Title :
A conjugate point theory for nonlinear programming problems
Author :
Hidefumi, Kawasaki
Author_Institution :
Graduate Sch. of Math., Kyushu Univ., Fukuoka, Japan
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;
Conference_Titel :
Decision and Control, 2001. Proceedings of the 40th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
0-7803-7061-9
DOI :
10.1109/.2001.980411
