Scaled constraint qualifications and necessary optimality conditions for nonsmooth mathematical programs with second-order cone complementarity constraints
type: Item
instance of: scholarly article
title: Scaled constraint qualifications and necessary optimality conditions for nonsmooth mathematical programs with second-order cone complementarity constraints
zbMATH Open document ID: 1491.90163
author: A. Hajheidari
author: N. Movahedian
published in: Positivity
publication date: 2022-03-15T00:00:00Z
review text: The following minimization problem with second-order cone complementarity constraints is considered: \[ f(z) \rightarrow \min \text{ subject to } G_i(z) \in K_{m_i},~ H_i(z) \subset K_{m_i},~ (G_i(z),H_i(z)) = 0,~ i = 1,\dots, J, \] where \(f: \mathbb{R}^n \rightarrow \mathbb{R},~ G_i: \mathbb{R}^n \rightarrow \mathbb{R}^{m_i},~ i = 1,\dots J\) and \(K_{m_i}\) denotes for all \(i\) the \(m_i\)-dimensional second-order cone. Applications of the minimization problem and their modifications are outlined. It is shown that usually used constraint qualifications as Mangasarian-Fromowitz constraint qualifications cannot be used for this problem. The authors propose new constraint qualifications and study properties of the corresponding new stationary concepts.
reviewed by: Karel Zimmermann
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 7490100
zbMATH Keywords: mathematical program with second-order cone complementarity constraints
zbMATH Keywords: constraint qualification
zbMATH Keywords: M-stationary
zbMATH Keywords: S-stationary
zbMATH Keywords: nonsmooth analysis
zbMATH Keywords: necessary optimality condition
MaRDI profile type: Publication
full work available at URL: s11117-022-00878-1
OpenAlex ID: W4211173658
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DOI: 10.1007/S11117-022-00878-1
description: scientific article; zbMATH DE number 7490100