Relaxations of factorable functions with convex-transformable intermediates

• 成果类型: Article
• 署名作者: Khajavirad, Aida; Michalek, Jeremy J.; Sahinidis, Nikolaos V.
• 署名单位: International Business Machines (IBM); IBM USA; Carnegie Mellon University; Carnegie Mellon University; Carnegie Mellon University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-012-0618-8
• 发表日期: 2014
• 页码: 107-140
• 关键词: global optimization; concave functions; ENVELOPES; PROGRAMS; nonconvex; underestimation

摘要

We propose to strengthen standard factorable relaxations of global optimization problems through the use of functional transformations of intermediate expressions. In particular, we exploit convex transformability of the component functions of factorable programs as a tool in the generation of bounds. We define suitable forms of transforming functions and assess, theoretically and computationally, the sharpness of the resulting relaxations in comparison to existing schemes.