An approach for solving nonlinear programming problems

Authors:
H. Basirzadeh;A. V. Kamyad;S. Effati
Affiliations:
Dept. of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran;Dept. of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran;Dept. of Mathematics, Teacher Training University of Sabzevar, Sabzevar, Iran
Venue:
The Korean Journal of Computational & Applied Mathematics
Year:
2002

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Abstract

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.