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A feasible point adaptation of the Blankenship and Falk algorithm for semi-infinite programming

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Abstract

Discretization methods for semi-infinite programming do not provide a feasible point in a finite number of iterations. We propose a method that computes a feasible point with an objective value better than or equal to a target value f 0 or proves that such a point does not exist. Then a binary search on the space of objective values can be performed to obtain a feasible, \({\epsilon}\)-optimal solution. The algorithm is based on the algorithm proposed in (Blankenship JW, Falk JE in J Optim Theory Appl 19(2):261–281, 1976). Under mild assumptions it terminates in a finite number of iterations.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, RMIT University, Melbourne, Australia

    Angelos Tsoukalas

  2. Department of Computing, Imperial College, London, UK

    Berç Rustem

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  1. Angelos Tsoukalas
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  2. Berç Rustem
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Correspondence to Angelos Tsoukalas.

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Tsoukalas, A., Rustem, B. A feasible point adaptation of the Blankenship and Falk algorithm for semi-infinite programming. Optim Lett 5, 705–716 (2011). https://doi.org/10.1007/s11590-010-0236-4

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  • DOI: https://doi.org/10.1007/s11590-010-0236-4

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