An Inexact Newton Method for Nonconvex Equality Constrained Optimization

Richard Byrd(richardcs.colorado.edu)
Frank Curtis(f-curtisnorthwestern.edu)
Jorge Nocedal(nocedalece.northwestern.edu)

Abstract: We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For sufficiently convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd, Curtis, and Nocedal [2]. For nonconvex problems, the methodology developed in this paper allows for the presence of negative curvature without requiring information about the inertia of the primal-dual iteration matrix. The complete algorithm is characterized by its emphasis on sufficient reductions in a model of an exact penalty function. We analyze the global behavior of the algorithm and present numerical results on a collection of test problems.

Keywords: large-scale optimization, constrained optimization, nonconvex programming, inexact linear system solvers, Krylov subspace methods

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Citation: Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, August 2007

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Entry Submitted: 08/10/2007
Entry Accepted: 08/10/2007
Entry Last Modified: 08/10/2007

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