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A PENALTY METHOD FOR SOLVING BILEVEL LINEAR FRACTIONAL/LINEAR PROGRAMMING PROBLEMS

HERMINIA I. CALVETE

Dpto. de Métodos Estadísticos, Universidad de Zaragoza, Pedro Cerbuna, 12, 50009 Zaragoza, Spain

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and

CARMEN GALÉ

Dpto. de Métodos Estadísticos, Universidad de Zaragoza, Pedro Cerbuna, 12, 50009 Zaragoza, Spain

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https://doi.org/10.1142/S0217595904000205Cited by:7 (Source: Crossref)

Abstract

Bilevel programming involves two optimization problems where the constraint region of the first-level problem is implicitly determined by another optimization problem. This model has been applied to decentralized planning problems involving a decision process with a hierarchical structure. In this paper, we consider the bilevel linear fractional/linear programming problem, in which the objective function of the first-level is linear fractional, the objective function of the second level is linear, and the common constraint region is a polyhedron. For this problem, taking into account the relationship between the optimization problem of the second level and its dual, a global optimization approach is proposed that uses an exact penalty function based on the duality gap of the second-level problem.

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