Integer and combinatorial optimization
Integer and combinatorial optimization
Experiments in quadratic 0-1 programming
Mathematical Programming: Series A and B
Quadratic programming is in NP
Information Processing Letters
Nonlinear optimization: complexity issues
Nonlinear optimization: complexity issues
A cutting plane approach for chance constrained linear programs
Operations Research
SIAM Review
Duality bound method for the general quadratic programming problem with quadratic constraints
Journal of Optimization Theory and Applications
Introduction to Linear Optimization
Introduction to Linear Optimization
A Convex Envelope Formula for Multilinear Functions
Journal of Global Optimization
A New Semidefinite Programming Bound for Indefinite Quadratic Forms Over a Simplex
Journal of Global Optimization
Dual Bounds and Optimality Cuts for All-Quadratic Programs with Convex Constraints
Journal of Global Optimization
Enhancing RLT relaxations via a new class of semidefinite cuts
Journal of Global Optimization
A Global Optimization Algorithm using Lagrangian Underestimates and the Interval Newton Method
Journal of Global Optimization
Some Fundamental Properties of Successive Convex Relaxation Methods on LCP and Related Problems
Journal of Global Optimization
Global optimization approach to unequal sphere packing problems in 3D
Journal of Optimization Theory and Applications
Packing equal circles in a square: a deterministic global optimization approach
Discrete Applied Mathematics
Convexification and Global Optimization in Continuous And
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A Facet Generation Procedure for Solving 0/1 Integer Programs
Operations Research
Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations
Computational Optimization and Applications
Computational Optimization and Applications
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave Envelopes
Journal of Global Optimization
Convex envelopes for edge-concave functions
Mathematical Programming: Series A and B
A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs
Mathematical Programming: Series A and B
On Solving Nonconvex Optimization Problems by Reducing The Duality Gap
Journal of Global Optimization
Journal of Global Optimization
Using a Mixed Integer Quadratic Programming Solver for the Unconstrained Quadratic 0-1 Problem
Mathematical Programming: Series A and B
A robust algorithm for quadratic optimization under quadratic constraints
Journal of Global Optimization
Local search heuristics for Quadratic Unconstrained Binary Optimization (QUBO)
Journal of Heuristics
The global solver in the LINDO API
Optimization Methods & Software - GLOBAL OPTIMIZATION
Optimization Methods & Software - GLOBAL OPTIMIZATION
Convex envelopes of products of convex and component-wise concave functions
Journal of Global Optimization
Relaxations of multilinear convex envelopes: dual is better than primal
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
GloMIQO: Global mixed-integer quadratic optimizer
Journal of Global Optimization
Journal of Global Optimization
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This article addresses the generation of strong polyhedral relaxations for nonconvex, quadratically constrained quadratic programs (QCQPs). Using the convex envelope of multilinear functions as our starting point, we develop a polyhedral relaxation for QCQP, along with a cutting plane algorithm for its implementation. Our relaxations are multiterm, i.e. they are derived from the convex envelope of the sum of multiple bilinear terms of quadratic constraints, thereby providing tighter bounds than the standard termwise relaxation of the bilinear functions. Computational results demonstrate the usefulness of the proposed cutting planes.