A line search exact penalty method using steering rules
type: Item
instance of: scholarly article
title: A line search exact penalty method using steering rules
zbMATH Open document ID: 1254.90221
author: Gabriel Lopez-Calva
author: R. H. Byrd
author: Jorge Nocedal
published in: Mathematical Programming. Series A. Series B
publication date: 2012-06-26T00:00:00Z
review text: The article of Richard H. Bryd, Gabriel Lopez-Calva and Jorge Nocedal is a valuable contribution to the field of numerical nonlinear optimization - such to say, another milestone in the series of the authors' contributions to this important area of Applied and Industrial Mathematics and Operational Research. This work impresses by the appropriate, elegant and comfortable use and combination of some basic ideas and principles of optimization theory and numerical mathematics, well directed and eventually proven to be successful. As the authors point out, line search algorithms for nonlinear programming must include safeguards to permit global convergence. This article presents an exact penalization approach which extends the class of problems solvable by a line search sequential quadratic programming algorithm. In the new methods, the penalty parameter is adjusted at every iteration to guarantee sufficient progress in the linear feasibility and to promote acceptance of the step. A trust region is assists in the determination of the penalty parameter, however, not in the step computation. It is shown that the algorithm enjoys favorable global convergence properties. Numerical experiments illustrate the behavior of the algorithm on various difficult situations. The mathematically deep and strong article paper is well-written and well-structured. Problems, formulas, algorithms and tables are put with care, meaningful and with success. The five sections of the paper are as follows: 1. Introduction, 2. A line search penalty method, 3. Convergence analysis, 4. Numerical experiments, and 5. Final remarks. In future, further deep methods and results can be expected, prepared and supported by this research paper. These advances can lead to a great progress in the areas of science, engineering, economics, finance, OR, medicine and healthcare and, herewith, to improvements of the living conditions and expectations of the peoples on earth.
reviewed by: Gerhard-Wilhelm Weber
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M37
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 6050439
zbMATH Keywords: Line search
zbMATH Keywords: Sequential quadratic programming
zbMATH Keywords: Exact penalty method
zbMATH Keywords: Steering rules
zbMATH Keywords: Trust region
zbMATH Keywords: Convergence
describes a project that uses: KNITRO
describes a project that uses: SNOPT
describes a project that uses: filterSQP
MaRDI profile type: Publication
full work available at URL: s10107-010-0408-0
OpenAlex ID: W2079309016
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DOI: 10.1007/S10107-010-0408-0
description: scientific article; zbMATH DE number 6050439