Global optimization of the complex systems complex systems
Abstract. Purpose. We consider the optimization models of complex systems. Such problems arise in the design, construction and management of complex systems. In most cases, such problems are multiextremal. These classes include optimization problems with continuous, integer, Boolean variables, the problem on permutations, the problem with smooth and nonsmooth functions. We develop effective methods for the solution of such classes of problems. Methodology. We transform classes of problems to a single canonical form that allows to use the offered modification of a duality for a canonical problem. Findings. Transformation use of the exact quadratic regularization, which allows us to find global solutions to the problems of nonlinear optimization. The canon ical form is the task of maximizing the norm of a vector on a convex set. This set we is approximate by intersection of balls. The problem of the maximum norm of the vector at the intersection of the balls effectively solved the dual method. Originality. We have developed new methodology for the solution of difficult optimizing problems which arise at modelling of difficult systems. We modify the theory of a duality for the solution of multiextreme problems. Practical value. The considered technique for solving complex problems of nonlinear optimization is implemented in software. Comparative experiments confirm the effectiveness of this method for solving problems of nonlinear optimization classes.
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Kosolap A. I. Metody globalnoy optimizatsii [Methods of global optimization]. Dnepropetrovsk, Nauka i obrasovanie, 2013, 316 p. (in Russian)
Kosolap A. I. Globalnaya optimizatsiya. Metod tochnoy kvadratichnoy regulyarizatsii [Global optimization. A method of exact quadratic regularization].Dnepropetrovsk, PGASA, 2015, 164 p. (in Russian)
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GOST Style Citations
1. Косолап А. И. Методы глобальной оптимизации / А. И. Косолап. – Днепропетровск: Наука и образование, 2013. –316 с.
2. Косолап А. И. Глобальная оптимизация. Метод точной квадратичной регуляризации / А. И. Косолап –Днепропетровск: ПГАСА, 2015 – 164 с.
3. Floudas C. A. Deterministic global optimization: theory, algorithms and applications/ C. A. Floudas. – Kluwer AcademicPublishers, 2000. – 57 p.
4. Floudas С. A. A review of recent advances in global optimization / C.A. Floudas, C.E. Gounaris // J. Glob. Optim. – 2009. –v. 45, no. 1. – P. 3–38.
5. Horst R. Global Optimization: Deterministic Approaches /R. Horst, H. Tuy. – 3rd ed.,Berlin: Springer–Verlag, 1996. – 727 p.
6. Kenneth V. P. Differential Evolution. A Practical Approach to Global Optimization / V.P. Kenneth, R.M. Storn, J.A. Lampinen. –BerlinHeidelberg: Springer-Verlag, 2005. – 542 p.
7. Liberti L. Introduction to Global Optimization/L. Liberti. –DEI, Politecnico di Milano, Pizza L. da Vinci 32, 20133Milano,Italy, 2006. – 42 p.
8. Nocedal J. Numerical optimization / J. Nocedal, S. J. Wright. – Springer, 2006. – 685 p.
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