Scientific Projects

Optimality conditions for multiobjective problems

A study explored existence of solutions and Fritz–John and Karush–Kuhn–Tucker optimality conditions for nonlinear programming via Gordan’s alternative. It extends these results to multiobjective problems and examines invexity and KT-invexity, showing KKT conditions are necessary and sufficient in the broadest problem class.

Constraint qualification conditions for nonlinear programming problems

A continuation of prior research on Karush–Kuhn–Tucker conditions under key constraint qualifications (LICQ, Mangasarian–Fromovitz, Abadie, Guignard), examining their interrelations and impact on Lagrange multipliers. Using Motzkin’s Alternative Theorem and linear-programming duality, it aims to explore additional qualifications and extend findings to multiobjective optimization.