A Robust Trust Region Method for Constrained Nonlinear Programming Problems
A Robust Trust Region Method for Constrained Nonlinear Programming Problems
复制标题
求解约束非线性规划问题的鲁棒信赖域方法
DOI：
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复制
发表时间：
1992
影响因子：
3.1
通讯作者：
J. Burke
中科院分区：
文献类型：
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作者：
J. Burke
大多数已发表的约束优化信赖域算法的研究成果都是由Fletcher关于不可微精确罚函数信赖域算法的原始研究成果衍生而来。这些方法仅限于可以给出最优库恩-塔克乘子向量大小的合理估计的应用。最近，人们努力将信任域方法扩展到Wilson、Han和Powell的顺序二次规划（SQP）算法中。所有这些对Wilson-Han-Powell SQP算法的扩展都只考虑等式约束的情况，并且需要强全局正则性假设。本文提出了约束问题的信任域算法的一般框架，该框架不需要这种正则性假设，并且允许非常一般的约束。该方法是在Powell给出的凸复合优化问题的基础上建模的，并由线性子问题驱动，这些子问题可以对o的值产生可行的估计。
Most of the published work on trust region algorithms for constrained optimization is derived from the original work of Fletcher on trust region algorithms for nondifferentiable exact penalty functions. These methods are restricted to applications where a reasonable estimate of the magnitude of an optimal Kuhn–Tucker multiplier vector can be given. More recently an effort has been made to extend the trust region methodology to the sequential quadratic programming (SQP) algorithm of Wilson, Han, and Powell. All of these extensions to the Wilson–Han–Powell SQP algorithm consider only the equality-constrained case and require strong global regularity hypotheses. This paper presents a general framework for trust region algorithms for constrained problems that does not require such regularity hypotheses and allows very general constraints. The approach is modeled on the one given by Powell for convex composite optimization problems and is driven by linear subproblems that yield viable estimates for the value o...