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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2026. Vol 57

The Problem of Optimizing a Set of Quadratic Criteria Relative to a Linear Multi-Step Control System

Author(s)

Vladimir A. Srochko, Vladimir G. Antonik, Alexander V. Arguchintsev

Irkutsk State University, Irkutsk, Russian Federation

Abstract
A linear-quadratic problem of optimal control in a discrete-time formulation and multi-objective setting is considered: a linear system, a set of quadratic objective functions in state and control variables, multi-objective optimization, and Pareto-optimal solutions. Based on a linear scalarization of criteria, a reduction to a parametric scalar optimization problem is performed, requiring a global solution without any convexity assumptions. The dependence of the aggregate objective function on state variables is eliminated. Using extremal eigenvalues, conditions on the parameters that ensure the convexity property in the scalar problem are formulated. Furthermore, two optimization problems with respect to the parameters are announced; these problems improve the defining matrix of the resulting quadratic form in terms of conditioning and convergence. As a result of the proposed regularization procedure, a family of multi-extremal problems is reduced to convex programming problems with a quadratic objective function that admit a guaranteed solution. This solution constitutes a Pareto-optimal control for the original non-convex linear-quadratic problem.
About the Authors

Vladimir A. Srochko, Dr. Sci. (Phys.-Math.), Prof., Irkutsk State University, Irkutsk, 664003, Russian Federation, srochko@math.isu.ru 

Vladimir G. Antonik, Cand. Sci. (Phys.-Math.), Assoc. Prof., Irkutsk State University, Irkutsk, 664003, Russian Federation, vga@math.isu.ru

Alexander V. Arguchintsev, Dr. Sci. (Phys.-Math.), Prof., Irkutsk State University, Irkutsk, 664003, Russian Federation, arguch@math.isu.ru

For citation
Srochko V. A., Antonik V. G., Arguchintsev A. V. The Problem of Optimizing a Set of Quadratic Criteria Relative to a Linear Multi-Step Control System. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 57, pp. 35–47. (in Russian) https://doi.org/10.26516/1997-7670.2026.57.35
Keywords
linear-quadratic problem of optimal control, discrete-time variant, multiobjective formulation, auxiliary scalar optimization problem, extraction of convex problems For citation: Srochko V. A., Antonik V. G., Arguchintsev A. V. The Problem of Optimizing a Set of Quadratic Criteria Relative to a Linear Multi-Step Control System. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 57, pp. 35–47. (in Russian) https://doi.org/10.26516/1997-7670.2026.57.35
UDC
517.977
MSC
49M25, 49N10
DOI
https://doi.org/10.26516/1997-7670.2026.57.35
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