In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear ...In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.展开更多
In this paper, we propose a theoretical framework of an infeasible interior-point algorithm for solving monotone linear cornplementarity problems over symmetric cones （SCLCP）. The new algorithm gets Newton-like dire...In this paper, we propose a theoretical framework of an infeasible interior-point algorithm for solving monotone linear cornplementarity problems over symmetric cones （SCLCP）. The new algorithm gets Newton-like directions from the Chen-Harker-Kanzow-Smale （CHKS） smoothing equation of the SCLCP. It possesses the following features： The starting point is easily chosen; one approximate Newton step is computed and accepted at each iteration; the iterative point with unit stepsize automatically remains in the neighborhood of central path; the iterative sequence is bounded and possesses （9（rL） polynomial-time complexity under the monotonicity and solvability of the SCLCP.展开更多
In this paper we present a large-update primal-dual interior-point algorithm for convex quadratic semi-definite optimization problems based on a new parametric kernel function.The goal of this paper is to investigate ...In this paper we present a large-update primal-dual interior-point algorithm for convex quadratic semi-definite optimization problems based on a new parametric kernel function.The goal of this paper is to investigate such a kernel function and show that the algorithm has the best complexity bound.The complexity bound is shown to be O(√n log n log n/∈).展开更多
This paper treats multi-objective problem for manufacturing process design. A purpose of the process design is to decide combinations of work elements assigned to different work centers. Multiple work elements are ord...This paper treats multi-objective problem for manufacturing process design. A purpose of the process design is to decide combinations of work elements assigned to different work centers. Multiple work elements are ordinarily assigned to each center. Here, infeasible solutions are easily generated by precedence relationship of work elements in process design. The number of infeasible solutions generated is ordinarily larger than that of feasible solutions generated in the process. Therefore, feasible and infeasible solutions are located in any neighborhood in solution space. It is difficult to seek high quality Pareto solutions in this problem by using conventional multi-objective evolutional algorithms. We consider that the problem includes difficulty to seek high quality solutions by the following characteristics： （1） Since infeasible solutions are resemble to good feasible solutions, many infeasible solutions which have good values of objective functions are easily sought in the search process, （2） Infeasible solutions are useful to select new variable conditions generating good feasible solutions in search process. In this study, a multi-objective genetic algorithm including local search is proposed using these characteristics. Maximum value of average operation times and maximum value of dispersion of operation time in all work centers are used as objective functions to promote productivity. The optimal weighted coefficient is introduced to control the ratio of feasible solutions to all solutions selected in crossover and selection process in the algorithm. This paper shows the effectiveness of the proposed algorithm on simple model.展开更多
This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one c...This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O（√nL） iteration complexity which is the best result for convex quadratic programming so far.展开更多
Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with si...Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods （IPMs） for semidefinite optimization （SDO） is designed. And the iteration complexity of the algorithm as O（n^3/4 log n/ε） with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O（n log n/ε） in large-updates case.展开更多
In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming （LP） problems. The algorithms are based on a few kernel functions, including both serf-regular functio...In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming （LP） problems. The algorithms are based on a few kernel functions, including both serf-regular functions and non-serf-regular ones. The dynamic step size is compared with fixed step size for the algorithms in inner iteration of Newton step. Numerical tests show that the algorithms with dynaraic step size are more efficient than those with fixed step size.展开更多
In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions a...In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions and the strategy of the central path.At each iteration, only full-Newton steps are used.Finally, the favorable polynomial complexity bound for the algorithm with the small-update method is deserved, namely, O(√n log n /ε).展开更多
The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off betwee...The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interiorpoint method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.展开更多
A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theore...A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theorems of the algorithm is established.In addition,some numerical results are reported.展开更多
In this paper, we propose two hybrid inertial CQ projection algorithms with linesearch process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the ...In this paper, we propose two hybrid inertial CQ projection algorithms with linesearch process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the iteration to accelerate the convergence of the algorithm, and adopt flexible rules for selecting the stepsize and the shrinking projection region, which makes an optimal stepsize available at each iteration. The shrinking projection region is the intersection of three sets, which are the set C and two hyperplanes. Furthermore, we modify the Armijo-type line-search step in the presented algorithm to get a new algorithm.The algorithms are shown to be convergent under certain mild assumptions. Besides, numerical examples are given to show that the proposed algorithms have better performance than the general CQ algorithm.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
基金Supported by University Science Research Project of Anhui Province(2023AH052921)Outstanding Youth Talent Project of Anhui Province(gxyq2021254)。
文摘In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.
