Necessary and Sufficient Optimality Conditions for Non-regular Problems

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization Pub Date : 2023-08-04 DOI:10.1080/01630563.2023.2235614

V. Vivanco-Orellana, R. Osuna-Gómez, M. Rojas-Medar

引用次数: 0

Abstract

Abstract We derive new necessary and sufficient optimality conditions for optimization problems with multi-equality and inequality constraints through the Dubovitskii-Milyutin formalism, characterizing the feasible and tangent directions cones in a neighborhood of a non-regular point. We also establish conditions of 2-regularity under which necessary optimality conditions are non-degenerate. These conditions apply when the phenomenon of non-regularity (or abnormality) take place. In addition examples that illustrate our results are presented.

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非正则问题最优性的充要条件

摘要我们通过Dubovitskii-Milyutin形式推导了具有多重等式和不等式约束的优化问题的新的充要最优性条件，刻画了非正则点邻域中的可行方向锥和切线方向锥。我们还建立了2-正则性的条件，在该条件下，必要的最优性条件是非退化的。当发生不规则（或异常）现象时，这些条件适用。此外，还举例说明了我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal. Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.