Linear-quadratic programming and its application to data correction of improper linear programming problems

Abstract

The problem of maximizing a linear function with linear and quadratic constraints is considered. The solution of the problem is obtained in a constructive form using the Lagrange function and the optimality conditions. Many optimization problems can be reduced to the problem of this type. In this paper, as an application, we consider an improper linear programming problem formalized in the form of maximization of the initial linear criterion with a restriction to the Euclidean norm of the correction vector of the right-hand side of the constraints or the Frobenius norm of the correction matrix of both sides of the constraints.

Multi-Criteria Optimization as the Methodology of Ensuring Sustainable Development of Regions: Tula Region of the Russian Federation

“…The first of them contains data for a set of objects of the same type (elements, subsystems of regions), the second set contains data for elements and subsystems of only one object (region). This approach is in line with studies [39][40][41], where the goal is determined a priori. We use models of the first type to determine the standards, the achievement of which is the purpose of the functioning of the SEES elements.…”

“…A natural solution is the application of a welldeveloped mathematical apparatus used in the management of the technical and techno-economic systems to the tasks of state and municipal management. Gorelik and Zolotova [39,40] presents an approach to determining the principle of optimality when making a decision in conditions of incomplete information, based on game theory. The same authors considered the issues of optimal control based on the information theory of hierarchical systems [41].…”