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Vietnam Journal of Mathematics 35:4(2007) 523-539

 On Branch-and-Bound Algorithms for Global Optimal Solutions to Mathematical Programs with Affine Equilibrium Constraints

Le Dung Muu and Nguyen Van Quy

Abstract.  Mathematical programming problems with affine equilibrium constraints, shortly AMPEC, have many applications in different fields of engineering and economics. AMPEC contains several classes of optimization problems such as bilevel convex quadratic programming, optimization over the efficient set as special cases. AMPEC is known to be very difficult to solve globally due to its nested structure. We propose a relaxation algorithm for globally solving AMPEC by using a branch-and-bound strategy. The proposed algorithm uses a binary tree enumeration search for bounding and branching. We also discuss bounding operations by linear programming relaxation and the convex envelope. Numerical experiences and results for the proposed algorithm are discussed and reported.

 

1991 Mathematics Subject Classification: 90C29.

Keywords: Optimization with equilibrium constraints, brach-and-bound, relaxation, bilevel convex quadratic program, optimization over the efficient set, enumeration binary tree.

 

 

 

 

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