Large-scale nonlinear constrained optimization: a

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Jan 31, 1994 - In this survey paper we will attempt to give an overview of the .... it is reasonable to ask the question `Is it worthwhile to design algorithms that are unsuitable ... much storage (O(n2)) and too much work per iteration (O(n3) ops). ..... Chapter 7 of the same reference serves as a detailed manual on the format.
Large-scale nonlinear constrained optimization: a current survey

by A.R. Conn1 , Nick Gould2 , and Ph.L. Toint3 Report 94/1

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IBM T.J. Watson Research Center, P.O.Box 218, Yorktown Heights, NY 10598, USA Email : [email protected] 2

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January 31, 1994

CERFACS, 42 Avenue Gustave Coriolis, 31057 Toulouse Cedex, France, EC Email : [email protected] or [email protected] Current reports available by anonymous ftp from the directory \pub/reports" on camelot.cc.rl.ac.uk (internet 130.246.8.61)

Department of Mathematics, Facultes Universitaires ND de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium, EC Email : [email protected] Current reports available by anonymous ftp from the directory \pub/reports" on thales.math.fundp.ac.be (internet 138.48.4.14) To appear in Algorithms for Continuous Optimization: State of the Art, L. Dixon, D. F. Shanno and E. Spedicato, Editors, Kluwer Academic Publishers, 1994.

Keywords : Large-scale, constraints, nonlinear optimization.

Large-scale nonlinear constrained optimization: a current survey Andrew R. Conn IBM T.J. Watson Research Center, Yorktown Heights, USA Nick Gould CERFACS, Toulouse, France, EC Philippe L. Toint Department of Mathematics, FUNDP, Namur, Belgium, EC

Abstract Much progress has been made in constrained nonlinear optimization in the past ten years, but most large-scale problems still represent a considerable obstacle. In this survey paper we will attempt to give an overview of the current approaches, including interior and exterior methods and algorithms based upon trust regions and line searches. In addition, the importance of software, numerical linear algebra and testing will be addressed. We will try to explain why the diculties arise, how attempts are being made to overcome them and some of the problems that still remain. Although there will be some emphasis on the LANCELOT and CUTE projects, the intention is to give a broad picture of the state-of-the-art. Keywords: Large-scale, constraints, nonlinear optimization.

1 Introduction We shall rst state the most general form of the problem that we are addressing, namely minimize f (x) x2