A conjugate points theory for a nonlinear programming problem

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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

All Science Journal Classification (ASJC) codes

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

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