Nonlinear programming: theory, algorithms, and applications
Nonlinear programming: theory, algorithms, and applications
Global minimization by reducing the duality gap
Mathematical Programming: Series A and B
A Finite Algorithm for Global Minimization ofSeparable Concave Programs
Journal of Global Optimization
Semidefinite Relaxations of Fractional Programs via Novel Convexification Techniques
Journal of Global Optimization
Improving Discrete Model Representations via Symmetry Considerations
Management Science
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
A finite branch-and-bound algorithm for two-stage stochastic integer programs
Mathematical Programming: Series A and B
Optimization Methods & Software - GLOBAL OPTIMIZATION
Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
Valid inequalities for the pooling problem with binary variables
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
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In the tradition of modeling languages for optimization, a single model is passed to a solver for solution. In this paper, we extend BARON's modeling language in order to facilitate the communication of problem-specific relaxation information from the modeler to the branch-and-bound solver. This effectively results into two models being passed from the modeling language to the solver. Three important application areas are identified and computational experiments are presented. In all cases, nonlinear constraints are provided only to the relaxation constructor in order to strengthen the lower bounding step of the algorithm without complicating the local search process. In the first application area, nonlinear constraints from the reformulation---linearization technique (RLT) are added to strengthen a problem formulation. This approach is illustrated for the pooling problem and computational results show that it results in a scheme that makes global optimization nearly as fast as local optimization for pooling problems from the literature. In the second application area, we communicate with the relaxation constructor the first-order optimality conditions for unconstrained global optimization problems. Computational experiments with polynomial programs demonstrate that this approach leads to a significant reduction of the size of the branch-and-bound search tree. In the third application, problem-specific nonlinear optimality conditions for the satisfiability problem are used to strengthen the lower bounding step and are found to significantly expedite the branch-and-bound algorithm when applied to a nonlinear formulation of this problem.