An inexact Newton method for nonconvex equality constrained optimization

• 成果类型: Article
• 署名作者: Byrd, Richard H.; Curtis, Frank E.; Nocedal, Jorge
• 署名单位: Northwestern University; University of Colorado System; University of Colorado Boulder; Northwestern University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-008-0248-3
• 发表日期: 2010
• 页码: 273-299
• 关键词: convergence; 2ND-ORDER; algorithm; point

摘要

We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351-369, 2008]. 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. Negative curvature may arise from second-order information of the problem functions, but in fact exact second derivatives are not required in the approach. 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.