I. V. Sergienko

Optimal control of distributed systems with conjugation conditions

Preface.- Control of Systems Described by Elliptic-Type Partial-Differential Equations Under Conjugation Conditions.- Control of a Conditionally Correct System Described by the Neumann Problem for an Elliptic-Type Equation Under Conjugation Conditions.- Control of a System Described by a One-Dimensional Quartic Equation Under Conjugation Conditions.- Control of a System Described by a Two-Dimensional Quartic Equation Under Conjugation Conditions.- Control of a System Described by a Parabolic Equation Under Conjugation Conditions.- Control of a System Described by a Parabolic Equation in the Presence of Concentrated Heat Capacity.- Control of a System Described by a Pseudoparabolic Equation Under Conjugation Conditions.- Control of a System Described by a Hyperbolic Equation Under Conjugation Conditions.- Control of a System Described by a Pseudohyperbolic Equation Under Conjugation Conditions.- Optimal Control of a Deformed Complicated Solid Body State.- References.

Limiting Representations of Weighted Pseudoinverse Matrices with Positive Definite Weights. Problem Regularization

Limiting representations for weighted pseudoinverse matrices with positive definite weights are derived. It is shown that regularized problems can be constructed based on such limiting representations intended for evaluation of weighted pseudoinverse matrices and weighted normal pseudosolutions with positive definite weights. The results obtained, concerning regularization of problems on evaluation of weighted normal pseudosolutions, are employed for regularization of least-squares problems with constraints.

Existence of Solutions in Vector Optimization Problems

Conditions for the existence of various effective solutions of vector optimization problems with an unbounded convex closed feasible set of solutions are established. The study is based on the use of the properties of recession cones of sets of feasible solutions and cones of perspective directions of optimization problems.

Expansions and Polynomial Limit Representations of Weighted Pseudoinverses

Expansions of weighted pseudoinverses with positive definite or singular weights in matrix power series or power products with negative exponents and arbitrary positive parameters are proposed and analyzed. Based on these expansions, polynomial limit representations of weighted pseudoinverses are obtained. Issues related to the construction of direct and iterative methods for calculating weighted pseudoinverses and weighted normal pseudosolutions, as well as solving constrained least squares problems, are examined.

Optimization Parallelizing for Discrete Programming Problems

Parallelizing of calculations is considered when discrete optimization problems are solved. A version of parallelizing of copies of an algorithm is proposed and analyzed. The results of computational experiments are given.

Weighted pseudoinverses and weighted normal pseudosolutions with singular weights

Weighted pseudoinverses with singular weights can be defined by a system of matrix equations. For one of such definitions, necessary and sufficient conditions are given for the corresponding system to have a unique solution. Representations of the pseudoinverses in terms of the characteristic polynomials of symmetrizable and symmetric matrices, as well as their expansions in matrix power series or power products, are obtained. A relationship is found between the weighted pseudoinverses and the weighted normal pseudosolutions, and iterative methods for calculating both pseudoinverses and pseudosolutions are constructed. The properties of the weighted pseudoinverses with singular weights are shown to extend the corresponding properties of weighted pseudoinverses with positive definite weights.

Simulation of Foreign Trade Activity under Transition Economy Conditions

A system of mathematical models of foreign economic activity under transition economy conditions is considered. Input-output optimization models and econometric micromodels are the basis of this system. Simulation using real data and the mentioned models is performed. The obtained results allow us to explain some features of the structure of the Ukrainian export.

Using categorical methods in computer science

Some categorical methods used in developing computer programs are considered. Relevant theorems are proved.

A Fuzzy Problem of Multiparametric Choice of Optimal Solutions

The problem of optimal choice of a set of parameters is considered in fuzzy formulation. The so-called S-functions (or bell-shaped functions) are used for interpretation of fuzziness. A method of defuzzification of linguistic variables is proposed. Some results on stability are given.

RESTART Technology for Solving Discrete Optimization Problems

The RESTART technology is proposed, which allows us to speed up the solution of discrete optimization problems.