NDLI: A Moving Balls Approximation Method for a Class of Smooth Constrained Minimization Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Auslender, Alfred Teboulle, Marc Shefi, Ron
Copyright Year	2010
Abstract	We introduce a new algorithm for a class of smooth constrained minimization problems which is an iterative scheme that generates a sequence of feasible points that approximates the constraints set by a sequence of balls and is accordingly called the Moving Balls Approximation algorithm (MBA). The computational simplicity of MBA, which uses first order data information, makes it suitable for large scale problems. Theoretical and computational properties of MBA in its primal and dual forms are studied, and convergence and global rate of convergence results are established for nonconvex and convex problems. We then introduce a variant of MBA that includes an active set technique and is particularly suitable for problems with a large number of constraints. This variant is as simple as MBA and is proven to preserve the convergence properties of MBA. Extension of MBA is also developed for a class of variational inequalities. Initial numerical experiments on quadratically constrained problems demonstrate the viability and performance of our methods when compared to some existing state-of-the-art optimization methods/software such as a sequential quadratic programming solver from the IMSL Library and the CVXOPT software package for convex optimization.
Starting Page	3232
Ending Page	3259
Page Count	28
File Format	PDF
ISSN	10526234
DOI	10.1137/090763317
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	6
Volume Number	20
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-10-26
Access Restriction	Subscribed
Subject Keyword	smooth constrained minimization active set techniques feasible methods CVXOPT Mathematical programming methods optimal gradient schemes convergence rate Quadratic programming variational inequalities sequential quadratic programming methods Convex programming Large-scale problems
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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