A conjugate point theory for nonlinear programming problems

Research output: Contribution to journalConference article


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)3558-3563
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Publication statusPublished - Dec 1 2001
Event40th IEEE Conference on Decision and Control (CDC) - Orlando, FL, United States
Duration: Dec 4 2001Dec 7 2001


All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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