Title: On the choice of the penalty parameter for discrete-continuous linear bi-level problems reformulation

Authors: Massimiliano Caramia; Renato Mari

Addresses: Dipartimento di Ingegneria dell'Impresa, Università di Roma 'Tor Vergata', Via del Politecnico, 1 – 00133 Rome, Italy ' Dipartimento di Ingegneria dell'Impresa, Università di Roma 'Tor Vergata', Via del Politecnico, 1 – 00133 Rome, Italy

Abstract: In this paper we focus on linear bi-level problems in which the variables controlled by the leader are discrete. It is known that such problems are equivalent to continuous linear bi-level problems in which the integrality requirements are relaxed and the leader's objective function is modified including a concave penalty function weighted by a parameter µ. The equivalence holds for a sufficiently large value of µ. A valid lower bound for µ is known in the literature. In the following, we provide an improvement of this lower bound and experiment the new lower bound on a set of test problems.

Keywords: linear programming; bi-level programming; concave penalty function; discrete-continuous programming; penalty parameters; problem reformulation.

DOI: 10.1504/IJMOR.2015.065959

International Journal of Mathematics in Operational Research, 2015 Vol.7 No.1, pp.103 - 118

Received: 22 Jun 2013
Accepted: 28 Jul 2013
Published online: 12 Jan 2015 *

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