A conjugate point theory for nonlinear programming problems

Hidefumi Kawasaki

    Research output: Contribution to journalConference articlepeer-review

    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)3558-3563
    Number of pages6
    JournalProceedings of the IEEE Conference on Decision and Control
    Volume4
    Publication statusPublished - 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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