Lagrange multiplier rules for non‐differentiable DC generalized semi‐infinite programming problems

Lagrange multiplier rules for non‐differentiable DC generalized semi‐infinite programming problems

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Article ID: iaor20134045
Volume: 56
Issue: 2
Start Page Number: 417
End Page Number: 430
Publication Date: Jun 2013
Journal: Journal of Global Optimization
Authors:
Keywords: differential equations, Programming (semi-infinite), Lagrangian methods
Abstract:

This paper aims to study a broad class of generalized semi‐infinite programming problems with (upper and lower level) objectives given as the difference of two convex functions, and (lower level) constraints described by a finite number of convex inequalities and a set constraints. First, we are interested in some various lower level constraint qualifications for the problem. Then, the results are used to establish efficient upper estimate of certain subdifferential of value functions. Finally, we apply the obtained subdifferential estimates to derive necessary optimality conditions for the problem.

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