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On Approximation Algorithms for Concave Mixed-Integer Quadratic Programming

Alberto Del Pia (delpia***at***wisc.edu)

Abstract: Concave Mixed-Integer Quadratic Programming is the problem of minimizing a concave quadratic polynomial over the mixed-integer points in a polyhedral region. In this work we describe an algorithm that finds an ε-approximate solution to a Concave Mixed-Integer Quadratic Programming problem. The running time of the proposed algorithm is polynomial in the size of the problem and in 1/ε, provided that the number of integer variables and the number of negative eigenvalues of the objective function are fixed. The running time of the proposed algorithm is expected unless P = NP.

Keywords: mixed-integer quadratic programming; approximation algorithms

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

Category 2: Global Optimization (Theory )

Citation: Submitted manuscript

Download: [PDF]

Entry Submitted: 05/28/2016
Entry Accepted: 05/29/2016
Entry Last Modified: 07/20/2017

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