On the Convergence of Successive Linear Programming Algorithms

Richard. H. Byrd (richardcs.colorado.edu)
Nicholas I. M. Gould (nimgrl.ac.uk)
Jorge Nocedal (nocedalece.northwestern.edu)
Richard A. Waltz (rwaltzece.northwestern.edu)

Abstract: We analyze the global convergence properties of a class of penalty methods for nonlinear programming. These methods include successive linear programming approaches, and more specifically the SLP-EQP approach presented in \cite{ByrdGoulNoceWalt02}. Every iteration requires the solution of two trust region subproblems involving linear and quadratic models, respectively. The interaction between the trust regions of these subproblems requires careful consideration. It is shown under mild assumptions that there exist an accumulation point which is a critical point for the penalty function.

Keywords: nonlinear optimization, successive linear programming, SLP-EQP, trust-region 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.

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

Entry Submitted: 04/23/2003
Entry Accepted: 04/23/2003
Entry Last Modified: 04/23/2003

Modify/Update this entry