System optimization by oscillation and stability criteria
The purpose of this important paper is to study a question concerning the generalized eigenvalue problem with self-adjoint and positive definite matrix operators. The problem of minimum eigenvalue maximization under constraints on the designed parameters of the system is stated. The constraints are given in the form of equalities and inequalities. The general case of the \(N\)-fold extreme eigenvalue is considered. Necessary conditions for a maximum similar to Kuhn-Tucker conditions are obtained. The conditions can be used for analytical and numerical studies and for the solution of optimal design problems. Cases when the necessary conditions of the extremum hold or do not hold are shown by given examples.
scientific article; zbMATH DE number 1158002