基金Supported by the National Natural Science Foundation of China(No.10671010)Specialized Research Fund for the Doctoral Program of Higher Education(200800040024)
文摘In this paper, we propose a theoretical framework of an infeasible interior-point algorithm for solving monotone linear cornplementarity problems over symmetric cones （SCLCP）. The new algorithm gets Newton-like directions from the Chen-Harker-Kanzow-Smale （CHKS） smoothing equation of the SCLCP. It possesses the following features： The starting point is easily chosen; one approximate Newton step is computed and accepted at each iteration; the iterative point with unit stepsize automatically remains in the neighborhood of central path; the iterative sequence is bounded and possesses （9（rL） polynomial-time complexity under the monotonicity and solvability of the SCLCP.
基金The authors gratefully acknowledge the help of the editor and anonymous referees in improving the readability of the paper.
文摘In this paper we present a large-update primal-dual interior-point algorithm for convex quadratic semi-definite optimization problems based on a new parametric kernel function.The goal of this paper is to investigate such a kernel function and show that the algorithm has the best complexity bound.The complexity bound is shown to be O(√n log n log n/∈).
文摘This paper treats multi-objective problem for manufacturing process design. A purpose of the process design is to decide combinations of work elements assigned to different work centers. Multiple work elements are ordinarily assigned to each center. Here, infeasible solutions are easily generated by precedence relationship of work elements in process design. The number of infeasible solutions generated is ordinarily larger than that of feasible solutions generated in the process. Therefore, feasible and infeasible solutions are located in any neighborhood in solution space. It is difficult to seek high quality Pareto solutions in this problem by using conventional multi-objective evolutional algorithms. We consider that the problem includes difficulty to seek high quality solutions by the following characteristics： （1） Since infeasible solutions are resemble to good feasible solutions, many infeasible solutions which have good values of objective functions are easily sought in the search process, （2） Infeasible solutions are useful to select new variable conditions generating good feasible solutions in search process. In this study, a multi-objective genetic algorithm including local search is proposed using these characteristics. Maximum value of average operation times and maximum value of dispersion of operation time in all work centers are used as objective functions to promote productivity. The optimal weighted coefficient is introduced to control the ratio of feasible solutions to all solutions selected in crossover and selection process in the algorithm. This paper shows the effectiveness of the proposed algorithm on simple model.
基金Project supported by the National Science Foundation of China (60574071) the Foundation for University Key Teacher by the Ministry of Education.
文摘This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O（√nL） iteration complexity which is the best result for convex quadratic programming so far.
基金Project supported by the National Natural Science Foundation of China （Grant No. 10117733）, the Shanghai Leading Academic Discipline Project （Grant No.J50101）, and the Foundation of Scientific Research for Selecting and Cultivating Young Excellent University Teachers in Shanghai （Grant No.06XPYQ52）
文摘Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods （IPMs） for semidefinite optimization （SDO） is designed. And the iteration complexity of the algorithm as O（n^3/4 log n/ε） with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O（n log n/ε） in large-updates case.
基金Project supported by Dutch Organization for Scientific Research(Grant No .613 .000 .010)
文摘In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming （LP） problems. The algorithms are based on a few kernel functions, including both serf-regular functions and non-serf-regular ones. The dynamic step size is compared with fixed step size for the algorithms in inner iteration of Newton step. Numerical tests show that the algorithms with dynaraic step size are more efficient than those with fixed step size.
基金supported by the Shanghai Pujiang Program (Grant No.06PJ14039)the Science Foundation of Shanghai Municipal Commission of Education (Grant No.06NS031)
文摘In this paper, a primal-dual path-following interior-point algorithm for linearly constrained convex optimization(LCCO) is presented.The algorithm is based on a new technique for finding a class of search directions and the strategy of the central path.At each iteration, only full-Newton steps are used.Finally, the favorable polynomial complexity bound for the algorithm with the small-update method is deserved, namely, O(√n log n /ε).
文摘The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interiorpoint method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.
文摘A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theorems of the algorithm is established.In addition,some numerical results are reported.
基金Supported by the National Natural Science Foundation of China(72071130)。
文摘In this paper, we propose two hybrid inertial CQ projection algorithms with linesearch process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the iteration to accelerate the convergence of the algorithm, and adopt flexible rules for selecting the stepsize and the shrinking projection region, which makes an optimal stepsize available at each iteration. The shrinking projection region is the intersection of three sets, which are the set C and two hyperplanes. Furthermore, we modify the Armijo-type line-search step in the presented algorithm to get a new algorithm.The algorithms are shown to be convergent under certain mild assumptions. Besides, numerical examples are given to show that the proposed algorithms have better performance than the general CQ algorithm.
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.
