Division of Information Technology, Engineering and the Environment
School of Mathematics and Statistics
School of Mathematics and Statistics
Abstract:
The notion of a secant for locally Lipschitz continuous functions is
introduced and a new algorithm to locally minimize nonsmooth, nonconvex
functions based on secants is developed. We demonstrate that the secants
can be used to design an algorithm to find descent directions of locally
Lipschitz continuous functions. This algorithm is applied to design a
minimization method, called a secant method. It is proved that the
secant method generates a sequence converging to Clarke stationary
points. Numerical results are presented demonstrating the applicability
of the secant method in a wide variety of nonsmooth, nonconvex
optimization problems. We also compare the proposed algorithm with the
bundle method using numerical results.
Biosketch:
Asef has submitted his PhD thesis on 2nd March 2009 (still waiting for
assessment result) in nonsmooth optimization area under supervision of
Dr. Adil Bagirov and Dr. Musa Mammadov. The PhD study, which is done at
the University of Ballarat, was about designing derivative free
algorithms for nonsmooth and global optimization problems. This kind of
problems has many applications in real world for example in Data Mining
and Clustering. At the moment, he is working as a research associate at
the University of South Australia. Under supervision of Prof. Jerzy
Filar and Assoc. Prof. John Boland at the School of Mathematics and
Statistics since March 2009, he is doing research in optimization and
management of renewable energies specially wind farms and investigating
the effects of such energies in the electricity market and grid.
Indian Institute of Technology-Kanpur, India
Vector variational inequalities are motivated from the necessary optimality conditions for smooth vector optimization problems over convex sets. There are several types of vector variational inequalities but in this talk we concentrate on the Stampacchia type weak vector variational inequality. Our main aim is to devise some scalar valued gap functions which lead to constrained and unconstrained reformulations of the vector variational inequality problem. We also use these gap functions to devise error bounds for the Stampacchia type weak vector variational inequality problem.
