Variational Analysis of Regularity/Transversality Properties with Applications to Optimisation

PhD

Variational Analysis of Regularity/Transversality Properties with Applications to Optimisation

Outline

Regularity properties of real-valued functions, set-valued mappings and collections of sets to be investigated using techniques of variational analysis and applied to constraint qualifications in optimisation problems, qualification conditions in subdifferential and co-derivative calculus and convergence of computational algorithms.

This involves developing necessary and sufficient, primal and dual, linear and nonlinear conditions for error bounds, metric (sub- and semi-)regularity, Aubin property, calmness, and (sub-, semi- and intrinsic) transversality.

Stability of generalised equations subject to canonical and more general nonlinear perturbations to be studied.

The topic is broad, and the actual scope of the project can be further discussed and adjusted depending on the experience and research interests of the applicant. Several PhD projects within the above tentative topic are possible.

Supervisory Team

Principal Supervisor: Prof Alexander Kruger

Co-supervisors:

A/Prof David Yost

Dr Minh Dao