金supported by National Natural Science Foundation of China(Grant Nos.12125108,11971466,11991021,11991020,12021001 and 12288201)Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.ZDBS-LY-7022)CAS(the Chinese Academy of Sciences)AMSS(Academy of Mathematics and Systems Science)-PolyU(The Hong Kong Polytechnic University)Joint Laboratory of Applied Mathematics.
文摘The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real applications.In the cases where subproblems do not have closed-form solutions,e.g.,due to complex constraints,infeasible subsolvers are indispensable,giving rise to an infeasible inexact PALM(PALM-I).Numerous efforts have been devoted to analyzing the feasible PALM,while little attention has been paid to the PALM-I.The usage of the PALM-I thus lacks a theoretical guarantee.The essential difficulty of analysis consists in the objective value nonmonotonicity induced by the infeasibility.We study in the present work the convergence properties of the PALM-I.In particular,we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact criterion.Based upon these,we manage to establish the stationarity of any accumulation point,and moreover,show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz property.The prominent advantages of the PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3-dimensional anisotropic frictional contact.
基金supported by the China Postdoctoral Science Foundation under Grant Nos.2015M571135,2015M570155,and 2015M571134the National Natural Science Foundation of China under Grant Nos.71271196,71201156,71403055,and 21307150+1 种基金Science Funds for Creative Research Groups of the National Natural Science Foundation of ChinaUniversity of Science and Technology of China under Grant Nos.71121061 and WK2040160008
文摘When the allocated fixed cost is treated as the complement of other costs, conventional data envelopment analysis(DEA) researches have ignored the effect of the return to scale(RTS) in fixed cost allocation problems. This paper first demonstrates why the RTS should be considered in fixed cost allocation problems. Then treating the fixed cost as a complementary input, the authors investigate the relationship between the allocated cost and the variable return to scale(VRS) efficiency based on the super BCC DEA model. However, the infeasibility problem may exist in this situation.To deal with it, the authors propose an algorithm. The authors find that the super BCC efficiency is a monotone non-increasing function of the allocated cost. Based on the relationship, the authors finally propose a fixed cost allocation approach in terms of principles as:(i) The fixed cost proportion allocated to inelastic DMUs should be consistent with their consumed cost proportion, and(ii) the same efficiency satisfaction degree to the rest DMUs. The optimal allocation scheme is unique. A numerical example and a real example of allocating fixed costs among 13 subsidiaries are employed to illustrate the proposed approach.
文摘ORTHOGONAL arrays (OAs) have important applications to many fields. A lot of OAs and their construction methods have been introduced in the experimental design literature (for example, Box, Hunter and Dey). These OAs are used for an experimenter to choose in practice.
基金Project supported by the National Natural Science Foundation of China.
文摘Orthogonal arrays (OAs) are used in many fields such as industry, agriculture, medi-cine, quality control of products and other scientific experiments. There are a lot of OAsin the existing experimental design literature. But when an experimenter wants to choosean OA in practice, it still often happens tha any existing OA contains someunsuitable factor-level combinations. For example, in a chemical experiment withtemperature and pressure as its two factors, high temperature and high pressure
基金Supported by the National Natural Science Foundation of China(71071119)
文摘This paper proposes an infeasible interior-point algorithm for linear complementarity problem with full-Newton steps.The main iteration consists of a feasibility step and several centrality steps.No more than O(n log(n /ε))iterations are required for getting ε-solution of the problem at hand,which coincides with the best-known bound for infeasible interior-point algorithms.
文摘We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iteration consisted of one socalled feasibility step and a few centering steps.Here,each iteration consists of only a feasibility step.Thus,the new algorithm improves the number of iterations and the improvement is due to a lemma which gives an upper bound for the proximity after the feasibility step.The complexity result coincides with the best-known iteration bound for infeasible interior-point methods.
文摘In this paper,we present a path-following infeasible interior-point method for P∗(κ)horizontal linear complementarity problems(P∗(κ)-HLCPs).The algorithm is based on a simple kernel function for finding the search directions and defining the neighborhood of the central path.The algorithm follows the central path related to some perturbations of the original problem,using the so-called feasibility and centering steps,along with only full such steps.Therefore,it has the advantage that the calculation of the step sizes at each iteration is avoided.The complexity result shows that the full-Newton step infeasible interior-point algorithm based on the simple kernel function enjoys the best-known iteration complexity for P∗(κ)-HLCPs.
基金Supported by The National Natural Science Foundation of China ( No.794 3 0 0 2 2 )
文摘In this paper, the structure of infeasible solutions to Job Shop Scheduling Problem (JSSP) is quantitatively analyzed, and a necessary and sufficient condition of the deadlock for JSSP is also given. For a simple JSSP with 2 machines and N jobs, a formula for calculating the infeasible solutions is proposed, which shows that the infeasible solution possesses the majority of search space and only those heuristic algorithms which do not produce infeasible solutions are valid.