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Vietnam Journal of Mathematics 35:4(2007)
523-539
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On Branch-and-Bound Algorithms for Global Optimal
Solutions to Mathematical Programs with Affine Equilibrium Constraints
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Le Dung Muu and
Nguyen Van Quy
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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.
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1991 Mathematics Subject Classification: 90C29.
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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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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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