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A Newton’s method for the continuous quadratic knapsack problem

Roberto Cominetti (rccc***at***dii.uchile.cl)
Walter F. Mascarenhas (walter.mascarenhas***at***gmail.com)
Paulo J. S. Silva (pjssilva***at***ime.usp.br)

Abstract: We introduce a new efficient method to solve the continuous quadratic knapsack problem. This is a highly structured quadratic program that appears in different contexts. The method converges after O(n) iterations with overall arithmetic complexity O(n²). Numerical experiments show that in practice the method converges in a small number of iterations with overall linear complexity, and is faster than the state-of-the-art algorithms based on median finding, variable fixing, and secant techniques.

Keywords: continuous quadratic knapsack, simplex projections, semismooth Newton, duality

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Quadratic Programming )


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Entry Submitted: 08/15/2012
Entry Accepted: 08/15/2012
Entry Last Modified: 10/14/2013

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