Second-order analysis of penalty function
type: Item
instance of: scholarly article
title: Second-order analysis of penalty function
zbMATH Open document ID: 1229.90146
published in: Journal of Optimization Theory and Applications
publication date: 2010-11-10T00:00:00Z
review text: The authors study global exact penalty properties for general nonlinear programming problems. Global exact penalty properties are conditions under which every global minimum of the original problem is also a global minimum of the penalized problem. The global second-order sufficient conditions are similar to those in [\textit{X. Q. Yang}, Math. Program. 81, 327--347 (1998; Zbl 0919.90125)]. More precisely, the authors use a weak second-order sufficient condition, together with a generalized representation condition and prove that these conditions ensure the existence of a global exact penalty function. The representation condition requires the objective function and constraint functions to have a specific kind of second-order representation, and it is satisfied by quadratic or linear fractional functions, as well as by functions with a surjective Hessian. In the last section, the authors apply their results to several specially structured penalty functions for a general nonlinear programming problem and in particular to a nonconvex quadratic program with a two-sided quadratic constraint. For such a quadratic problem, the authors show that a global exact penalty function exists if the Hessian of the Lagrangian is positive definite. For a class of linearly fractionally constrained linear fractional programs with the same denominator, the authors obtain the existence of a global exact penalty function by using a first-order condition.
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49N15
zbMATH DE Number: 5814304
zbMATH Keywords: weak second-order sufficient conditions
zbMATH Keywords: generalized representation conditions
zbMATH Keywords: global exact penalty functions
author: Xiao Qi Yang
author: Yuying Zhou
reviewed by: R. S. Burachik
MaRDI profile type: Publication
full work available at URL: s10957-010-9666-5
OpenAlex ID: W1988336553
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DOI: 10.1007/S10957-010-9666-5
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description: scientific article; zbMATH DE number 5814304