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.
On convex envelopes for bivariate functions over polytopes / M. Locatelli;F. Schoen. - In: MATHEMATICAL PROGRAMMING. - ISSN 0025-5610. - STAMPA. - 144:(2014), pp. 65-91. [10.1007/s10107-012-0616-x]
On convex envelopes for bivariate functions over polytopes
SCHOEN, FABIO
2014
Abstract
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.File | Dimensione | Formato | |
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