An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
Solving mixed integer programming problems using automatic reformulation
Operations Research
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
An improved branch and bound algorithm for mixed integer nonlinear programs
Computers and Operations Research
Solving mixed integer nonlinear programs by outer approximation
Mathematical Programming: Series A and B
Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming
Computational Optimization and Applications
Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition
INFORMS Journal on Computing
On the optimality of nonlinear fractional disjunctive programming problems
Computers & Mathematics with Applications
Globally optimal solutions of max---min systems
Journal of Global Optimization
A review of recent advances in global optimization
Journal of Global Optimization
The Chvátal-Gomory Closure of a Strictly Convex Body
Mathematics of Operations Research
The chvátal-gomory closure of an ellipsoid is a polyhedron
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Mathematical and Computer Modelling: An International Journal
An algorithmic framework for convex mixed integer nonlinear programs
Discrete Optimization
Mixed-integer nonlinear programs featuring "on/off" constraints
Computational Optimization and Applications
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Generalized Disjunctive Programming (GDP) has been introduced recently as an alternative to mixed-integer programming for representing discrete/continuous optimization problems. The basic idea of GDP consists of representing these problems in terms of sets of disjunctions in the continuous space, and logic propositions in terms of Boolean variables. In this paper we consider GDP problems involving convex nonlinear inequalities in the disjunctions. Based on the work by Stubbs and Mehrotra [21] and Ceria and Soares [6], we propose a convex nonlinear relaxation of the nonlinear convex GDP problem that relies on the convex hull of each of the disjunctions that is obtained by variable disaggregation and reformulation of the inequalities. The proposed nonlinear relaxation is used to formulate the GDP problem as a Mixed-Integer Nonlinear Programming (MINLP) problem that is shown to be tighter than the conventional “big-M” formulation. A disjunctive branch and bound method is also presented, and numerical results are given for a set of test problems.