Generalized scaling for the constrained maximum-entropy sampling problem
成果类型：
Article
署名作者：
Chen, Zhongzhu; Fampa, Marcia; Lee, Jon
署名单位：
University of Michigan System; University of Michigan; Universidade Federal do Rio de Janeiro
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-024-02101-3
发表日期：
2025
页码：
177-216
关键词：
摘要：
The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a variety of concave continuous relaxations of the objective function. A standard and computationally-important bound-enhancement technique in this context is (ordinary) scaling, via a single positive parameter. Scaling adjusts the shape of continuous relaxations to reduce the gaps between the upper bounds and the optimal value. We extend this technique to generalized scaling, employing a positive vector of parameters, which allows much more flexibility and thus potentially reduces the gaps further. We give mathematical results aimed at supporting algorithmic methods for computing optimal generalized scalings, and we give computational results demonstrating the performance of generalized scaling on benchmark problem instances.