A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties
A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties
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DOI：
10.1137/s1052623401392123
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发表时间：
2003-01-01
影响因子：
3.1
通讯作者：
Lawrence, CT
中科院分区：
文献类型：
--
作者：
Tits, AL;Wächter, A;Lawrence, CT
一种基于精确罚函数的方案，灵感来自 Mayne 和 Polak [Math. Program., 11 ( 1976), pp. 67-80]-提出将不等式约束问题的任何给定可行内点方法扩展到一般平滑约束优化问题。结果表明，原对偶内点框架允许比该方案的创始人在可行方向的一阶方法的背景下讨论和分析的惩罚参数更新规则更简单的惩罚参数更新规则。在温和的假设下证明了强大的全局和局部收敛结果。特别是，(i) 所提出的算法不会遇到 Wachter 和 Biegler 最近指出的常见陷阱 [Math.计划，88（2000），第 565-574 页]； (ii) 算法原始版本中对 Hessian 估计的正定性假设被放宽，允许使用精确的 Hessian 信息，从而导致局部二次收敛。报道了有希望的数值结果。
An exact-penalty-function-based scheme-inspired from an old idea due to Mayne and Polak [Math. Program., 11 ( 1976), pp. 67-80]-is proposed for extending to general smooth constrained optimization problems any given feasible interior-point method for inequality constrained problems. It is shown that the primal-dual interior-point framework allows for a simpler penalty parameter update rule than the one discussed and analyzed by the originators of the scheme in the context of first order methods of feasible direction. Strong global and local convergence results are proved under mild assumptions. In particular, (i) the proposed algorithm does not suffer a common pitfall recently pointed out by Wachter and Biegler [Math. Program., 88 (2000), pp. 565-574]; and (ii) the positive definiteness assumption on the Hessian estimate, made in the original version of the algorithm, is relaxed, allowing for the use of exact Hessian information, resulting in local quadratic convergence. Promising numerical results are reported.