Global optimization of the complex systems complex systems

A. I. Kosolap

Abstract


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.


Keywords


complex systems; nonlinear optimization; multiextremal problems; the exact quadratic regularization; modified a duality theory.

References


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)

Floudas C. A. Deterministic global optimization: theory, algorithms and applications. Kluwer Academic Publishers, 2000. 57 p.

Floudas С. A.and Gounaris C.E. A review of recent advances in global optimization. J. Glob. Optim., 2009, v. 45, no. 1. pp. 3–38.

Horst R. and Tuy H. Global Optimization: Deterministic Approaches. 3rd ed.,Berlin, Springer–Verlag, 1996. 727 p.

Kenneth V.P., Storn R.M. and Lampinen J.A. Differential Evolution. A Practical Approach to Global Optimization.Berlin Heidelberg, Springer-Verlag, 2005, 542 p.

Liberti L. Introduction to Global Optimization. DEI, Politecnico di Milano, Pizza L. da Vinci 32, 20133Milano,Italy, 2006. 42 p.

Nocedal J. and Wright S. J. Numerical optimization. Springer, 2006. 685 p.


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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