Some Duality Results in Multiple Objective Linear and Nonlinear Programming and a Nonmonotone Quasi-Newton Algorithm for Unconstrained Multiple Objective Optimization, Ph.D. Dissertation Sharif University of Technology ; Mahdavi Amiri, Nezam Oddin (Supervisor)
Abstract
Recently, Luc defined a dual program for a multiple objective linear program. The dual problem is also a multiple objective linear problem and the weak duality and strong duality theorems for these primal and dual problems have been established.Here, we use these results to establish some relationships between multiple objective linear primal and dual problems. We extend the available results on single objective linear primal and dual problems to multiple objective linear primal and dual problems. Complementary slackness conditions for efficient solutions, and conditions for the existence of weakly efficient solution sets and existence of strictly primal and dual feasible points are...
Cataloging briefSome Duality Results in Multiple Objective Linear and Nonlinear Programming and a Nonmonotone Quasi-Newton Algorithm for Unconstrained Multiple Objective Optimization, Ph.D. Dissertation Sharif University of Technology ; Mahdavi Amiri, Nezam Oddin (Supervisor)
Abstract
Recently, Luc defined a dual program for a multiple objective linear program. The dual problem is also a multiple objective linear problem and the weak duality and strong duality theorems for these primal and dual problems have been established.Here, we use these results to establish some relationships between multiple objective linear primal and dual problems. We extend the available results on single objective linear primal and dual problems to multiple objective linear primal and dual problems. Complementary slackness conditions for efficient solutions, and conditions for the existence of weakly efficient solution sets and existence of strictly primal and dual feasible points are...
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