An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
Lagrangean decomposition: A model yielding stronger lagrangean bounds
Mathematical Programming: Series A and B
Solving mixed integer nonlinear programs by outer approximation
Mathematical Programming: Series A and B
A branch and bound method for stochastic global optimization
Mathematical Programming: Series A and B
Journal of Global Optimization
A Lagrangian Based Branch-and-Bound Algorithm for Production-transportation Problems
Journal of Global Optimization
Convexification and Global Optimization in Continuous And
Convexification and Global Optimization in Continuous And
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
Outer approximation algorithms for separable nonconvex mixed-integer nonlinear programs
Mathematical Programming: Series A and B
A Global Optimization Method, QBB, for Twice-Differentiable Nonconvex Optimization Problem
Journal of Global Optimization
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
Dual decomposition in stochastic integer programming
Operations Research Letters
A review of recent advances in global optimization
Journal of Global Optimization
A dynamic convexized method for nonconvex mixed integer nonlinear programming
Computers and Operations Research
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In this work we present a global optimization algorithm for solving a class of large-scale nonconvex optimization models that have a decomposable structure. Such models, which are very expensive to solve to global optimality, are frequently encountered in two-stage stochastic programming problems, engineering design, and also in planning and scheduling. A generic formulation and reformulation of the decomposable models is given. We propose a specialized deterministic branch-and-cut algorithm to solve these models to global optimality, wherein bounds on the global optimum are obtained by solving convex relaxations of these models with certain cuts added to them in order to tighten the relaxations. These cuts are based on the solutions of the sub-problems obtained by applying Lagrangean decomposition to the original nonconvex model. Numerical examples are presented to illustrate the effectiveness of the proposed method compared to available commercial global optimization solvers that are based on branch and bound methods.