Constructive Fixed Point Theory and Duality in Nonlinear Programming.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1971
- Accession Number
- AD0731773
Entities
People
- Michael Howard Wagner
Organizations
- Massachusetts Institute of Technology