A mixed-integer branching approach for very small formulations of disjunctive constraints

We study the existence and construction of very small formulations for disjunctive constraints in optimization problems: that is, formulations that use very few integer variables and extra constraints. To accomplish this, we present a novel mixed-integer branching formulation framework, which preserves many of the favorable algorithmic properties of a traditional mixed-integer programming formulation, including amenability … Read more

Interdiction Branching

This paper introduces interdiction branching, a new branching method for binary integer programs that is designed to overcome the difficulties encountered in solving problems for which branching on variables is inherently weak. Unlike traditional methods, selection of the disjunction in interdiction branching takes into account the best feasible solution found so far. In particular, the … Read more

Exploiting Second-Order Cone Structure for Global Optimization

Identifying and exploiting classes of nonconvex constraints whose feasible region is convex after branching can reduce the time to compute global solutions for nonlinear optimization problems. We develop techniques for identifying quadratic and nonlinear constraints whose feasible region can be represented as the union of a finite number of second-order cones, and we provide necessary … Read more