Solving quadratic convex bilevel programming problems using a smoothing method

In this paper, we present a smoothing sequential quadratic programming to compute a solution of a quadratic convex bilevel programming problem. We use the Karush–Kuhn–Tucker optimality conditions of the lower level problem to obtain a nonsmooth optimization problem known to be a mathematical program...

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Veröffentlicht in:Applied mathematics and computation Jg. 217; H. 15; S. 6680 - 6690
1. Verfasser: Etoa Etoa, Jean Bosco
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier Inc 01.04.2011
Elsevier
Schlagworte:
Approximation
Calculus of variations and optimal control
Complementary constraints
Computation
Convex bilevel problem
Difference and functional equations, recurrence relations
Exact sciences and technology
Finite differences and functional equations
Inducible solution
Mathematical analysis
Mathematical models
Mathematics
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Optimization
Programming
Quadratic programming
Sciences and techniques of general use
Semismooth equations
Sequential quadratic programming algorithm
Smoothing
Smoothing method
Sequential quadratic programming algorithm
Convex bilevel problem
Smoothing method
Semismooth equations
Inducible solution
Complementary constraints
Transcendental equation
Smoothing methods
Recurrence relation
Functional equation
Optimization method
Difference equation
Quadratic programming
Algorithm
Convex programming
Equation system
Non linear equation
Numerical analysis
Smoothing
Applied mathematics
Sequential method
Algebraic equation
Optimality condition
ISSN:0096-3003, 1873-5649
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Zusammenfassung:In this paper, we present a smoothing sequential quadratic programming to compute a solution of a quadratic convex bilevel programming problem. We use the Karush–Kuhn–Tucker optimality conditions of the lower level problem to obtain a nonsmooth optimization problem known to be a mathematical program with equilibrium constraints; the complementary conditions of the lower level problem are then appended to the upper level objective function with a classical penalty. These complementarity conditions are not relaxed from the constraints and they are reformulated as a system of smooth equations by mean of semismooth equations using Fisher–Burmeister functional. Then, using a quadratic sequential programming method, we solve a series of smooth, regular problems that progressively approximate the nonsmooth problem. Some preliminary computational results are reported, showing that our approach is efficient.
Bibliographie:ObjectType-Article-2
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.01.066