Journal
MATHEMATICAL PROGRAMMING
Volume 137, Issue 1-2, Pages 371-408Publisher
SPRINGER
DOI: 10.1007/s10107-011-0496-5
Keywords
Convex envelope; Global optimization; Factorable relaxations; Perspective transformation; Submodular functions
Categories
Funding
- National Science Foundation [CMII-1030168]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1030168] Funding Source: National Science Foundation
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We consider the problem of constructing the convex envelope of a lower semi-continuous function defined over a compact convex set. We formulate the envelope representation problem as a convex optimization problem for functions whose generating sets consist of finitely many compact convex sets. In particular, we consider nonnegative functions that are products of convex and component-wise concave functions and derive closed-form expressions for the convex envelopes of a wide class of such functions. Several examples demonstrate that these envelopes reduce significantly the relaxation gaps of widely used factorable relaxation techniques.
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