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Saddle Point Criteria in Nonsmooth Semi-Infinite Minimax Fractional Programming Problems

Journal of Systems Science & Complexity 2018年第2期31卷 446-462页

作者： MISHRA S K SINGH Yadvendra VERMA R U Department of Mathematics Banaras Hindu University Varanasi-221005 India. Department of Mathematics Texas State University USA

This paper considers a nonsmooth semi-infinite minimax fractional programming problem（SIMFP） involving locally Lipschitz invex functions. The authors establish necessary optimality conditions for SIMFP. The authors establish the relationship between an optimal solution of SIMFP and saddle point of scalar lagrange function for SIMFP. Further, the authors study saddle point criteria of a vector lagrange function defined for SIMFP.

关键词： Generalized convexity lagrange function nonsmooth programming problems saddlepoint semi-infinite minimax fractional programming problems.

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On the use of simplex methods in constructing quadratic models

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Science China Mathematics 2007年第7期50卷 913-924页

作者： Qing-hua ZHOU 1 College of Mathematics and Computer,Hebei University,Baoding 071002,China 2 State Key Laboratory of Scientific and Engineering Computing,Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China College of Mathematics and Computer Hebei University Baoding China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces. And the quadratic model is solved in the new subspaces. The motivation is to use the information disclosed by the former steps to construct more promising directions. For most tested problems, the number of functions evaluations have been reduced obviously through our algorithms.

关键词： unconstrained optimization trust region method quadratic model lagrange function simplex methods direct methods 90C56

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Optimal cash holding decision with uncertain control

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Journal of Control and Decision 2021年第3期8卷 292-302页

作者： Zhengyan Wang Guanghua Xu School of Economics and Management Yancheng Institute of TechnologyYanchengPeople’s Republic of China Department of Economics and Management Nanjing University of Science and TechnologyNanjingPeople’s Republic of China

The decision-making of cash holdings is very important for the daily operation of *** present paper tries to establish uncertain optimal cash holding models with the constraint of safe cash holding area,and discusses the solutions of the models by establishing lagrange function under KKT *** the one hand,this paper enriches the existing cash holding models,on the other hand,it is also a comprehensive discussion on the application of uncertainty theory in cash holding management.

关键词： Cash holding uncertain model safe area lagrange function

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The Second-Order Differential Equation System with the Feedback Controls for Solving Convex Programming

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Open Journal of Applied Sciences 2022年第6期12卷 977-989页

作者： Xingxu Chen Li Wang Juhe Sun Yanhong Yuan School of Science Shenyang Aerospace University Shenyang China College of Economics and Management Taiyuan University of Technology Taiyuan China

In this paper, we establish the second-order differential equation system with the feedback controls for solving the problem of convex programming. Using lagrange function and projection operator, the equivalent operator equations for the convex programming problems under the certain conditions are obtained. Then a second-order differential equation system with the feedback controls is constructed on the basis of operator equation. We prove that any accumulation point of the trajectory of the second-order differential equation system with the feedback controls is a solution to the convex programming problem. In the end, two examples using this differential equation system are solved. The numerical results are reported to verify the effectiveness of the second-order differential equation system with the feedback controls for solving the convex programming problem.

关键词： Convex Programming lagrange function Projection Operator Second-Order Differential Equation

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