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一个求解无约束优化的改进共轭梯度法及其应用

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数学进展 2024年第4期53卷 883-894页

作者：刘鹏杰刘玉凤简金宝邵虎广西民族大学数学与物理学院广西应用数学中心广西南宁530006 中国矿业大学数学学院江苏徐州221116 桂林电子科技大学电子工程与自动化学院广西桂林541004

本文对[***.,2021,40(5):Paper No.174,24 pp.]提出的JJSL共轭梯度法进行一些改进,改进后的方法具有更好的性质.首先,改进后的方法独立于任何线搜索有充分下降性.其次,采用弱Wolfe线搜索计算产生步长,改进后的方法有全局收敛性.最后,初... 详细信息

本文对[***.,2021,40(5):Paper No.174,24 pp.]提出的JJSL共轭梯度法进行一些改进,改进后的方法具有更好的性质.首先,改进后的方法独立于任何线搜索有充分下降性.其次,采用弱Wolfe线搜索计算产生步长,改进后的方法有全局收敛性.最后,初步数值试验和应用结果表明改进后的方法是有效的.

关键词：无约束优化共轭梯度法弱Wolfe线搜索充分下降性全局收敛性

A SSLE-TYPE ALGORITHM OF QUASI-STRONGLY SUB-FEASIBLE DIRECTIONS FOR INEQUALITY CONSTRAINED MINIMAX PROBLEMS

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Journal of Computational Mathematics 2023年第1期41卷 133-152页

作者： jinbao jian Guodong Ma Yufeng Zhang College of Mathematics and Physics Guangxi Key Laboratory of Hybrid Computation and IC Design AnalysisCenter for Applied Mathematics and Artificial IntelligenceGuangxi University for NationalitiesNanning 530006China School of Mathematics and Information Science Guangxi UniversityNanning 530004China

In this paper,we discuss the nonlinear minimax problems with inequality *** on the stationary conditions of the discussed problems,we propose a sequential systems of linear equations(SSLE)-type algorithm of quasi-strongly sub-feasible directions with an arbitrary initial iteration *** means of the new working set,we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix of the system of linear equations(SLE).At each iteration,two systems of linear equations(SLEs)with the same uniformly nonsingular coefficient matrix are *** mild conditions,the proposed algorithm possesses global and strong ***,some preliminary numerical experiments are reported.

关键词： Inequality constraints Minimax problems Method of quasi-strongly subfeasible directions SSLE-type algorithm Global and strong convergence

A GLOBALLY CONVERGENT QP-FREE ALGORITHM FOR INEQUALITY CONSTRAINED MINIMAX OPTIMIZATION

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Acta Mathematica Scientia 2020年第6期40卷 1723-1738页

作者： jinbao jian Guodong MA College of Mathematics and Physics Guangxi University for NationalitiesNanning 530006China School of Mathematics and Statistics Yulin Normal UniversityYulin 537000China

Although QP-free algorithms have good theoretical convergence and are effective in practice,their applications to minimax optimization have not yet been *** this article,on the basis of the stationary conditions,without the exponential smooth function or constrained smooth transformation,we propose a QP-free algorithm for the nonlinear minimax optimization with inequality *** means of a new and much tighter working set,we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient *** each iteration,to obtain the search direction,two reduced systems of linear equations with the same coefficient are *** mild conditions,the proposed algorithm is globally ***,some preliminary numerical experiments are reported,and these show that the algorithm is promising.

关键词： minimax optimization inequality constraints QP-free algorithm global convergence

A 2.79 COMPETITIVE ON-LINE ALGORITHM FOR TWO PROCESSOR REAL-TIME SYSTEMS WITH UNIFORM VALUE DENSITY

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Applied Mathematics:A Journal of Chinese Universities 1997年第3期 83-92页

作者： jian jinbao

Ａ２．７９ＣＯＭＰＥＴＩＴＩＶＥＯＮ┐ＬＩＮＥＡＬＧＯＲＩＴＨＭＦＯＲＴＷＯＰＲＯＣＥＳＳＯＲＲＥＡＬ┐ＴＩＭＥＳＹＳＴＥＭＳＷＩＴＨＵＮＩＦＯＲＭＶＡＬＵＥＤＥＮＳＩＴＹＹＡＮＧＱＩＦＡＮＡｂｓｔｒａｃｔ．Ｗｅｃ... 详细信息

Ａ２．７９ＣＯＭＰＥＴＩＴＩＶＥＯＮ┐ＬＩＮＥＡＬＧＯＲＩＴＨＭＦＯＲＴＷＯＰＲＯＣＥＳＳＯＲＲＥＡＬ┐ＴＩＭＥＳＹＳＴＥＭＳＷＩＴＨＵＮＩＦＯＲＭＶＡＬＵＥＤＥＮＳＩＴＹＹＡＮＧＱＩＦＡＮＡｂｓｔｒａｃｔ．Ｗｅｃｏｎｓｉｄｅｒｔｈｅｐｒｏｂｌｅｍ...

