On convex envelopes for bivariate functions over polytopes

• 成果类型: Article
• 署名作者: Locatelli, Marco; Schoen, Fabio
• 署名单位: University of Parma; University of Florence
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-012-0616-x
• 发表日期: 2014
• 页码: 65-91
• 关键词: rational functions; bound algorithm; branch; optimization; relaxations; monomials; nonconvex; PROGRAMS; SUM

摘要

In this paper we discuss convex envelopes for bivariate functions, satisfying suitable assumptions, over polytopes. We first propose a technique to compute the value and a supporting hyperplane of the convex envelope over a general two-dimensional polytope through the solution of a three-dimensional convex subproblem with continuously differentiable constraint functions. Then, for quadratic functions as well as for some polynomial and rational ones, again satisfying suitable assumptions, we show how the same computations can be carried out through the solution of a single semidefinite problem.