Accession Number : AD0731773

Title :   Constructive Fixed Point Theory and Duality in Nonlinear Programming.

Descriptive Note : Technical rept.,

Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE OPERATIONS RESEARCH CENTER

Personal Author(s) : Wagner,Michael Howard

Report Date : SEP 1971

Pagination or Media Count : 188

Abstract : The computational usefulness of constructive fixed point theory and duality in nonlinear programming is considered. The author uses the previously established result that a particular dual of a general nonlinear programming problem provides lower bounds on the optimal value of the primal. Methods for solving the dual problem are considered. One of the main results is the statement of sufficient conditions under which the dual cutting plane algorithm is convergent. Kakutani's fixed point theorem gives sufficient conditions that a point-to-set map M have a fixed point u belongs to M(u). The author extracts an algorithmic map from the dual cutting plane algorithm, shows that a fixed point of this map is an optimal solution to the dual problem, and develops a procedure based upon the methods of Scarf and Eaves for finding such a fixed point. The general approach is extended to other algorithmic maps. (Author)

Descriptors :   (*NONLINEAR PROGRAMMING, ALGORITHMS), SET THEORY, MAPPING(TRANSFORMATIONS), APPROXIMATION(MATHEMATICS), CONVERGENCE, NUMERICAL ANALYSIS, OPTIMIZATION, THEOREMS, THESES

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE