Convex envelopes for edge-concave functions

• 成果类型: Article
• 署名作者: Meyer, CA; Floudas, CA
• 署名单位: Princeton University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0580-9
• 发表日期: 2005
• 页码: 207-224
• 关键词: trilinear monomials; triangulation; domains; facets; CUBE

摘要

Deterministic global optimization algorithms frequently rely on the convex underestimation of nonconvex functions. In this paper we describe the structure of the polyhedral convex envelopes of edge-concave functions over polyhedral domains using geometric arguments. An algorithm for computing the facets of the convex envelope over hyperrectangles in R-3 is described. Sufficient conditions are described under which the convex envelope of a sum of edge-concave functions may be shown to be equivalent to the sum of the convex envelopes of these functions.