Higher Order Iteration Schemes for Unconstrained Optimization

• 作者: Pingqi Pan Yangyang Shi
• 来源期刊: 美国运筹学期刊(英文)
• 学科: 数学
• 关键词: UNCONSTRAINED Optimization ITERATION Scheme ODE Method QUASI-NEWTON Update Convergence Analysis
• 年，卷（期）: 2011,（3）
• 页码范围: 73-83
• 页数: 11页
• 分类号: O1

摘要

Using a predictor-corrector tactic, this paper derives new iteration schemes for unconstrained optimization. It yields a point (predictor) by some line search from the current point;then with the two points it constructs a quadratic interpolation curve to approximate some ODE trajectory;it finally determines a new point (corrector) by searching along the quadratic curve. In particular, this paper gives a global convergence analysis for schemes associated with the quasi-Newton updates. In our computational experiments, the new schemes using DFP and BFGS updates outperformed their conventional counterparts on a set of standard test problems.