Constraint qualification conditions for nonlinear programming problems

Constraint qualification conditions for nonlinear programming problems

Federal University of Paraná (January 2017 – December 2017)

This project continues the previous work in which the Karush–Kuhn–Tucker necessary conditions were studied under the imposition of various constraint qualification conditions. We consider the most common qualification conditions found in the specialized literature, namely: the Linear Independence Constraint Qualification, the Mangasarian–Fromovitz Condition, Abadie’s Condition, and Guignard’s Condition. We also examine the relationships among these conditions and how they manifest in the set of Lagrange multipliers. To obtain our results, we employ Motzkin’s Alternative Theorem and the Duality Theory of Linear Programming. The natural continuation of this work is to investigate other qualification conditions and to extend the studied results to multiobjective optimization problems.

Doctoral Members: Lucelina Batista dos Santos (PI)

Students: Everton Silva