关键词： ON-LINE TWO ALGORITHM COMPETITIVE

A NEWε-GENERALIZED PROJECTION METHOD OF STRONGLY SUB-FEASIBLE DIRECTIONS FOR INEQUALITY CONSTRAINED OPTIMIZATION

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Journal of Systems Science & Complexity 2011年第3期24卷 604-618页

作者： jinbao jian Guodong MA Chuanhao GUO College of Mathematics and Information Science Guangxi University Nanning 530004 China Department of Mathematics and Computer Science Yulin Normal University Yulin 537000 China College of Science Shanghai University Shanghai 200444 China.

In this paper, the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and the s-generalized projection technique, a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented. At each iteration, the search direction is generated by a new s-generalized projection explicit formula, and the step length is yielded by a new Armijo line search. Under some necessary assumptions, not only the algorithm possesses global and strong convergence, but also the iterative points always get into the feasible set after finite iterations. Finally, some preliminary numerical results are reported.

关键词： E-generalized projection global and strong convergence inequality constraints method of strongly sub-feasible directions optimization.

A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION

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Acta Mathematica Scientia 2023年第1期43卷 1-24页

作者：简金宝张晨刘鹏杰 College of Mathematics and Physics Guangxi Key Laboratory of Hybrid Computation and IC Design AnalysisCenter for Applied Mathematics and Artificial IntelligenceGuangxi Minzu UniversityNanning530006China School of Mechanical Engineering University of Shanghai for Science and TechnologyShanghai200093China School of Mathematics China University of Mining and TechnologyXuzhou221116China

This paper discusses the two-block large-scale nonconvex optimization problem with general linear *** on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is ***,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in ***,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)***,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO ***,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.

关键词： large scale optimization two-block smooth optimization splitting method feasible sequential quadratic optimization method superlinear convergence

A Superlinearly Convergent Combined PhaseⅠ-PhaseⅡ Subfeasible Method

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Systems Science and Systems Engineering 1994年第2期4卷 104-111页

作者： jian jinbao(Mathematics and Information Science Department of Guangxi University,Nanning 530004, Guangxi)

This paper presents a new algorithm for optimization problems with nonlinear inequality constricts. At each iteration, the algorithm generates the search direction by solving only one quadratic programming (QP), and then making a simple correction for the solution of the QP, moreover this new algorithm needn’t to do searching. The other advantage is that it may not only choose any point in En as a starting point, but also escape from the complex penalty function and diameter. moreover the iteration point will be a feasible descent sequence whenever some iteration point gets into the feasible region. So we call it subfeasible *** mild assumptions,the new algorithm is shown to possess global and two step superlinear convergence.

关键词： constrained optimization quadratic programming phase Ⅰ-hase Ⅱ global and superlinear convergence arbitrary starting point subfeasible method.

A　Fastly　Convergent　Directly　Feasible　Directions　Method　for　Nonlinearly　Inequality　Constrained　Optimization

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Systems Science and Systems Engineering 1997年第1期7卷 5-14页

作者： jian jinbao Math. and Information Science Department, Guangxi University, Nanning530004, China

In this paper, a new superlinearly convergent algorithm for nonlinearly constrained optimization problems is presented. The search directions are directly computed by a few formulas, and neither quadratic programming nor linear equation need to be sovled. Under mild assumptions, the new algorithm is shown to possess global and superlinear convergence.

关键词： Nonlinearly constrained optimization direct search directions feasible directions method global and superlinear convergence.

A Strong Subfeasible Directions Algorithm with Superlinear Convergence

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Systems Science and Systems Engineering 1996年第3期6卷 287-296页

作者： jian jinbao(Dept. of Math. and Information Science, Guangxi University Nanning 530304, China)

This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is monotonically increasing. The search directions only depend on solving one quadratic proraming and its simple correction, its line search is simple straight search and does not depend on any penalty function. Under suit assumptions, the algorithm is proved to possess global and superlinear convergence.

关键词： Inequality constrained optimization successive quadratic programming strong subfeasible directions algorithm globl and superlinear convergence.