Constraint aggregation for rigorous global optimization
Constraint aggregation for rigorous global optimization
复制标题
用于严格全局优化的约束聚合
作者：
F. Domes;A. Neumaier
在严格的全局优化中，目标函数上的上限有助于减少搜索空间通过本地优化很容易找到，但是在本文中，验证通常会失败。从本地优化的结果中提取的信息仍可以在许多情况下使用，以减少搜索空间。使用最佳条件，双面线性放松，高斯 - 约旦算法和有向的修改后的Cholesky分解的有价值的违规措施。冗余的约束在可行的集合上变成了强大的界限，因为它在全局优化器的微小社区中也有用，从而减少了一个简单的介绍示例大型基准的性能。
In rigorous constrained global optimization, upper bounds on the objective function help to reduce the search space. Obtaining a rigorous upper bound on the objective requires finding a narrow box around an approximately feasible solution, which then must be verified to contain a feasible point. Approximations are easily found by local optimization, but the verification often fails. In this paper we show that even when the verification of an approximate feasible point fails, the information extracted from the results of the local optimization can still be used in many cases to reduce the search space. This is done by a rigorous filtering technique called constraint aggregation. It forms an aggregated redundant constraint, based on approximate Lagrange multipliers or on a vector valued measure of constraint violation. Using the optimality conditions, two-sided linear relaxations, the Gauss–Jordan algorithm and a directed modified Cholesky factorization, the information in the redundant constraint is turned into powerful bounds on the feasible set. Constraint aggregation is especially useful since it also works in a tiny neighborhood of the global optimizer, thereby reducing the cluster effect. A simple introductory example demonstrates how our new method works. Extensive tests show the performance on a large benchmark.