A sequential linear programming approach to solve mixed integer programming problems
Abstract
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In this work, we propose a global optimization approach for mixed-integer programming problems. To this aim, we preliminarily define an exact penalty algorithm model for globally solving general problems and we show its convergence properties. Then, we describe a particular versi
We introduce a new Integer Linear Programming (ILP) approach for solving Integer Programming (IP) problems with bilinear objectives and linear constraints. The approach relies on a series of ILP approximations of the bilinear IP. We compare this approach with standard linearizati
In this paper, we examine a mixed integer linear programming (MILP) reformulation for mixed integer bilinear problems where each bilinear term involves the product of a nonnegative integer variable and a nonnegative continuous variable. This reformulation is obtained by first rep
One method to obtain high-quality bid prices for network revenue management problems involves using the approximate linear programming approach on the dynamic programming formulation of the problem. This approach ends up with a linear program whose number of constraints increases
We present a polynomial-sized linear program (LP) for the n-city TSP drawing upon “complex flow” modeling ideas by the first two authors who used an O(n)×O(n) model*. Here we have only O(n) variables and O(n) constraints. We do not model explicit cycles of the cities, and our mod
We propose a unified framework to address family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, principal anal