The critical tangent cone in second-order conditions for optimal control

Z. Páles, V. Zeidan

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper the notion of critical tangent cone CT(x|Q) is introduced. When Q is closed, convex with nonempty interior, x ∈ Q, then the nonemptiness of the Dubovitskii-Milyutin set of second-order admissible variations, V (x, d|Q), is characterized by the condition d ∈ CT(x|Q). More verifiable characterization is obtained for the cases where Q is the set of continuous or L selections of a certain set-valued map. In the latter case, a strong normality condition in terms of CT(x(t)|Q(t)) is defined in order that the Lagrange multiplier corresponding to the L-selections set be represented via integrable functions. Finally these results are applied to a general optimal control problem and second-order optimality conditions are derived in terms of the original data.

Original languageEnglish
Pages (from-to)1149-1161
Number of pages13
JournalNonlinear Analysis
Volume47
Issue number2
DOIs
Publication statusPublished - Aug 2001

Fingerprint

Second-order Conditions
Tangent Cone
Lagrange multipliers
Cones
Optimal Control
Second-order Optimality Conditions
Set-valued Map
Normality
Optimal Control Problem
Interior
Closed

Keywords

  • Critical cone
  • Critical tangent cone
  • First- and second-order optimality conditions
  • Set-valued constraints

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Mathematics(all)

Cite this

The critical tangent cone in second-order conditions for optimal control. / Páles, Z.; Zeidan, V.

In: Nonlinear Analysis, Vol. 47, No. 2, 08.2001, p. 1149-1161.

Research output: Contribution to journalArticle

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