joint work with Ewa Szczepanik, Alexey Tret'yakov
The focus of this talk is on nonregular optimization problems with inequality constraints. We are interested in the case when classical regularity assumptions (constraint qualifications) are not satisfied at a solution. We propose new necessary and sufficient optimality conditions for optimization problems with inequality constraints in the finite dimensional spaces. We present generalized KKT-type optimality conditions for nonregular optimization problems using the construction of a p-factor operator. The results are illustrated by some examples.
joint work with Nadia Soledad Fazzio, Maria Laura Schuverdt, Raul Pedro Vignau
We consider optimization problems with equality, inequality and additional abstract set constraints. We extend the notion of Quasinormality Constraint Qualification for problems with additional abstract set constraints. Also, we analyse the global convergence of the Augmented Lagrangian method when the algorithm is applied to problems with abstract set constraints. Motivated by the results obtained, we also studied the possibility to extend the definitions of others constraint qualifications well known in the literature for the case in which abstract set constraints is considered.
The article aims to study the Karush-Kuhn-Tucker optimality condition for a class of a fractional interval multivalued programming problem. For the solution concept, LU and LS-Pareto optimality are discussed, and some nontrivial examples are illustrated. The concepts of LU-V-invex and LS-V-invex for a fractional interval problem are introduced and using these assumptions, the Karush-Kuhn-Tucker optimality conditions for the problem have been established. Non-trivial examples are discussed throughout to make a clear understanding of the results established.