Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/convex-envelopes-generated-from-finitely-many-compact-convex-sets-mEXOu5Fgh5
References (40)
-
F. Tardella (2008)
Existence and sum decomposition of vertex polyhedral convex envelopesOptimization Letters, 2
-
K. Hoffman, T. Ralphs (2013)
Integer and Combinatorial Optimization -
Xiaowei Bao, N. Sahinidis, Mohit Tawarmalani (2009)
Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programsOptimization Methods and Software, 24
-
M. Tawarmalani, N.V. Sahinidis (2002)
Convex extensions and convex envelopes of l.s.c. functionsMath. Program., 93
-
F. Al-Khayyal, J. Falk (1983)
Jointly Constrained Biconvex ProgrammingMath. Oper. Res., 8
-
E. Balas (1985)
Disjunctive programming and a hierarchy of relaxations for discrete optimization problemsSiam Journal on Algebraic and Discrete Methods, 6
-
M. Bussieck, A. Drud, A. Meeraus (2003)
MINLPLib - A Collection of Test Models for Mixed-Integer Nonlinear ProgrammingINFORMS J. Comput., 15
-
C. Meyer, C. Floudas (2004)
Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave EnvelopesJournal of Global Optimization, 29
-
L. Lovász (1982)
Mathematical Programming: The State of the Art -
A. Frangioni, C. Gentile (2006)
Perspective cuts for a class of convex 0–1 mixed integer programsMathematical Programming, 106
-
(2001)
Semidefinite relaxations of fractional programs via novel techniques for constructing convex envelopes of nonlinear functions -
D. Bertsekas (2009)
Convex Optimization Theory -
(1970)
Convex Analysis -
O. Günlük, Jeff Linderoth (2008)
Perspective Relaxation of Mixed Integer Nonlinear Programs with Indicator Variables -
Mohit Tawarmalani (2010)
Inclusion Certificates and Simultaneous Convexification of Functions -
H. Sherali (2009)
Disjunctive Programming -
(1911)
Theorie der Knovexen Körper, insbesondere begrundung ihres oberfla chenbegriffs -
Mohit Tawarmalani, N. Sahinidis (2005)
A polyhedral branch-and-cut approach to global optimizationMathematical Programming, 103
-
I. Grossmann, Sangbum Lee (2003)
Generalized Convex Disjunctive Programming: Nonlinear Convex Hull RelaxationComputational Optimization and Applications, 26
-
R.T. Rockafellar (1970)
Convex Analysis. Princeton Mathematical Series -
N. Sahinidis (1996)
BARON: A general purpose global optimization software packageJournal of Global Optimization, 8
-
C. Carathéodory (1911)
Über den variabilitätsbereich der fourier’schen konstanten von positiven harmonischen funktionenRendiconti del Circolo Matematico di Palermo (1884-1940), 32
-
Mohit Tawarmalani, Jean-Philippe Richard, Kwanghun Chung (2010)
Strong valid inequalities for orthogonal disjunctions and bilinear covering setsMathematical Programming, 124
-
Aida Khajavirad, N. Sahinidis (2012)
Convex envelopes of products of convex and component-wise concave functionsJournal of Global Optimization, 52
-
M. Jach, Dennis Michaels, R. Weismantel (2008)
The Convex Envelope of (n--1)-Convex FunctionsSIAM J. Optim., 19
-
Robert Stubbs, Sanjay Mehrotra (1999)
A branch-and-cut method for 0-1 mixed convex programmingMathematical Programming, 86
-
A. Bachem, B. Korte, M. Grötschel (1983)
Mathematical Programming The State of the Art, XIth International Symposium on Mathematical Programming, Bonn, Germany, August 23-27, 1982 -
D.M. Topkis (1998)
Supermodularity and Complementarity -
Mohit Tawarmalani, N. Sahinidis (2004)
Global optimization of mixed-integer nonlinear programs: A theoretical and computational studyMathematical Programming, 99
-
(2002)
Convex extensions and convex envelopes of l.s.c -
R.T. Rockafellar, R.J.-B. Wets (1998)
Variational Analysis. A Series of Comprehensive Studies in Mathematics -
C. Meyer, C. Floudas (2005)
Convex envelopes for edge-concave functionsMathematical Programming, 103
-
Sebastián Ceria, J. Soares (1999)
Convex programming for disjunctive convex optimizationMathematical Programming, 86
-
G. McCormick (1976)
Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problemsMathematical Programming, 10
-
J.-B. Hiriart-Urruty, C. Lemaréchal (2001)
Fundamentals of Convex Analysis -
H. Sherali (1997)
CONVEX ENVELOPES OF MULTILINEAR FUNCTIONS OVER A UNIT HYPERCUBE AND OVER SPECIAL DISCRETE SETS -
L. Lovász (1982)
Submodular functions and convexity -
Mohit Tawarmalani, Jean-Philippe Richard, Chuanhui Xiong (2010)
Explicit convex and concave envelopes through polyhedral subdivisionsMathematical Programming, 138
-
H. Minkowski (1911)
Gesammelte Abhandlungen von Hermann Minkowski, vol. 2 -
A. Rikun (1997)
A Convex Envelope Formula for Multilinear FunctionsJournal of Global Optimization, 10
- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Springer and Mathematical Optimization Society
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Mathematics of Computing; Numerical Analysis; Combinatorics; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
- ISSN
- 0025-5610
- eISSN
- 1436-4646
- DOI
- 10.1007/s10107-011-0496-5
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
Mathematical Programming – Springer Journals
Published: Oct 28, 2011