Abstract
AbstractThe 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.
Highlights
The problem of quadratic programming is the problem of maximizing a quadratic function with quadratic and/or linear constraints
In [5], the formalization of the improper linear programming (LP) problem with inconsistent constraints was proposed as the problem of minimizing the spectral or Frobenius norm of the data correction matrix with a lower bound on the initial criterion and its solution was found
Note that in [8] we have considered the task of the improper LP problem data correction with a restriction to the Frobenius norm of the correction matrix of the left-hand side of the constraints, which has certain specificity and demanded a slightly different approach
Summary
The problem of quadratic programming is the problem of maximizing a quadratic function (possibly with a linear part) with quadratic and/or linear constraints. In [5], the formalization of the improper LP problem with inconsistent constraints was proposed as the problem of minimizing the spectral or Frobenius norm of the data correction matrix with a lower bound on the initial criterion and its solution was found. If the improper problem of quadratic programming is formalized in the form of minimizing the l1-norm of the data correction matrix (for linear constraints) with restriction to the initial criterion value, we obtain a similar problem. The main content of the work is to present new results concerning its application to the solution of the task of the improper LP problem data correction with a restriction to the Euclidean norm of the correction vector of the right-hand side or the Frobenius norm of the correction matrix of both sides of the constraints. We confine ourselves to the latter (the first sub-case generates other mathematical problems of projection)
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