A SECOND ORDER η-APPROXIMATION METHOD FOR CONSTRAINED OPTIMIZATION PROBLEMS INVOLVING SECOND ORDER INVEX FUNCTIONS

Tadeusz Antczak

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A SECOND ORDER η-APPROXIMATION METHOD FOR CONSTRAINED OPTIMIZATION PROBLEMS INVOLVING SECOND ORDER INVEX FUNCTIONS

机译：涉及二阶积分函数的约束优化问题的二阶η-逼近方法

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摘要

A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order η-approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order η-approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear original mathematical programming problem and its associated second order η-approximated optimization problem is established under second order invexity assumption imposed on the functions constituting the original optimization problem.

机译：提出了一种利用二阶导数获得非线性数学规划问题的二阶充分条件的新方法。在所谓的二阶η-近似方法中，构造了与原始非线性规划问题相关的优化问题，该优化问题涉及构成原始问题的目标函数和约束函数的二阶η-近似。非线性原始数学规划问题与其相关的二阶η近似优化问题之间的等价关系是在对构成原始优化问题的函数施加二阶凸度假设的基础上建立的。

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来源
《Applications of Mathematics》 |2009年第5期|433-445|共13页
作者
Tadeusz Antczak;
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作者单位

Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland;

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正文语种 eng
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关键词
mathematical programming; second order η-approximated optimization problem; second order invex function; second order optimality conditions;

机译：数学编程;二阶η近似优化问题;二阶凸函数;二阶最优条件;

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专利

1. A second order $eta $-approximation method for constrained optimization problems involving second order invex functions [J] . Antczak Tadeusz Applications of mathematics . 2009,第5期

机译：用于涉及二阶凸函数的约束优化问题的二阶$ eta $-逼近方法
2. Saddle-point criteria in an eta-approximation method for nonlinear mathematical programming problems involving invex functions [J] . Antczak T Journal of Optimization Theory and Applications . 2007,第1期

机译：η近似方法中涉及凸函数的非线性数学规划问题的鞍点准则
3. Saddle-Point Criteria in an η-Approximation Method for Nonlinear Mathematical Programming Problems Involving Invex Functions [J] . T. Antczak Journal of Optimization Theory and Applications . 2007,第1期

机译：包含凸函数的非线性数学规划问题的η逼近方法中的鞍点准则
4. The Exact l_1 Penalty Function Method for Constrained Nonsmooth Invex Optimization Problems [C] . Tadeusz Antczak IFIP TC 7 conference on system modeling and optimization . 2013

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5. New acceleration potential method for supersonic unsteady aerodynamics of lifting surfaces, further extension of the nonplanar supersonic doublet point method, and nonlinear, nongradient optimized rational function approximations for supersonic, transient response unsteady aerodynamics. [D] . Tewari, Ashish. 1992

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6. Smoothing approximation to the lower order exact penalty function for inequality constrained optimization [O] . Shujun Lian, Nana Niu -1

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7. A second order $\eta $-approximation method for constrained optimization problems involving second order invex functions [O] . Antczak, Tadeusz 2009

机译：用于涉及二阶凸函数的约束优化问题的二阶$ \ eta $-逼近方法
8. I,II Convergence and Rate of Convergence Theorems for Constrained and Unconstrained Stochastic Approximation,via Weak Convergence Methods. III Numerical Studies for Constrained Stochastic Approximation Problems, [R] . kushner,harold j. lakshmivarahan, s. 1977

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A SECOND ORDER η-APPROXIMATION METHOD FOR CONSTRAINED OPTIMIZATION PROBLEMS INVOLVING SECOND ORDER INVEX FUNCTIONS

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