In the linear space X with a given subset C⊂X set are the mappings F1: X→Rk 1, F2: X→Rk 2 and a function f: X→R1 (k1 and k2 are given). Considered is optimization problem: f(x)→min, x∈C, F1(x)≤0, F2(x)=0. For the considered rather general problem, the necessary first- and second-order extremum conditions are determined. The conditions are valid at introduced smoothness assumptions for Fi, f and closed C. The main difference of these conditions from the known is that though obtained without a priori normality assumptions (non-degeneracy of constraints) they remain informative (not degenerate). A typical example for such type of optimization problem, in which C is a convex closed cone, is the problem of optimal control with pulse controls.

Authors

Journal

Number of issue

6

Language

Russian

Pages

727-731

Status

Published

Link

Volume

402

Year

2005

Organizations

^{1}Rossijskij Univ. Druzhby Narodov, Moscow, Russian Federation

Keywords

Constraint theory; Functions; Mathematical techniques; Optimal control systems; Optimization; Mathematical spaces; Optimal control; Pulse control; Set theory

Date of creation

19.10.2018

Date of change

19.10.2018

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Journal of Mathematical Sciences (United States).
Springer New York LLC.
Vol. 131.
2005.
P. 5606-5613

Doklady Akademii Nauk.
Vol. 401.
2005.
P. 301-305