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LP formulations for mixed-integer polynomial optimization problems

Daniel Bienstock (dano***at***columbia.edu)
Gonzalo Munoz (gonzalo***at***ieor.columbia.edu)

Abstract: We present polynomial-time algorithms for constrained optimization problems overwhere the intersection graph of the constraint set has bounded tree-width. In the case of binary variables we obtain exact, polynomial-size linear programming formulations for the problem. In the mixed-integer case with bounded variables we obtain polynomial-size linear programming representations that attain guaranteed optimality and feasibility bounds. As a consequence, we obtain approximation algorithms based on linear programming, with guaranteed bounds, for the AC-OPF problem on graphs with bounded tree-width.

Keywords: mixed-integer nonlinear programming

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Columbia University, 2014

Download: [PDF]

Entry Submitted: 01/19/2015
Entry Accepted: 01/19/2015
Entry Last Modified: 03/20/2015

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