Methods for Solving Generalized Systems of Inequalities With Application to Nonlinear Programming

In this thesis techniques for solving generalized systems of inequalities are developed. That is, given two real normed linear spaces X and Y, and a mapping g: X (--->) Y, iterative schemes are developed for the solution of the following problem: Find x (ELEM) X such that 0 (ELEM) g(x) + K, where K is a closed convex cone in Y. Such an x is called a solution to the generalized system of inequalities, g(x) (LESSTHEQ)(,K) 0, where the relation "(LESSTHEQ)(,K)" represents the usual partial order induced on Y by K. A wide variety of problems in optimization theory can be cast in this framework, e.g. solving systems of equations and inequalities, solving general nonlinear complementarity problems, and finding Karush-Kuhn-Tucker points for mathematical programs.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Burke, James Vincent

• Mathematics

Identifier

(UMI)AAI8409877

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71215