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L. N. Vicente, “Bilevel Programming: Introduction, History, and Overview,” In: Encyclopedia of Optimization, Kluwer Academic Publishers, Dordrecht, 2001, pp. 24-31. doi:10.1007/0-306-48332-7_38

has been cited by the following article:

• TITLE: An Inexact Restoration Package for Bilevel Programming Problems

  AUTHORS: Elvio A. Pilotta, Germán A. Torres

  KEYWORDS: Bilevel Programming Problems; INEXACT Restoration Methods; Algorithms

  JOURNAL NAME: Applied Mathematics, Vol.3 No.10A, November 1, 2012

  ABSTRACT: Bilevel programming problems are a class of optimization problems with hierarchical structure where one of the con-straints is also an optimization problem. Inexact restoration methods were introduced for solving nonlinear programming problems a few years ago. They generate a sequence of, generally, infeasible iterates with intermediate iterations that consist of inexactly restored points. In this paper we present a software environment for solving bilevel program-ming problems using an inexact restoration technique without replacing the lower level problem by its KKT optimality conditions. With this strategy we maintain the minimization structure of the lower level problem and avoid spurious solutions. The environment is a user-friendly set of Fortran 90 modules which is easily and highly configurable. It is prepared to use two well-tested minimization solvers and different formulations in one of the minimization subproblems. We validate our implementation using a set of test problems from the literature, comparing different formulations and the use of the minimization solvers.