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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
1
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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A New Full-NT-Step Infeasible Interior-Point Algorithm for SDP Based on a Specific Kernel Function 认领 引用
2
作者 Samir Bouali Samir Kabbaj 《Applied Mathematics》 2012年第9期1014-1022,共9页
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
关键词 Semidefinite Programming Full Nesterov-Todd Steps Infeasible Interior-Point Methods Polynomial Complexity Kernel Functions
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An O(rL)Infeasible Interior-point Algorithm for Symmetric Cone LCP via CHKS Function 认领 引用 被引量：1
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作者 Zi-yan Luo Nai-hua Xiu 《Acta Mathematicae Applicatae Sinica》 SCIE 2009年第4期593-606,共14页
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
关键词 Infeasible interior-point algorithm symmetric cone linear complementarity problem monotonicity polynomial complexity
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AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM 认领 引用 被引量：12
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作者 迟晓妮 刘三阳 《Acta Mathematica Scientia》 SCIE 2008年第3期551-559,共9页
A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorith... A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP. 展开更多
关键词 Second-order cone programming, infeasible-interior-point algorithm, predictor-corrector algorithm global convergence
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A FULL-NEWTON STEP INFEASIBLE INTERIOR-POINT ALGORITHM FOR P_*(κ) LINEAR COMPLEMENTARITY PROBLEM 认领 引用 被引量：1
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作者 ZHU Danhua ZHANG Mingwang 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2014年第5期1027-1044,共18页
This paper proposes a new infeasible interior-point algorithm with full-Newton steps for P_*(κ) linear complementarity problem(LCP),which is an extension of the work by Roos(SIAM J.Optim.,2006,16(4):1110-1136).The ma... This paper proposes a new infeasible interior-point algorithm with full-Newton steps for P_*(κ) linear complementarity problem(LCP),which is an extension of the work by Roos(SIAM J.Optim.,2006,16(4):1110-1136).The main iteration consists of a feasibility step and several centrality steps.The authors introduce a specific kernel function instead of the classic logarithmical barrier function to induce the feasibility step,so the analysis of the feasibility step is different from that of Roos' s.This kernel function has a finite value on the boundary.The result of iteration complexity coincides with the currently known best one for infeasible interior-point methods for P_*(κ) LCP.Some numerical results are reported as well. 展开更多
关键词 Full-Newton steps infeasible interior-point method P＊（κ） linear complementarity problems polynomial complexity
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A Path-Following Full Newton-Step Infeasible Interior-Point Algorithm for P∗(κ)-HLCPs Based on a Kernel Function 认领 引用
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作者 Soodabeh Asadi Hossein Mansouri Maryam Zangiabadi 《Journal of the Operations Research Society of China》 EI CSCD 2016年第1期77-96,共20页
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
关键词 Horizontal linear complementarity problem Infeasible interior-point method Central path Kernel function
A Primal-Dual Infeasible-Interior-Point Algorithm for Multiple Objective Linear Programming Problems 认领 引用
7
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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A New Infeasible Interior-point Method for Linear Complementarity Problem Based on Full Newton Step 认领 引用 被引量：1
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作者 龚小玉 胡振鹏 王先甲 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第4期624-632,共9页
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
关键词 complementarity problem infeasible interior-point methods full-Newton step polynomial complexity
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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
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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 NEW FRAMEWORK OF PRIMAL-DUAL INFEASIBLE INTERIOR-POINT METHOD FOR LINEAR PROGRAMMING 认领 引用
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作者 林正华 宋岱才 刘庆怀 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 1998年第2期183-194,共12页
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
关键词 Linear programming infeasible interior-point method homotopy method global convergence.
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Multi-Objective Genetic Algorithm to Design Manufacturing Process Line Including Feasible and Infeasible Solutions in Neighborhood 认领 引用
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作者 Masahiro Arakawa Takumi Wada 《Journal of Mathematics and System Science》 2014年第4期209-219,共11页
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
关键词 Process design process line feasible and infeasible solution multi-objective genetic algorithm mix production simulation
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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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Infeasibility test algorithm and fast repair algorithm of job shop scheduling problem 认领 引用 被引量：1
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作者 孙璐 黄志 +1 位作者 张惠民 顾文钧 《Journal of Southeast University(English Edition)》 EI CAS 2011年第1期88-91,共4页
To diagnose the feasibility of the solution of a job-shop scheduling problem（JSSP）,a test algorithm based on diagraph and heuristic search is developed and verified through a case study.Meanwhile,a new repair algori... To diagnose the feasibility of the solution of a job-shop scheduling problem（JSSP）,a test algorithm based on diagraph and heuristic search is developed and verified through a case study.Meanwhile,a new repair algorithm for modifying an infeasible solution of the JSSP to become a feasible solution is proposed for the general JSSP.The computational complexity of the test algorithm and the repair algorithm is both O（n） under the worst-case scenario,and O（2J＋M） for the repair algorithm under the best-case scenario.The repair algorithm is not limited to specific optimization methods,such as local tabu search,genetic algorithms and shifting bottleneck procedures for job shop scheduling,but applicable to generic infeasible solutions for the JSSP to achieve feasibility. 展开更多
关键词 infeasibility job shop scheduling repairing algorithm
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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
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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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