Browsing by Author "Kosolap, Anatolii"

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Finding the global minimum of the general quadratic problems during deterministic global optimization in Cyber-Physical Systems
(Lviv Politechnic Publishing House, 2019-02-26) Kosolap, Anatolii; University of Chemical Engineering, Dnipro
Cyber-Physical Systems (CPS) are integrations of computation and physical processes. We consider effective computations for designing difficult systems. In this paper, we propose new method of exact quadratic regularization for deterministic global optimization (EQR). This method can be used for the solution of a wide class of multiextreme problems, in particular, general quadratic problems. These problems will be transformed to maximization of norm a vector on convex set. The convex set is approximated by a polyhedron or intersection of balls. We offer the modified dual problem for maximization of norm a vector on intersection of balls. It allows to receive the solution of a primal problem. We use only local search (primal-dual interior point method) and a dichotomy method for search of a global extremum in the general quadratic problems.
The upper and lower bounds for solutions of general quadratic optimization problems
(Видавництво Львівської політехніки, 2013) Kosolap, Anatolii; Peretiatko, Anastasiia
We consider the general problem of quadratic minimization with quadratic constraints. We are searching for the upper and lower bounds for the values of the minimized function. Semidefinite optimization is used for finding the lower bound. This lower bound is used to obtain an upper bound by interior point method. Numerical experiments often show that obtained upper bound is the exact solution of the original problem.