An Exact Algorithm for the Continuous Quadratic Knapsack Problem via Infimal Convolution
In this chapter we present an algorithm of quasi-linear complexity, based on the calculation of the infimal convolution of convex quadratic functions, that leads to the determination of the analytical optimal solution of the Continuous Quadratic Knapsack problem. The algorithm both exactly and simultaneously solves a separable uniparametric family of quadratic programming problems resulting from varying the equality constraint. We prove that the analytical solution of the problem is piecewise quadratic, continuous and, under certain conditions, belongs to the class C 1. Moreover we analyze the complexity of the algorithm presented and prove that the complexity is quasi-linear in order. We demonstrate that our algorithm is able to deal with large-scale quadratic programming problems of this type. We present a very important application: the classical Problem of Economic Dispatch. Finally, we release the source code for our algorithm in the computer language Mathematica.
KeywordsQuadratic Program Exact Algorithm Quadratic Program Problem Active Constraint Thermal Plant
Unable to display preview. Download preview PDF.
- 5.Bayón, L., Grau, J.M., Ruiz, M.M., Suárez, P.M.: A quasi-linear algorithm for calculating the infimal convolution of convex quadratic functions. In: Vigo-Aguiar, J. (ed.) Proceedings of the 2010 International Conference on Computational and Mathematical Methods in Science and Engineering, vol. I, pp. 169–172 (2010)Google Scholar
- 10.Gould, N.I.M., Toint, P.L.: A Quadratic Programming Bibliography (2001), http://www.optimization-online.org/DB_HTML/2001/02/285.html
- 11.Gould, N.I.M., Toint, P.L.: A Quadratic Programming Page, http://www.numerical.rl.ac.uk/qp/qp.html
- 14.Mittelmann, H.D.: Decision Tree for Optimization Software, http://plato.asu.edu/guide.html
- 16.Stromberg, T.: The operation of infimal convolution. Diss. Math. 352 (1996)Google Scholar