Constructive Fixed Point Theory and Duality in Nonlinear Programming.
MASSACHUSETTS INST OF TECH CAMBRIDGE OPERATIONS RESEARCH CENTER
Pagination or Media Count:
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. Kakutanis fixed point theorem gives sufficient conditions that a point-to-set map M have a fixed point u belongs to Mu. 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
- Operations Research