We study the polyhedral convex hull of a mixed-integer set S defined by a collection of multilinear equations of the form yI = ∏ i∈I xi over the 0−1-cube. Such sets appear frequently in the factorable reformulation of mixed-integer nonlinear optimization problems. In particular, the set S represents the feasible region of a linearized unconstrained zeroone polynomial optimization problem. We de...

Spectrum sharing with quality of service (QoS) requirement and power constraint on cognitive users is studied. The objective is to maximize the system throughput. This problem is modeled as a mixed integer nonlinear programming problem and then transformed to a continuous nonlinear programming problem through eliminating integer variables. We propose the joint power control and spectrum allocat...

The Perspective Relaxation (PR) is a general approach for constructing tight approximations to Mixed-Integer NonLinear Problems with semicontinuous variables. The PR of a MINLP can be formulated either as a Mixed-Integer Second-Order Cone Program, provided that the original objective function is SOCP-representable, or as a Semi-Infinite MINLP. We show that under some further assumptions—rather ...

We study the polyhedral convex hull of a mixed-integer set S defined by a collection of multilinear equations of the form yI = ∏ i∈I xi over the 0−1-cube. Such sets appear frequently in the factorable reformulation of mixed-integer nonlinear optimization problems. In particular, the set S represents the feasible region of a linearized unconstrained binary polynomial optimization problem. We def...

Optimization is being increasing applied to engineering design problems throughout the world. iSIGHT is a generic engineering design environment that provides engineers with an optimization toolkit of leading optimization algorithms and an optimization advisor to solve their optimization needs. This paper focuses on the key role played by the toolkit’s genetic algorithm in providing a robust, g...

We study the generalization of split and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference of two convex sets with specific geometric structures. We introduce two techniques to give precise characterizations of such convex hulls and use them to construct split...

We present a Branch and Cut algorithm of the software package LaGO to solve nonconvex mixed-integer nonlinear programs (MINLPs). A linear outer approximation is constructed from a convex relaxation of the problem. Since we do not require an algebraic representation of the problem, reformulation techniques for the construction of the convex relaxation cannot be applied, and we are restricted to ...