Improvement of the estimations of solutions in the semidefinite programmin


  • A. I. Kosolap Department of specialized computer systems, State Higher Education Establishment “Ukrainian State University of Chemical Technology”, 40, Naberezhna Peremogy str., Dnipropetrovsk 49005, Ukraine



complex systems, semidefinite relaxation, quadratic problems, primer-dual interior point method, modification of semidefinite programming problems.


Purpose. We develop new methods for solving optimization models of complex systems. Such models arise in technology, artificial intelligence, design, construction and management of complex systems. Solving such optimization problems is a complex computational problem. This problem is to develop effective methods for solving such classes. Methodology. In this paper, we propose to transform the classes of problems to problems of semidefinite programming and to use their solutions for primer-dual interior point methods. We propose an iterative procedure for modifying the corresponding problem of semidefinite programming, which makes it possible to find exact solutions of the original problem. Findings. To solve the problems of quadratic optimization, semi-definite relaxation and a direct-dual method of the interior point are used. An iterative procedure for modifying semidefinite programming problems is constructed, which makes it possible to obtain an exact solution of the original problem. The obtained results are confirmed by numerical experiments. Originality. A new methodology for solving complex optimization problems that arise in modeling complex systems using semidefinite relaxation is developed. A sequential modification of the problems of semidefinite optimization is proposed. Practical value. We considered technique for solving complex quadratic optimization problems is realized in the form of software. Comparative experiments confirm the effectiveness of this technique in solving classes of problems of quadratic optimization.

Author Biography

A. I. Kosolap, Department of specialized computer systems, State Higher Education Establishment “Ukrainian State University of Chemical Technology”, 40, Naberezhna Peremogy str., Dnipropetrovsk 49005

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


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Computer systems and information technologies in education, science and management