On Optimal Properties of Special Nonlinear and Semi-infinite Problems Arising in Parametric Optimization

  • Olga Kostyukova Institute of Mathematics, National Academy of Science of Belarus
  • Tatiana Tchemisova University of Aveiro, Portugal
  • Maria Kurdina Institute of Mathematics, National Academy of Science of Belarus
DOI: https://doi.org/10.19139/soic.v5i2.303
Keywords: Parametric Optimization, Semi-Infinite programming, Nonlinear Programming

Abstract

We consider a  special nonlinear Programming problem  depending on integer parameters. For some values of these parameters (the "right'' ones), this problem satisfies certain properties used in study of differential properties of optimal solutions in parametric Semi-Infinite Programming. We deduce the conditions guaranteing the existence of the "right'' parameters values, and propose an algorithm for their determination. The conditions and the algorithm are essentially based on properties of a related linear-quadratic semi-infinite problem.

Author Biographies

Olga Kostyukova, Institute of Mathematics, National Academy of Science of Belarus
Department of mathematical theory of systems
Tatiana Tchemisova, University of Aveiro, Portugal
Department of Mathematics
Maria Kurdina, Institute of Mathematics, National Academy of Science of Belarus
Department of mathematical theory of systems

References

Ben-Tal A., Teboulle M. Hidden convexity in some nonconvex quadratically constrained quadratic programming. Mathematical Programming, 1996, No. 72, pp. 51-63.

Bonnans J.F., Shapiro A. Perturbation analysis of optimization problems, Springer-Verlag, New-York, 2000.

Eaves B.C. (1971) On Quadratic Programming Management Science, Vol. 17, No. 11, Theory Series, pp. 698-711.

Floudas C.A., Visweswaran V. (1995) Quadratic programming, in Handbook of Global Optimization. Kluwer Academic Publishers, Dordrecht.

Gill P.E., Murray W., Wright M.H. (1981) Practical optimization. Academic Press Inc., London.

Horst, R., Pardalos, P.M. and Thoai, N.V. (2000)Introduction to Global Optimization: non-convex optimization and its applications. Kluwer Academic Publishers, Dordrech.

Kim S., Kojima M. Exact solutions of some nonconvex quadratic optimization problems via SDP and SOCP relaxations. Computational Optimization and Applications, No 26 (2003) pp.143–154.

Kostyukova O.I., Tchemisova T.V., Kurdina M.A. A study of one class of NLP problems arising in parametric Semi-Infinite Programming, Optimization Methods and Software, published online September 2016, DOI: 10.1080/10556788.2016.1233974.

Levin V.L. Application of E. Helly's theorem to convex programming, problems of best approximation and related questions. Math. USSR Sbornik, Vol. 8, No. 2 (1969) pp. 235-247.

Published
2017-06-01
How to Cite
Kostyukova, O., Tchemisova, T., & Kurdina, M. (2017). On Optimal Properties of Special Nonlinear and Semi-infinite Problems Arising in Parametric Optimization. Statistics, Optimization & Information Computing, 5(2), 99-108. https://doi.org/10.19139/soic.v5i2.303
Issue
Vol 5 No 2 (2017)
Section
Research Articles
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