A simple feasible SQP algorithm for inequality constrained optimization
type: Item
instance of: scholarly article
title: A simple feasible SQP algorithm for inequality constrained optimization
zbMATH Open document ID: 1111.65057
published in: Applied Mathematics and Computation
publication date: 2007-01-11T00:00:00Z
review text: The author considers a constrained nonlinear minimization problem of the form \[ \text{minimize }f(x)\text{ subject to }g_j(x)\leq 0,\quad j= 1,\dots, m,\tag{\(*\)} \] where \(f: \mathbb{R}^n\to \mathbb{R}^1\), \(g_j: \mathbb{R}^n\to \mathbb{R}^1\) for \(j= 1,\dots, m\) are smooth functions. A new modification of the sequential quadratic programming (SQP) algorithm for solving this problem is proposed. The search direction is a suitable combination of a descent direction, a feasible direction, and a second-order direction. The proposed algorithm either stops at the Karush-Kuhn-Tucker point of problem \((*)\), or generates an infinite sequence \(\{x^k\}\), any accumulation point of which is a Karush-Kuhn-Tucker point of problem \((*)\). Global as well as superlinear convergence under suitable additional conditions is proved.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C55
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 5115370
zbMATH Keywords: sequential quadratic programming methods
zbMATH Keywords: nonlinear constrained minimization
zbMATH Keywords: global convergence
zbMATH Keywords: superlinear convergence
author: Zhibin Zhu
reviewed by: Karel Zimmermann
MaRDI profile type: Publication
full work available at URL: j.amc.2006.04.073
OpenAlex ID: W2146283958
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DOI: 10.1016/J.AMC.2006.04.073
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description: scientific article; zbMATH DE number 5115370