An exact penalty on bilevel programs with linear vector optimization lower level

We are interested in a class of linear bilevel programs where the upper level is a linear scalar optimization problem and the lower level is a linear multi-objective optimization problem. We approach this problem via an exact penalty method. Then, we propose an algorithm illustrated by numerical examples.

[1]  H. P. Benson,et al.  Optimization over the efficient set , 1984 .

[2]  H. P. Benson,et al.  Optimization over the efficient set: Four special cases , 1994 .

[3]  J. Morgan,et al.  Semivectorial Bilevel Optimization Problem: Penalty Approach , 2006 .

[4]  Paul H. Calamai,et al.  Bilevel and multilevel programming: A bibliography review , 1994, J. Glob. Optim..

[5]  Hiroshi Konno,et al.  A cutting plane algorithm for solving bilinear programs , 1976, Math. Program..

[6]  Philip B. Zwart.  Global Maximization of a Convex Function with Linear Inequality Constraints , 1974, Oper. Res..

[7]  T. Gal.  A general method for determining the set of all efficient solutions to a linear vectormaximum problem , 1977 .

[8]  S. Bolintinéanu,et al.  Pénalisation dans l'optimisation sur l'ensemble faiblement efficient , 1997 .

[9]  C. Tammer,et al.  Theory of Vector Optimization , 2003 .

[10]  Simone Dantas,et al.  A Note on a Penalty Function Approach for Solving Bilevel Linear Programs , 2000, J. Glob. Optim..

[11]  Giorgio Gallo,et al.  Bilinear programming: An exact algorithm , 1977, Math. Program..

[12]  S. Dempe.  Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints , 2003 .

[13]  K. Tamura,et al.  ON LINEAR VECTOR MAXIMIZATION PROBLEMS , 1977 .

[14]  A. Aboussoror,et al.  Weak linear bilevel programming problems : Existence of solutions via a penalty method , 2005 .

[15]  Harold P. Benson,et al.  Efficiency and proper efficiency in vector maximization with respect to cones , 1983 .

[16]  Heinz Isermann,et al.  The Enumeration of the Set of All Efficient Solutions for a Linear Multiple Objective Program , 1977 .

[17]  James E. Falk,et al.  A Successive Underestimation Method for Concave Minimization Problems , 1976, Math. Oper. Res..

[18]  S. Bolintineanu,et al.  Optimality Conditions for Minimization over the (Weakly or Properly) Efficient Set , 1993 .