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An Active-Set Projected trust region Algorithm for Box Constrained Optimization Problems

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Journal of Systems Science & Complexity 2015年第5期28卷 1128-1147页

作者： YUAN Gonglin WEI Zengxin ZHANG Maojun College of Mathematics and Information Science Guangxi University School of Mathematic and Computing Science Guilin University of Electronic Technology

An active-set projected trust region algorithm is proposed for box constrained optimization problems, where the given algorithm is designed by three steps. First, the projected gradient direction which normally has better numerical performance is introduced. Second, the projected trust region direction that often possesses good convergence is defined, where the matrix of trust region subproblem is updated by limited memory strategy. Third, in order to get both good numerical performance and convergence, the authors define the final search which is the convex combination of the projected gradient direction and the projected trust region direction. Under suitable conditions, the global convergence of the given algorithm is established. Numerical results show that the presented method is competitive to other similar methods.

关键词： Active-set strategy convergence trust region

An Affine Scaling Interior trust region Method via Optimal Path for Solving Monotone Variational Inequality Problem with Linear Constraints

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Chinese Annals of Mathematics,Series B 2008年第3期29卷 273-290页

作者： Yunjuan WANG Detong ZHU Mathematics and Science College Shanghai Normal University Shanghai 200234 ChinaArts and Science School Shanghai Dianji University Shanghai 200240 China Business College Shanghai Normal University Shanghai 200234 China

Based on a differentiable merit function proposed by Taji et al. in ＂Math. Prog. Stud., 58, 1993, 369-383＂, the authors propose an affine scaling interior trust region strategy via optimal path to modify Newton method for the strictly monotone variational inequality problem subject to linear equality and inequality constraints. By using the eigensystem decomposition and affine scaling mapping, the authors form an affine scaling optimal curvilinear path very easily in order to approximately solve the trust region subproblem. Theoretical analysis is given which shows that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions.

关键词： trust region Affine scaling Interior point Optimal path Variational inequality problem

A SELF-ADAPTIVE trust region ALGORITHM

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Journal of Computational Mathematics 2003年第2期21卷 229-236页

作者： Long Hei (Institute of Computational Mathematics and Scientific/Engineering Computing, Academy ofMathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China)(Department of Industrial Engineering and Management Sciences Northwestern University C2SO,2145 Sheridan Road Evanston, Illinois 60208, USA) Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Sciences Chinese Academy of Sciences 北京 100080

In this paper we propose a self-adaptive trust region algorithm. The trust region radius is updated at a variable rate according to the ratio between the actual reduction and the predicted reduction of the objective function, rather than by simply enlarging or reducing the original trust region radius at a constant rate. We show that this new algorithm preserves the strong convergence property of traditional trust region methods. Numerical results are also presented.

关键词： trust region Unconstrained optimization Nonlinear optimization.

A trust region Affine Scaling Method for Bound Constrained Optimization

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Acta Mathematica Sinica,English Series 2013年第1期29卷 159-182页

作者： Xiao WANG School of Mathematical Sciences University of Chinese Academy of Sciences

We study a new trust region affine scaling method for general bound constrained optimiza- tion problems. At each iteration, we compute two trial steps. We compute one along some direction obtained by solving an appropriate quadratic model in an ellipsoidal region. This region is defined by an affine scaling technique. It depends on both the distances of current iterate to boundaries and the trust region radius. For convergence and avoiding iterations trapped around nonstationary points, an auxiliary step is defined along some newly defined approximate projected gradient. By choosing the one which achieves more reduction of the quadratic model from the two above steps as the trial step to generate next iterate, we prove that the iterates generated by the new algorithm are not bounded away from stationary points. And also assuming that the second-order sufficient condition holds at some nondegenerate stationary point, we prove the Q-linear convergence of the objective function values. Preliminary numerical experience for problems with bound constraints from the CUTEr collection is also reported.

关键词： Bound constrained optimization affine scaling trust region approximate projected gradient

Global and Local Convergence of a New Affine Scaling trust region Algorithm for Linearly Constrained Optimization

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Acta Mathematica Sinica,English Series 2016年第10期32卷 1203-1213页

作者： Chao GU De Tong ZHU School of Mathematics and Information Shanghai LiXin University of Commerce Department of Mathematics Shanghai Normal University

Chen and Zhang [Sci. China, Set. A, 45, 1390-1397 （2002）] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence. In this paper, we derive a new affine scaling trust region algorithm with dwindling filter for linearly constrained optimization. Different from Chen and Zhang＇s work, the trial points generated by the new algorithm axe accepted if they improve the objective function or improve the first order necessary optimality conditions. Under mild conditions, we discuss both the global and local convergence of the new algorithm. Preliminary numerical results are reported.

关键词： Linearly constrained optimization affine scaling trust region dwindling filter~ conver-gence

A NONMONOTONE trust region ALGORITHM FOR NONLINEAR OPTIMIZATION SUBJECT TO GENERAL CONSTRAINTS

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Journal of Computational Mathematics 2003年第2期21卷 237-246页

作者： Hongchao Zhang+ (Department of Mathematics, University of Florida, Gainesville, FL, USA 32611 ) Department of Mathematics University of Florida 美国 Gainesville

In this paper we present a nonmonotone trust region algorithm for general nonlinear constrained optimization problems. The main idea of this paper is to combine Yuan's technique[1] with a nonmonotone method similar to Ke and Han [2]. This new algorithm may not only keep the robust properties of the algorithm given by Yuan, but also have some advantages led by the nonmonotone technique. Under very mild conditions, global convergence for the algorithm is given. Numerical experiments demonstrate the efficiency of the algorithm.

关键词： Nonlinear optimization Nonmonotone algorithm trust region General con-straintss

An Active-Set Projected trust region Algorithm for Box Constrained Optimization Problems

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Journal of Systems Engineering and Electronics 2015年第5期26卷 1128-1147页

作者： YUAN Gonglin WEI Zengxin ZHANG Maojun College of Mathematics and Information Science Guangxi University School of Mathematic and Computing Science Guilin University of Electronic Technology

关键词： Active-set strategy convergence trust region

A Modified Filter trust region Method for Nonlinear Programming

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A Modified Filter Trust Region Method for Nonlinear Programm...

An Affine Scaling trust region Algorithm with Interior Backtracking Technique for Solving Bound-constrained Nonlinear Systems

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作者： Su Ke1,2 1.Department of Mathematics,Tongji University,Shanghai 200092,P.R.China 2.College of Mathematics and Computer,Hebei University,Baoding 071002,P.R.China

Sequential quadratic programming（SQP）type method is one of the most effective methods for solving nonlinear ***,filter method,for its good numerical results,are extensively studied to handle nonlinear programming *** this paper,a new modified approach combined the filter technique and SQP trust region method is proposed to tackle the original problem,which ensures that every trail point will not be far away from the feasible *** convergence results of the proposed algorithm are established under suitable *** numerical results are reported in this paper.

关键词： Filter Method trust region Sequential Quadratic Programming Nonlinear Programming

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An Affine Scaling Trust Region Algorithm with Interior Backt...