Optimality conditions and Lagrangian duality for vector optimization of invex set-valued functions

Wen Song

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Optimality conditions and Lagrangian duality for vector optimization of invex set-valued functions

机译：凸集值函数向量优化的最优性条件和拉格朗日对偶

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摘要

A constraint qualification and the equivalence be- tween the vector-valued Lagrangian condition and the Kuhn-Tucker condition are presented. By using them, a Lagrangian duality the- orem for the weak minimality of vector optimization for invex set- valued functions is proved. A necessary optimality condition and a duality theorem for the proper minimality are also given.

机译：提出了约束条件和向量值拉格朗日条件与库恩-塔克条件之间的等价关系。通过使用它们，证明了凸集值函数向量优化的弱极小性的拉格朗日对偶定理。还给出了一个必要的最优性条件和一个对偶定理，以求适当的极小值。

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《Control and Cybernetics》 |1997年第1期|p.68-85|共18页
作者
Wen Song;
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正文语种 eng
中图分类控制论、信息论（数学理论）;自动化技术、计算机技术;
关键词
invex set-valued function; vector optimization lagrangian condition; kuhn-Tucker condition;

机译：凸集值函数;向量优化拉格朗日条件;库恩-塔克条件;

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专利

1. Sufficient Optimality Conditions and Duality in Vector Optimization with Invex-Convexlike Functions [J] . P. Q. Khanh Journal of Optimization Theory and Applications . 1995,第2期

机译：具有凸-凸函数的向量优化中的充分最优条件和对偶
2. Sufficient Optimality Conditions and Duality in Vector Optimization with Invex-Convexlike Functions [J] . P. Q. Khanh Journal of Optimization Theory and Applications . 1995,第2期

机译：具有凸-凸函数的向量优化中的充分最优条件和对偶
3. Lagrangian duality for vector optimization problems with set-valued mappings [J] . Long X.-J., Peng J.-W. Taiwanese journal of mathematics . 2013,第1期

机译：集值映射的向量优化问题的拉格朗日对偶
4. Kuhn-Tucker Type Optimality Conditions and Lagrangian Duality for Maximizations of Set-Valued Function [C] . C. Ling National conference on Multiple Criteria Decision Making; 19950815-16; Beijing(CN) . 1995

机译：集值函数最大化的Kuhn-Tucker型最优条件和拉格朗日对偶
5. Optimal restoration of distribution systems using the Lagrangian dual relaxation. [D] . Perez-Guerrero, Raul Enrique. 2008

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6. Optimality for set-valued optimization in the sense of vector and set criteria [O] . Xiangyu Kong, GuoLin Yu, Wei Liu -1

机译：向量和设置标准意义上的集值优化的最优性
7. Optimality and Duality in Nonsmooth Multiobjective Optimization Involving V-Type I Invex Functions [O] . RaviP Agarwal, I Ahmad, Z Husain, 2010

机译：涉及V型I凸函数的非光滑多目标优化中的最优性和对偶性

Optimality conditions and Lagrangian duality for vector optimization of invex set-valued functions

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