An interior-point trust-funnel algorithm for nonlinear optimization

• 成果类型: Article
• 署名作者: Curtis, Frank E.; Gould, Nicholas I. M.; Robinson, Daniel P.; Toint, Philippe L.
• 署名单位: Lehigh University; UK Research & Innovation (UKRI); Science & Technology Facilities Council (STFC); STFC Rutherford Appleton Laboratory; Johns Hopkins University; University of Namur; University of Namur
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1003-9
• 发表日期: 2017
• 页码: 73-134
• 关键词: 2nd-derivative sqp method; GLOBAL CONVERGENCE; penalty-function; region method; implementation

摘要

We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math Prog 122(1):155-196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism, but has the additional capability of being able to solve problems with both equality and inequality constraints. The prominent features of our algorithm are that (i) the subproblems that define each search direction may be solved with matrix-free methods so that derivative matrices need not be formed or factorized so long as matrix-vector products with them can be performed; (ii) the subproblems may be solved approximately in all iterations; (iii) in certain situations, the computed search directions represent inexact sequential quadratic optimization steps, which may be desirable for fast local convergence; (iv) criticality measures for feasibility and optimality aid in determining whether only a subset of computations need to be performed during a given iteration; and (v) no merit function or filter is needed to ensure global convergence.