• DocumentCode
    2184794
  • Title

    A conjugate point theory for nonlinear programming problems

  • Author

    Hidefumi, Kawasaki

  • Author_Institution
    Graduate Sch. of Math., Kyushu Univ., Fukuoka, Japan
  • Volume
    4
  • fYear
    2001
  • fDate
    2001
  • Firstpage
    3558
  • 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? The 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
  • Keywords
    matrix algebra; minimisation; nonlinear programming; partial differential equations; Jacobi equation; calculus of variations; conjugate point theory; extremal problems; necessary and sufficient optimality conditions; nonlinear programming problems; optimal control; Calculus; Differential equations; Erbium; Jacobian matrices; Mathematical programming; Mathematics; Nonlinear equations; Optimal control; Shortest path problem;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Decision and Control, 2001. Proceedings of the 40th IEEE Conference on
  • Conference_Location
    Orlando, FL
  • Print_ISBN
    0-7803-7061-9
  • Type

    conf

  • DOI
    10.1109/.2001.980411
  • Filename
    980411
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2184794