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A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on Algebraic Equivalent Transformation 认领 引用
1
作者 Jing GE Mingwang ZHANG Panjie TIAN 《Journal of Mathematical Research with Applications》 CSCD 2025年第4期555-568,共14页
In this paper,we propose a new full-Newton step feasible interior-point algorithm for the special weighted linear complementarity problems.The proposed algorithm employs the technique of algebraic equivalent transform... In this paper,we propose a new full-Newton step feasible interior-point algorithm for the special weighted linear complementarity problems.The proposed algorithm employs the technique of algebraic equivalent transformation to derive the search direction.It is shown that the proximity measure reduces quadratically at each iteration.Moreover,the iteration bound of the algorithm is as good as the best-known polynomial complexity for these types of problems.Furthermore,numerical results are presented to show the efficiency of the proposed algorithm. 展开更多
关键词 interior-point algorithm weighted linear complementarity problem algebraic equivalent transformation search direction iteration complexity
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A Full-Newton Step Interior-Point Algorithm Based on a New Search Direction for P*(κ)-Linear Complementarity Problem 认领 引用
2
作者 WANG Li ZHANG Mingwang 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2025年第2期159-168,共10页
In this paper,a fu-Newton step interior-point algorithm is proposed for solving P*(k)-linear complementarity problem based on a new search direction,which is an extension of Grimes'algorithm.It is proved that t... In this paper,a fu-Newton step interior-point algorithm is proposed for solving P*(k)-linear complementarity problem based on a new search direction,which is an extension of Grimes'algorithm.It is proved that the number of iterations of the algorithm is O(n1/2(1+4κ)logn/ε),which matches the best known iteration bound of the interior-point method for P*(k)-linear complementarity problem.Some numerical results have proved the feasibility and efficiency of the proposed algorithm. 展开更多
关键词 full-Newton step interior-point method P*(k)-linear complementarity problem polynomial complexity
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A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING 认领 引用 被引量：6
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作者 余谦 黄崇超 江燕 《Acta Mathematica Scientia》 SCIE 2006年第2期265-270,共6页
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
关键词 Convex quadratic programming predictor-corrector interior-point algorithm
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A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function 认领 引用 被引量：2
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作者 GENG Jie ZHANG Mingwang ZHU Dechun 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2024年第1期29-37,共9页
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
关键词 interior-point algorithm weighted linear complementarity problem full-Newton step kernel function iteration complexity
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A new primal-dual path-following interior-point algorithm for linearly constrained convex optimization 认领 引用 被引量：1
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作者 张敏 白延琴 王国强 《Journal of Shanghai University(English Edition)》 2008年第6期475-480,共6页
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
关键词 linearly constrained convex optimization （LCCO） interior-point algorithm small-update method polynomial complexity
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A POSITIVE INTERIOR-POINT ALGORITHM FOR NONLINEAR COMPLEMENTARITY PROBLEMS 认领 引用
6
作者 马昌凤 梁国平 陈新美 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第3期355-362,共8页
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
关键词 nonlinear complementarity problems positive interior-point algorithm non-smooth equations
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SOLVING CONVEX QUADRATIC PROGRAMMING BY POTENTIAL-REDUCTION INTERIOR-POINT ALGORITHM 认领 引用
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作者 LIANG Xi-ming MA Long-hua QIAN Ji-xin 《Journal of Zhejiang University Science》 2001年第1期67-71,共5页
The solution of quadratic programming problems is an important issue in the field of mathematical programming and industrial applications.In this paper,we solve convex quadratic programming by a potential-reduction in... The solution of quadratic programming problems is an important issue in the field of mathematical programming and industrial applications.In this paper,we solve convex quadratic programming by a potential-reduction interior-point algorithm.It is proved that the potential-reduction interior-point algorithm is globally convergent.Some numerical experiments were made. 展开更多
关键词 potential-reduction interior-point algorithm convex quadratic programming convergence numerical experiments
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A Wide Neighborhood Arc-Search Interior-Point Algorithm for Convex Quadratic Programming 认领 引用 被引量：2
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作者 YUAN Beibei ZHANG Mingwang HUANG Zhengwei 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2017年第6期465-471,共7页
In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the ent... In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O（nlog（（ x^0）~TS^0/ε）） which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient. 展开更多
关键词 arc-search interior-point algorithm polynomial complexity convex quadratic programming
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Interior-Point Algorithm for Linear Optimization Based on a New Kernel Function 认领 引用 被引量：2
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作者 CHEN Donghai ZHANG Mingwang LI Weihua 《Wuhan University Journal of Natural Sciences》 CAS 2012年第1期12-18,共7页
In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barr... In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions. 展开更多
关键词 linear optimization interior-point algorithms pri- mal-dual methods kernel function polynomial complexity
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Complexity analysis of interior-point algorithm based on a new kernel function for semidefinite optimization 认领 引用 被引量：3
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作者 钱忠根 白延琴 王国强 《Journal of Shanghai University(English Edition)》 2008年第5期388-394,共7页
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
关键词 interior-point algorithm primal-dual method semidefinite optimization （SDO） polynomial complexity
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Primal-Dual Interior-Point Algorithms with Dynamic Step-Size Based on Kernel Functions for Linear Programming 认领 引用 被引量：3
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作者 钱忠根 白延琴 《Journal of Shanghai University(English Edition)》 2005年第5期391-396,共6页
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
关键词 linear programming （LP） interior-point algorithm small-update method large-update method.
