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Global optimization of generalized semi-infinite programs via restriction of the right hand side


  • Alexander Mitsos


  • Angelos Tsoukalas


The algorithm proposed in Mitsos (Optimization 60(10–11):1291–1308, 2011 ) for the global optimization of semi-infinite programs is extended to the global optimization of generalized semi-infinite programs. No convexity or concavity assumptions are made. The algorithm employs convergent lower and upper bounds which are based on regular (in general nonconvex) nonlinear programs (NLP) solved by a (black-box) deterministic global NLP solver. The lower bounding procedure is based on a discretization of the lower-level host set; the set is populated with Slater points of the lower-level program that result in constraint violations of prior upper-level points visited by the lower bounding procedure. The purpose of the lower bounding procedure is only to generate a certificate of optimality; in trivial cases it can also generate a global solution point. The upper bounding procedure generates candidate optimal points; it is based on an approximation of the feasible set using a discrete restriction of the lower-level feasible set and a restriction of the right-hand side constraints (both lower and upper level). Under relatively mild assumptions, the algorithm is shown to converge finitely to a truly feasible point which is approximately optimal as established from the lower bound. Test cases from the literature are solved and the algorithm is shown to be computationally efficient. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Alexander Mitsos & Angelos Tsoukalas, 2015. "Global optimization of generalized semi-infinite programs via restriction of the right hand side," Journal of Global Optimization, Springer, vol. 61(1), pages 1-17, January.
  • Handle: RePEc:spr:jglopt:v:61:y:2015:i:1:p:1-17
    DOI: 10.1007/s10898-014-0146-6

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    References listed on IDEAS

    1. Stein, Oliver & Still, Georg, 2002. "On generalized semi-infinite optimization and bilevel optimization," European Journal of Operational Research, Elsevier, vol. 142(3), pages 444-462, November.
    2. Alexander Mitsos, 2010. "Global solution of nonlinear mixed-integer bilevel programs," Journal of Global Optimization, Springer, vol. 47(4), pages 557-582, August.
    3. Still, G., 1999. "Generalized semi-infinite programming: Theory and methods," European Journal of Operational Research, Elsevier, vol. 119(2), pages 301-313, December.
    4. Harald Günzel & Hubertus Jongen & Oliver Stein, 2007. "On the closure of the feasible set in generalized semi-infinite programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 15(3), pages 271-280, September.
    5. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
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    1. repec:eee:csdana:v:119:y:2018:i:c:p:99-117 is not listed on IDEAS

    More about this item


    SIP; NLP; Slater point; Nonconvex; Global optimization;


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