Convex and concave envelopes: revisited and new perspectives

DOI10.1016/j.orl.2017.06.008zbMath1409.90229OpenAlexW2724989293MaRDI QIDQ1728297

Guanglei Wang, Walid Ben-Ameur, Adam Ouorou

Publication date: 22 February 2019

Published in: Operations Research Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.orl.2017.06.008

zbMATH Keywords

polyhedral approximationconvex envelopefinite cover

Mathematics Subject Classification ID

Semidefinite programming (90C22) Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Quadratic programming (90C20)

Related Items (4)

Mathematical programming methods for microgrid design and operations: a survey on deterministic and stochastic approaches ⋮ Exploiting sparsity for the min \(k\)-partition problem ⋮ A new technique to derive tight convex underestimators (sometimes envelopes) ⋮ A Lagrange decomposition based branch and bound algorithm for the optimal mapping of cloud virtual machines

Uses Software

• YALMIP

Cites Work

• On the computational complexity of membership problems for the completely positive cone and its dual
• A hierarchy of relaxations leading to the convex hull representation for general discrete optimization problems
• The Boolean quadratic polytope: Some characteristics, facets and relatives
• A convex envelope formula for multilinear functions
• Convex envelopes of multilinear functions over a unit hypercube and over special discrete sets
• Multipolar robust optimization
• Convex envelopes for edge-concave functions
• A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs
• Some results on the strength of relaxations of multilinear functions
• On convex relaxations for quadratically constrained quadratic programming
• Explicit convex and concave envelopes through polyhedral subdivisions
• Convex underestimators of polynomials
• On convex envelopes for bivariate functions over polytopes
• Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs
• On Nonconvex Quadratic Programming with Box Constraints
• Jointly Constrained Biconvex Programming
• Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
• Geometry of cuts and metrics

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