Global minimization of large-scale constrained concave quadratic problems by separable programming
Mathematical Programming: Series A and B
An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
On a class of functions attaining their maximum at the vertices of a polyhedron
Discrete Applied Mathematics
Global minimization by reducing the duality gap
Mathematical Programming: Series A and B
Journal of Combinatorial Theory Series A
A Convex Envelope Formula for Multilinear Functions
Journal of Global Optimization
Convexification and Global Optimization in Continuous And
Convexification and Global Optimization in Continuous And
MINLPLib--A Collection of Test Models for Mixed-Integer Nonlinear Programming
INFORMS Journal on Computing
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
Pooling Problem: Alternate Formulations and Solution Methods
Management Science
IBM Journal of Research and Development
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 polyhedral branch-and-cut approach to global optimization
Mathematical Programming: Series A and B
Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming (International Series of Numerical Mathematics)
Decomposition Methods for Solving Nonconvex Quadratic Programs via Branch and Bound*
Journal of Global Optimization
Mathematical Programming: Series A and B
Studies of the behavior of recursion for the pooling problem
ACM SIGMAP Bulletin
An Exact Reformulation Algorithm for Large Nonconvex NLPs Involving Bilinear Terms
Journal of Global Optimization
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
The small octagon with longest perimeter
Journal of Combinatorial Theory Series A
A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations
Mathematical Programming: Series A and B
A scaling algorithm for polynomial constraint satisfaction problems
Journal of Global Optimization
Cutting circles and polygons from area-minimizing rectangles
Journal of Global Optimization
Column enumeration based decomposition techniques for a class of non-convex MINLP problems
Journal of Global Optimization
Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
Branching and bounds tighteningtechniques for non-convex MINLP
Optimization Methods & Software - GLOBAL OPTIMIZATION
The global solver in the LINDO API
Optimization Methods & Software - GLOBAL OPTIMIZATION
Optimization Methods & Software - GLOBAL OPTIMIZATION
A review of recent advances in global optimization
Journal of Global Optimization
A new Lagrangean approach to the pooling problem
Journal of Global Optimization
On Nonconvex Quadratic Programming with Box Constraints
SIAM Journal on Optimization
Constraint integer programming: a new approach to integrate CP and MIP
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Constraint propagation on quadratic constraints
Constraints
Computable representations for convex hulls of low-dimensional quadratic forms
Mathematical Programming: Series A and B - Series B - Special Issue: Combinatorial Optimization and Integer Programming
Mathematical Programming: Series A and B - Series B - Special Issue: Combinatorial Optimization and Integer Programming
Rigorous Enclosures of Ellipsoids and Directed Cholesky Factorizations
SIAM Journal on Matrix Analysis and Applications
Mathematical Programming: Series A and B - Special Issue on Cone Programming and its Applications
Mathematical Programming: Series A and B
Reduced RLT representations for nonconvex polynomial programming problems
Journal of Global Optimization
An algorithmic framework for convex mixed integer nonlinear programs
Discrete Optimization
Operations Research Letters
Discrete Applied Mathematics
Global optimization of bilinear programs with a multiparametric disaggregation technique
Journal of Global Optimization
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This paper introduces the global mixed-integer quadratic optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs to $${\varepsilon}$$-global optimality. The algorithmic components are presented for: reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, partitioning the search space, bounding the variables, and finding good feasible solutions. To demonstrate the capacity of GloMIQO, we extensively tested its performance on a test suite of 399 problems of diverse size and structure. The test cases are taken from process networks applications, computational geometry problems, GLOBALLib, MINLPLib, and the Bonmin test set. We compare the performance of GloMIQO with respect to four state-of-the-art global optimization solvers: BARON 10.1.2, Couenne 0.4, LindoGLOBAL 6.1.1.588, and SCIP 2.1.0.