Recognition problems for special classes of polynomials in 0-1 variables
Mathematical Programming: Series A and B
On the equivalence of paved-duality and standard linearization of nonlinear 0–1 optimization
Selected papers on First international colloquium on pseudo-boolean optimization and related topics
Concave extensions for nonlinear 0–1 maximization problems
Mathematical Programming: Series A and B
A Convex Envelope Formula for Multilinear Functions
Journal of Global Optimization
Analysis of Bounds for Multilinear Functions
Journal of Global Optimization
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
A new global optimization method for univariate constrained twice-differentiable NLP problems
Journal of Global Optimization
Journal of Global Optimization
Tight convex underestimators for $${{\mathcal C}^2}$$-continuous problems: I. univariate functions
Journal of Global Optimization
Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
A review of recent advances in global optimization
Journal of Global Optimization
Convex relaxation for solving posynomial programs
Journal of Global Optimization
On convex relaxations of quadrilinear terms
Journal of Global Optimization
An Efficient Global Approach for Posynomial Geometric Programming Problems
INFORMS Journal on Computing
A comparison of methods for the computation of affine lower bound functions for polynomials
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
Convex envelopes of products of convex and component-wise concave functions
Journal of Global Optimization
Compact relaxations for polynomial programming problems
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
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
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Convex underestimators of nonconvex functions, frequently used in deterministic global optimization algorithms, strongly influence their rate of convergence and computational efficiency. A good convex underestimator is as tight as possible and introduces a minimal number of new variables and constraints. Multilinear monomials over a coordinate aligned hyper-rectangular domain are known to have polyhedral convex envelopes which may be represented by a finite number of facet inducing inequalities. This paper describes explicit expressions defining the facets of the convex and concave envelopes of trilinear monomials over a box domain with bounds of opposite signs for at least one variable. It is shown that the previously used approximations based on the recursive use of the bilinear construction rarely yield the convex envelope itself.