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On the Convergence of Successive Linear-Quadratic Programming Algorithms

Richard H. Byrd (richard***at***cs.colorado.edu)
Nicholas I. M. Gould (n.i.m.gould***at***rl.ac.uk)
Jorge Nocedal (nocedal***at***ece.northwestern.edu)
Richard A. Waltz (rwaltz***at***ece.northwestern.edu)

Abstract: The global convergence properties of a class of penalty methods for nonlinear programming are analyzed. These methods include successive linear programming approaches, and more specifically, the successive linear-quadratic programming approach presented by Byrd, Gould, Nocedal and Waltz (Math. Programming 100(1):27--48, 2004). Every iteration requires the solution of two trust-region subproblems involving piecewise linear and quadratic models, respectively. It is shown that, for a fixed penalty parameter, the sequence of iterates approaches stationarity of the penalty function. A procedure for dynamically adjusting the penalty parameter is described, and global convergence results for it are established.

Keywords: nonlinear programming, SLQP, penalty methods

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Technical Report OTC 2002/5, Optimization Technology Center, Northwestern University, Evanston, IL, USA 2002 (revised Oct. 2004).

Download: [Postscript][Compressed Postscript][PDF]

Entry Submitted: 10/19/2004
Entry Accepted: 10/19/2004
Entry Last Modified: 10/19/2004

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