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A smoothing method for Solving Bilevel Multiobjective Programming Problems

Journal of the Operations Research Society of China 2014年第4期2卷 511-525页

作者： Yi-Bing Lü Zhong-Ping Wan School of Information and Mathematics Yangtze UniversityJingzhou 434023HubeiChina School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

In this paper,a bilevel multiobjective programming problem,where the lower level is a convex parameter multiobjective program,is *** the KKT optimality conditions of the lower level problem,this kind of problem is transformed into an equivalent one-level nonsmooth multiobjective optimization ***,a sequence of smooth multiobjective problems that progressively approximate the nonsmooth multiobjective problem is *** is shown that the Pareto optimal solutions(stationary points)of the approximate problems converge to a Pareto optimal solution(stationary point)of the original bilevel multiobjective programming *** results showing the viability of the smoothing approach are reported.

关键词： Bilevel multiobjective programming Stationary point Constraint qualification smoothing method

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A Novel smoothing method for Symmetric Conic Linear Programming

A Novel Smoothing Method for Symmetric Conic Linear Programm...

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The 2011 International Conference on Computing,Information and Control(ICCIC 2011)

作者： Xiaoni Chi June Liu College of Mathematics and Information Science Huanggang Normal University

We present a novel smoothing method for solving the symmetric conic linear programming based on the Chen-Harker-Kanzow-Smale（CHKS） smoothing function. Unlike interior point methods, the proposed algorithm can start from an arbitrary point. Our algorithm solves only one linear system of equations and performs only one line search at each iteration. Without uniform nonsingularity, the proposed algorithm is shown to be globally convergent. Numerical results indicate that our algorithm is promising.

关键词： symmetric conic linear programming smoothing method ChenHarker-Kanzow-Smale smoothing function global convergence

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A Novel smoothing method for Symmetric Conic Linear Programming

A Novel Smoothing Method for Symmetric Conic Linear Programm...

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2010 Second International Seminar On Business and Information Management (ISBIM 2010)

作者： Xiaoni Chi June Liu College of Mathematics and Information Science Huanggang Normal University Huanggang 438000 Hubei P.R. China

We present a novel smoothing method for solving the symmetric conic linear programming based on the Chen-Harker-Kanzow-Smale （CHKS） smoothing function. Unlike interior point methods, the proposed algorithm can start from an arbitrary point. Our algorithm solves only one linear system of equations and performs only one line search at each iteration. Without uniform nonsingularity, the proposed algorithm is shown to be globally convergent. Numerical results indicate that our algorithm is promising.

关键词： symmetric conic linear programming smoothing method Chen-Harker-Kanzow-Smale smoothing function global convergence

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A smoothing TRUST REGION method FOR NCPS BASED ON THE smoothing GENERALIZED FISCHER-BURMEISTER FUNCTION

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Journal of Computational Mathematics 2011年第3期29卷 261-286页

作者： Xuebin Wang Changfeng Ma Meiyan Li School of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 China School of Mathematics and Computing Science Guilin University of Electronic Technology Guilin 5~100~ China

Based on a reformulation of the complementarity problem as a system of nonsmooth equations by using the generMized Fischer-Burmeister function, a smoothing trust re- gion Mgorithm with line search is proposed for solving general （not necessarily monotone） nonlinear complementarity problems. Global convergence and, under a nonsingularity assumption, local Q-superlinear/Q-quadratic convergence of the algorithm are established. In particular, it is proved that a unit step size is always accepted after a finite number of iterations. Numerical results also confirm the good theoretical properties of our approach.

关键词： Nonlinear complementarity problem smoothing method Trust region method Global convergence Local superlinear convergence.

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NONSMOOTH MODEL FOR PLASTIC LIMIT ANALYSIS AND ITS smoothing ALGORITHM

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Applied Mathematics and Mechanics(English Edition) 2006年第8期27卷 1081-1088页

作者：李建宇潘少华李兴斯 State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of TechnologyDalian 116023P.R.China Department of Applied Mathematics South China University of TechnologyGuangzhou 510641P.R.China

By means of Lagrange duality of Hill＇s maximum plastic work principle theory of the convex program, a dual problem under Mises＇ yield condition has been derived and whereby a non-differentiable convex optimization model for the limit analysis is developed. With this model, it is not necessary to linearize the yield condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subject to linear constraints. Aimed at resolving the non-differentiability of Euclidean norms, a smoothing algorithm for the limit analysis of perfect-plastic continuum media is proposed. Its efficiency is demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems.

关键词： plastic limit analysis duality nonsmooth optimization smoothing method

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Error Bounds of Two smoothing Approximations for Semi-infinite Minimax Problems

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Acta Mathematicae Applicatae Sinica 2009年第4期25卷 685-696页

作者： Hong-xia Yin Department of Mathematics and Statistics Minnesota State University Mankato 273 Wissink Hall Mankato MN 56001 USA

In the paper we investigate smoothing method for solving semi-infinite minimax problems. Not like most of the literature in semi-infinite minimax problems which are concerned with the continuous time version（i.e., the one dimensional semi-infinite minimax problems）, the primary focus of this paper is on multi- dimensional semi-infinite minimax problems. The global error bounds of two smoothing approximations for the objective function are given and compared. It is proved that the smoothing approximation given in this paper can provide a better error bound than the existing one in literature.

关键词： Semi-infinite minimax problem smoothing method aggregate function error bound polynomial interpolation

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A New Unified Path to smoothing Nonsmooth Exact Penalty Function for the Constrained Optimization

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Open Journal of Optimization 2021年第3期10卷 61-70页

作者： Bingzhuang Liu School of Mathematics and Statistics Shandong University of Technology Zibo China

We propose a new unified path to approximately smoothing the nonsmooth exact penalty function in this paper. Based on the new smooth penalty function, we give a penalty algorithm to solve the constrained optimization ... 详细信息

关键词： Penalty Function Constrained Optimization smoothing method Optimal Solution

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