New Lagrange multipliers rules for constrained quasidifferentiable optimization
type: Item
instance of: scholarly article
title: New Lagrange multipliers rules for constrained quasidifferentiable optimization
zbMATH Open document ID: 1026.49012
author: Yan Gao
published in: Vietnam Journal of Mathematics
publication date: 2003-12-08T00:00:00Z
review text: The paper contains some new first-order Lagrange multiplier rules for quasi-differentiable optimization problems with equality and inequality constraints. Let the optimization problem be given by \[ \begin{alignedat}{2} \text{minimize} &\qquad f_0(x),\\ \text{subject to} &\qquad f_i(x)\leq 0, &&\qquad i=1,\dots,m,\\ &\qquad h_j(x)=0, &&\qquad j= 1,\dots, p,\end{alignedat} \] where \(f_i,h_j: \mathbb{R}^n\to \mathbb{R}\) be quasidifferentiable functions. The author presents three necessary John type optimality conditions by means of the quasidifferentials but also by the Clarke subdifferentials of the functions using special algebraic sums and differences (in the sense of Demyanov and in the sense of Rubinov/Akhundov, respectively) of these sets. Moreover, assuming generalized convexity assumptions (generalized quasiconvexity and generalized pseudoconvexity), it is shown that the associated Kuhn-Tucker conditions are also sufficient for optimality.
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 1885676
zbMATH Keywords: first-order Lagrange multiplier rules
zbMATH Keywords: quasi-differentiable optimization
zbMATH Keywords: constraints
zbMATH Keywords: necessary John type optimality conditions
zbMATH Keywords: quasidifferentials
zbMATH Keywords: Clarke subdifferentials
zbMATH Keywords: convexity
zbMATH Keywords: quasiconvexity
zbMATH Keywords: pseudoconvexity
zbMATH Keywords: Kuhn-Tucker conditions
reviewed by: Jörg Thierfelder
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1885676