Universal software for optimization of complex systems


  • A. I. Kosolap Department of specialized computer systems, State Higher Education Establishment “Ukrainian State University of Chemical Technology”, Ukraine https://orcid.org/0000-0001-7338-6707


complex systems, nonlinear optimization, multiextremal problems, the exact quadratic regularization, software


. Purpose. We consider the class of problems of nonlinear optimization. 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 non-smooth functions. For each class of such problems developed many different methods and software that creates difficulties in solving them.

Methodology. We transform classes of problems to a single canonical form that allows to use only one method and use a single software. 

Findings. Transformation use of the exact quadratic regularization, which allows us to find global solutions to the problems of nonlinear optimization. The canonical form is the task of maximizing the norm of a vector on a convex set. The method Kelly converted to the maximization norm of a vector on a convex polyhedron. At using exact quadratic regularization of a convex polyhedron transform to the intersection of the balls. The problem of the maximum norm of the vector at the intersection of the balls effectively solved the dual method using the same software.

Originality. We have developed new methodology for the solution of difficult optimizing problems which arise at modelling of difficult systems.

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.

Author Biography

A. I. Kosolap, Department of specialized computer systems, State Higher Education Establishment “Ukrainian State University of Chemical Technology”

Dr. Sc. (Phys.-Math.), Prof.


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Computer systems and information technologies in education, science and management