Linear Complementarity as a General Solution Method to Combinatorial Problems

Authors:
Laura Di Giacomo;Giacomo Patrizi;Emanuele Argento
Affiliations:
Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università “La Sapienza,” 00185 Rome, Italy;Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università “La Sapienza,” 00185 Rome, Italy;Dipartimento di Informatica Università “La Sapienza,” 00185 Rome, Italy
Venue:
INFORMS Journal on Computing
Year:
2007

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Abstract

This paper shows how many types of combinatorial problems can be embedded in continuous space and solved as nonconvex optimization problems. If the objective function and the constraints are linear, problems of this kind can be formulated as linear complementarity problems. An algorithm is presented to solve this type of problem and indicate its convergence properties. Computational comparisons are carried out using general solution codes.