Necessary and sufficient KKT optimality conditions in non-convex optimization

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• 作者：Quyen Ho
• 关键词：Convex optimization ; Slater’s condition ; Level set ; Karush–Kuhn–Tucker optimality conditions
• 刊名：Optimization Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：11
• 期：1
• 页码：41-46
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Optimization; Operation Research/Decision Theory; Computational Intelligence; Numerical and Computational Physics, Simulation;
• 出版者：Springer Berlin Heidelberg
• ISSN：1862-4480
• 卷排序：11

文摘

We study the optimization problems \(\min _\mathbf{x }\left\{ f(\mathbf{x }):g_j(\mathbf{x })\le 0, j=1,\ldots ,m\right\} \) where Slater’s condition holds without the convexity of the feasible set and of the functions \(f,~ g_j\). At a feasible point \(\mathbf{x }\) under question the functions \(g_j\) are assumed to satisfy a non-degeneracy assumption, necessary and sufficient KKT optimality conditions are then considered in relation to the convexity of the level sets of f.