An inexact Newton method for nonconvex equality constrained optimization

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 CR Subject Classification 49M37, 65K05, 90C06, 90C26, 90C30

• Type: Journal
• Year: 2010
• Where: MP
• Authors: Richard H. Byrd, Frank E. Curtis, Jorge Nocedal
• Keywords: Inexact Step Computations, Keywords Large-scale Optimization, Line Search Algorithm, MP 2010