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A new primal-dual interior-point algorithm for convex quadratic optimization 认领 引用 被引量：9
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作者 王国强 白延琴 +1 位作者 刘勇 张敏 《Journal of Shanghai University(English Edition)》 2008年第3期189-196,共8页
In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization （CQO） based on a kernel function is presented. The proposed function has some properties that are easy for checking. These ... In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization （CQO） based on a kernel function is presented. The proposed function has some properties that are easy for checking. These properties enable us to improve the polynomial complexity bound of a large-update interior-point method （IPM） to O（√n log nlog n/e）, which is the currently best known polynomial complexity bound for the algorithm with the large-update method. Numerical tests were conducted to investigate the behavior of the algorithm with different parameters p, q and θ, where p is the growth degree parameter, q is the barrier degree of the kernel function and θ is the barrier update parameter. 展开更多
关键词 convex quadratic optimization （CQO） interior-point methods （IPMs） large-update method polynomial complexity
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A class of polynomial primal-dual interior-point algorithms for semidefinite optimization 认领 引用 被引量：6
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作者 王国强 白延琴 《Journal of Shanghai University(English Edition)》 2006年第3期198-207,共10页
In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to... In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to its growth term increasing linearly. Some new analysis tools were developed which can be used to deal with complexity ＂analysis of the algorithms which use analogous strategy in [5] to design the search directions for the Newton system. The complexity bounds for the algorithms with large- and small-update methodswere obtained, namely,O（qn^（p＋q/q（P＋1）log n/ε and O（q^2√n）log n/ε,respectlvely. 展开更多
关键词 semidefinite optimization （SDO） primal-dual interior-point methods large- and small-update methods polynomial complexity
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Interior-point algorithm based on general kernel function for monotone linear complementarity problem 认领 引用
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作者 刘勇 白延琴 《Journal of Shanghai University(English Edition)》 2009年第2期95-101,共7页
A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Un... A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP. 展开更多
关键词 monotone linear complementarity problem （MLCP） interior-point method kernel function polynomial complexity
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Predictor-corrector interior-point algorithm for linearly constrained convex programming 认领 引用
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作者 LIANG Xi-ming 《Journal of Central South University》 SCIE EI CAS 2001年第3期208-212,共5页
Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming.Interior-po int method is one of the most effective choices for linear programming.In th... Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming.Interior-po int method is one of the most effective choices for linear programming.In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed.In eac h iteration,the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory.Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required.It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method.Numerical experiments on twenty-six standard test problems are made.The result s show that the proposed algorithm is stable and robust. 展开更多
关键词 linearly constrained convex programming predictor corrector interior point algorithm numerical experiment
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A CORRECTOR-PREDICTOR ARC SEARCH INTERIOR-POINT ALGORITHM FOR SYMMETRIC OPTIMIZATION 认领 引用
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作者 M.PIRHAJI M.ZANGIABADI H.MANSOURI 《Acta Mathematica Scientia》 SCIE CSCD 2018年第4期1269-1284,共16页
In this paper, a corrector-predictor interior-point algorithm is proposed for sym- metric optimization. The algorithm approximates the central path by an ellipse, follows the ellipsoidal approximation of the central-p... In this paper, a corrector-predictor interior-point algorithm is proposed for sym- metric optimization. The algorithm approximates the central path by an ellipse, follows the ellipsoidal approximation of the central-path step by step and generates a sequence of iter- ates in a wide neighborhood of the central-path. Using the machinery of Euclidean Jordan algebra and the commutative class of search directions, the convergence analysis of the algo- rithm is shown and it is proved that the algorithm has the complexity bound O （√τL） for the well-known Nesterov-Todd search direction and O （τL） for the xs and sx search directions. 展开更多
关键词 symmetric optimization ellipsoidal approximation wide neighborhood interior-point methods polynomial complexity
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A Modified Full-NT-Step Infeasible Interior-Point Algorithm for SDP Based on a Specific Kernel Function 认领 引用
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作者 Yadan Wang Hongwei Liu Zexian Liu 《Journal of Harbin Institute of Technology(New Series)》 CAS 2019年第2期41-47,共7页
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
关键词 semidefinite programming infeasible interior-point methods full Nesterov-Todd steps kernel functions polynomial complexity
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Polynomial-time interior-point algorithm based on a local self-concordant finite barrier function 认领 引用
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作者 金正静 白延琴 《Journal of Shanghai University(English Edition)》 2009年第4期333-339,共7页
The choice of self-concordant functions is the key to efficient algorithms for linear and quadratic convex optimizations, which provide a method with polynomial-time iterations to solve linear and quadratic convex opt... The choice of self-concordant functions is the key to efficient algorithms for linear and quadratic convex optimizations, which provide a method with polynomial-time iterations to solve linear and quadratic convex optimization problems. The parameters of a self-concordant barrier function can be used to compute the complexity bound of the proposed algorithm. In this paper, it is proved that the finite barrier function is a local self-concordant barrier function. By deriving the local values of parameters of this barrier function, the desired complexity bound of an interior-point algorithm based on this local self-concordant function for linear optimization problem is obtained. The bound matches the best known bound for small-update methods. 展开更多
关键词 linear optimization self-concordant function finite barrier interior-point methods polynomial-time complexity
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A predictor-corrector interior-point algorithmfor monotone variational inequality problems 认领 引用 被引量：2
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作者 梁昔明 钱积新 《Journal of Zhejiang University Science》 2002年第3期321-325,共5页
Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the a... Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented. 展开更多
关键词 Variational inequality problems(VIP) Predictor corrector interior point algorithm Numerical experiments
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A Primal-Dual Infeasible-Interior-Point Algorithm for Multiple Objective Linear Programming Problems 认领 引用
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作者 HUANG Hui FEI Pu-sheng YUAN Yuan 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第2期351-354,共4页
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 confini... 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
关键词 multiple objective linear programming primal dual infeasible interior point algorithm
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