A globally convergent primal-dual interior-point filter method for nonlinear programming

• 成果类型: Article
• 署名作者: Ulbrich, M; Ulbrich, S; Vicente, LN
• 署名单位: University of Hamburg; University of Munich; Universidade de Coimbra; Rice University; Rice University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-003-0477-4
• 发表日期: 2004
• 页码: 379-410
• 关键词: quadratic convergence; local convergence; algorithm

摘要

In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primal-dual interior-point algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, whose sizes are controlled by a trust-region type parameter. Each entry in the filter is a pair of coordinates: one resulting from feasibility and centrality, and associated with the normal step; the other resulting from optimality (complementarity and duality), and related with the tangential step. Global convergence to first-order critical points is proved for the new primal-dual interior-point filter algorithm.