Bibliographic Details
| Title: |
To the theory of extremum for abnormal problems |
| Authors: |
Arutyunov, A. V., Jaćimović, V. |
| Publisher Information: |
Springer US, New York, NY; Pleiades Publishing (Allerton Press), New York, NY; MAIK ``Nauka/Interperiodica'', Moscow |
| Subject Terms: |
abnormal extremal problems, necessary conditions, problems with restrictions of inequality types, Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) |
| Description: |
The article considers the problem of minimization with constraints in the form of equations \[ f(x) \to \min, \quad x \in X, \quad F(x) = 0, \quad \tag{1} \] where \(X\) is a vector space, \(f: X \to E\), \(F: X \to E^k\) are smooth mappings and \(E^k\) is \(k\)-dimensional arithmetic space. Let \(x_0\) be a solution to the problem (1). If \(x_0\) is an abnormal point, then the rule of Lagrange multipliers gives for a multiplier such a value that classical necessary conditions of the second order are, generally speaking, not true. In the article the necessary conditions are received for abnormal extremum problems (1). They strengthen the earlier received results. |
| Document Type: |
Article |
| File Description: |
application/xml |
| Access URL: |
https://zbmath.org/1701798 |
| Accession Number: |
edsair.c2b0b933574d..f41df108e786d0655d06b13475b9ed61 |
| Database: |
OpenAIRE |