A conjugate points theory for a nonlinear programming problem

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The conjugate point is an important global concept in the calculus of variations and optimal control. In these extremal problems, the variable is not a vector in Rn but a function. So a simple and natural question arises. Is it possible to establish a conjugate points theory for a nonlinear programming problem, Min f(x) on x ∈ Rn? This paper positively answers this question. We introduce the Jacobi equation and conjugate points for the nonlinear programming problem, and we describe necessary and sufficient optimality conditions in terms of conjugate points.

Original languageEnglish
Pages (from-to)54-63
Number of pages10
JournalSIAM Journal on Control and Optimization
Volume40
Issue number1
DOIs
Publication statusPublished - 2002

Fingerprint

Conjugate points
Nonlinear programming
Nonlinear Programming
Jacobi Equation
Necessary and Sufficient Optimality Conditions
Extremal Problems
Calculus of variations
Optimal Control

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics
  • Control and Optimization

Cite this

A conjugate points theory for a nonlinear programming problem. / Kawasaki, Hidefumi.

In: SIAM Journal on Control and Optimization, Vol. 40, No. 1, 2002, p. 54-63.

Research output: Contribution to journalArticle

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