Branching and bounds tighteningtechniques for non-convex MINLP
Optimization Methods & Software - GLOBAL OPTIMIZATION
A review of recent advances in global optimization
Journal of Global Optimization
Verification methods: rigorous results using floating-point arithmetic
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Accurate and reliable computing in floating-point arithmetic
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Selecting Optimal Alternatives and Risk Reduction Strategies in Decision Trees
Operations Research
Combined bound-grid-factor constraints for enhancing RLT relaxations for polynomial programs
Journal of Global Optimization
Integer Programming Subject to Monomial Constraints
SIAM Journal on Optimization
Identification of Transport Coefficient Models in Convection-Diffusion Equations
SIAM Journal on Scientific Computing
Convergence rate of McCormick relaxations
Journal of Global Optimization
Brief paper: Oops! I cannot do it again: Testing for recursive feasibility in MPC
Automatica (Journal of IFAC)
Reduced RLT representations for nonconvex polynomial programming problems
Journal of Global Optimization
Packing congruent hyperspheres into a hypersphere
Journal of Global Optimization
ICN-RE: redundancy elimination for information-centric networking
Proceedings of the second edition of the ICN workshop on Information-centric networking
An efficient compact quadratic convex reformulation for general integer quadratic programs
Computational Optimization and Applications
Optimization and homotopy methods for the Gibbs free energy of simple magmatic mixtures
Computational Optimization and Applications
Two-stage stochastic optimization for optimal power flow under renewable generation uncertainty
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on simulation in complex service systems
GloMIQO: Global mixed-integer quadratic optimizer
Journal of Global Optimization
Journal of Global Optimization
Journal of Global Optimization
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A variety of nonlinear, including semidefinite, relaxations have been developed in recent years for nonconvex optimization problems. Their potential can be realized only if they can be solved with sufficient speed and reliability. Unfortunately, state-of-the-art nonlinear programming codes are significantly slower and numerically unstable compared to linear programming software.In this paper, we facilitate the reliable use of nonlinear convex relaxations in global optimization via a polyhedral branch-and-cut approach. Our algorithm exploits convexity, either identified automatically or supplied through a suitable modeling language construct, in order to generate polyhedral cutting planes and relaxations for multivariate nonconvex problems. We prove that, if the convexity of a univariate or multivariate function is apparent by decomposing it into convex subexpressions, our relaxation constructor automatically exploits this convexity in a manner that is much superior to developing polyhedral outer approximators for the original function. The convexity of functional expressions that are composed to form nonconvex expressions is also automatically exploited.Root-node relaxations are computed for 87 problems from globallib and minlplib, and detailed computational results are presented for globally solving 26 of these problems with BARON 7.2, which implements the proposed techniques. The use of cutting planes for these problems reduces root-node relaxation gaps by up to 100% and expedites the solution process, often by several orders of magnitude.