An upper bound on the number of local maxima in the problem of maximizing the norm of the vector on the convex set
Keywords:
multiextremal problems; the exact quadratic regularization
Abstract
In this paper we consider of nonlinear optimization multiextremal the problem. These problems are converted by the exact quadratic regularization to one-extremal or to the maximum norm of the vector on a convex set. Under this transformation, the number of local extreme is greatly reduced, there by simplifying the solution of the original problem. We have found an upper bound on the number of different local extreme transformed of multiextremal problem.
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References
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Horst R., Tuy H. Global Optimization: Deterministic Approaches, 3rd ed. Springer-Verlag, Berlin, 1996. – 726 p.
Floudas С. A., Gounaris C. E. A review of recent advances in global optimization // J. Glob. Optim. – 2009. – v. 45, no. 1. – P. 3–38.
Kenneth V. P., Storn R. M., Lampinen J. A. Differential Evolution. A Practical Approach to Global Optimization.– Berlin Heidelberg: Springer-Verlag, 2005.– 542 p.
Cagnina L. C., Esquivel S. C., Coello C. A. C. Solving constrained optimization problems with a hybrid particle swarm optimization algorithm // Engineering Optimization, v. 43, No. 8, 2011. P. 843–866.
Nocedal, J., Wright S. J. Numerical optimization. – Springer, 2006. – 685 p.
Published
2015-05-29
How to Cite
Косолап, А. И., & Черноусова, Ю. (2015). An upper bound on the number of local maxima in the problem of maximizing the norm of the vector on the convex set. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 26(1156), 107-114. Retrieved from https://periodicals.karazin.ua/mia/article/view/14219
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