Saturday, 16:30 - 18:30 - Room 105
Stream: Multi-objective optimization
The aim of this paper is to prove that the sensitivity of a vector convex optimization program can be measured in terms of the paratingent derivative by the solution of a dual program and its sensitivity. By doing so, we complete a study initiated in two previous works, showing that the aforementioned dual program becomes an useful instrument to measure sensitivity in vector convex programming through
the four main notions of tangency used in set-valued analysis, namely, the contingent, adjacent, circatangent and paratingent derivatives.
We present in this talk characterizations of the weak efficient solutions, efficient solutions, and isolated efficient solutions of vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. These characterizations involve different data qualifications and either Karusk-Kuhn-Tucker multipliers, or an ad hoc gap function, or continuous linear functionals on the constraint space.
The talk is based on joint papers with F. Guerra-Vazquez and M. I. Todorov (2016), and N. Kanzi (submitted).
We present some properties of weakly sequentially complete Banach spaces which were investigated in number of papers, see e.g. Rosenthal, Banach. In this talk we present sufficient conditions for a Banach space Y to be weakly sequentially complete. These sufficient conditions are expressed in terms of existence of directional derivatives for cone convex mappings. There will be some discussion about normal cones and cone convex mappings.
Optimization methods are widely applied in data mining. The amount and variability of data that are generated by information systems increases considerably every year. It can be observed two main directions of development of optimization methods for mining of such data. The first direction is related to methods with huge amount of variables. The second one is focused on on-line optimization. In this paper we will show how application of multiple-criteria analysis will improve mining of big data. The on-line optimization approach that consider several criteria will be presented.