Constraint aggregation for rigorous global optimization
成果类型：
Article
署名作者：
Domes, Ferenc; Neumaier, Arnold
署名单位：
University of Vienna
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-014-0851-4
发表日期：
2016
页码：
375-401
关键词：
摘要：
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.