Research objectives and content
In this project we will apply recently discovered techniques and results of the rapidly developing Subdifferential Theory to the study of the various classes of generalized convex functions. These classes, apart from their independent interest, usually meet a large field of applications in Microeconomics. In a very recent research work we have discovered an intrinsic property (i.e. cyclicity) of the subdifferentials of the generalized convex functions. This very promising tool will be used in order to establish duality schemes between the classes of generalized convex functions and corresponding classes of generalized monotone operators. In the same line of research we wish to clarify the exact relation between pseudoconvex and semistrictly quasiconvex functions, since both classes have important properties in Optimization theory. Asplund spaces, which enjoy an elegant dual geometric characterization, often provide the minimal framework of an adequate subdifferential theory. Our next objective will be to extend and clarify the exact geometric impact of the classes of Banach spaces in which a sufficient subdifferential theory exists for a given subdifferential. To this end, recent advances on the so-called reliable Banach spaces will be of use. Next, we shall study certain applications of the subdifferential theory in optimization problems with non-polyhedral constraints by refining the notion of coderivative and developing the relevant calculus. In the same spirit we will study properties of the second order subderivatives in connection to stability problems in Sensitivity Analysis.
Training content (objective, benefit and expected impact)
By working for a period of twenty four months in the research area of Non-smooth Analysis with a well-known expert of the field, the applicant wishes to improve his own expertise and go deeper into certain application areas of Economics, Control Theory and Sensitivity Analysis. The experience acquired in this period as much as the familiarity obtained with some new research techniques will form a valuable resource for the applicant to his future research career returning back to his country. Links with industry / industrial relevance (22)
No industrial relevance is directly involved on the proposal