A lifting method for generalized semi-infinite programs based on lower level Wolfe duality
A lifting method for generalized semi-infinite programs based on lower level Wolfe duality
复制标题
基于低级Wolfe对偶性的广义半无限规划提升方法
DOI：
--
复制
发表时间：
2013
影响因子：
2.2
通讯作者：
P. Steuermann
中科院分区：
文献类型：
--
作者：
M. Diehl;B. Houska;O. Stein;P. Steuermann
广义半无限优化问题（GSIP）是一类在设计定心问题、鲁棒优化问题和许多工程科学领域中自然出现的数学优化问题，本文介绍了一类新的数值求解策略。gsip可以看作是双层优化问题，为了检验上层最小化问题的可行性，需要解决一个参数下层最大化问题。本文利用Wolfe对偶的概念，讨论了将这类问题转化为等价有限最小化问题的几种策略。在这里，主要的贡献是讨论了在各种假设下相应公式的非简并性。最后，原始GSIP的这些非退化的重新表述允许我们应用标准的非线性优化算法。
This paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be solved in order to check feasibility of the upper level minimization problem. The current paper discusses several strategies to reformulate this class of problems into equivalent finite minimization problems by exploiting the concept of Wolfe duality for convex lower level problems. Here, the main contribution is the discussion of the non-degeneracy of the corresponding formulations under various assumptions. Finally, these non-degenerate reformulations of the original GSIP allow us to apply standard nonlinear optimization algorithms.