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Zbl 1046.90093
Stein, Oliver; Still, Georg
Solving semi-infinite optimization problems with interior point techniques. (English)
[J] SIAM J. Control Optimization 42, No. 3, 769-788 (2003). ISSN 0363-0129; ISSN 1095-7138/e

Summary: We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads to central path conditions for the lower level problems, where for a given path parameter a smooth nonlinear finite optimization problem has to be solved. The solution of the semi-infinite optimization problem then amounts to driving the path parameter to zero.\par We show convergence properties of the method and give a number of numerical examples from design centering and from robust optimization, where actually so-called generalized semi-infinite optimization problems are solved. The presented method is easy to implement, and in our examples it works well for dimensions of the semi-infinite index set at least up to 150.

MSC 2000:: *90C34 Semi-infinite programming
90C25 Convex programming
49M37 Methods of nonlinear programming type
65K05 Mathematical programming (numerical methods)

Keywords: generalized semi-infinite optimization; convexity; Stackelberg game; nonlinear complementarity problem function; smoothing; optimality condition

Cited in: Zbl 1202.90256 Zbl 1135.65333

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