Optimization Online


Explicit Convex and Concave Envelopes through Polyhedral Subdivisions

Mohit Tawarmalani(mtawarma***at***purdue.edu)
Jean-Philippe Richard(richard***at***ise.ufl.edu)
Chuanhui Xiong(cxiong***at***purdue.edu)

Abstract: In this paper, we derive explicit characterizations of convex and concave envelopes of several nonlinear functions over various subsets of a hyper-rectangle. These envelopes are obtained by identifying polyhedral subdivisions of the hyper-rectangle over which the envelopes can be constructed easily. In particular, we use these techniques to derive, in closed-form, the concave envelopes of concave-extendable supermodular functions and the convex envelopes of disjunctive convex functions.

Keywords: convex envelopes, supermodularity, disjunctive functions

Category 1: Global Optimization (Theory )

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 3: Combinatorial Optimization (Polyhedra )

Citation: Krannert Working Paper

Download: [PDF]

Entry Submitted: 06/01/2010
Entry Accepted: 06/01/2010
Entry Last Modified: 06/01/2010

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society