DMS Colloquium: Charles E. Chidume

Speaker: Charles E. Chidume, FTWAS, FAS, FNMS

Title: On the Strong Convergence of the Proximal Point Algorithm of Martinet and Rockafellar

Abstract: Rockafellar proved that the sequence of the celebrated proximal point algorithm introduced by Martinet for approximating a zero of a maximal monotone operator on a real Hilbert Space converges weakly. He then posed the following question: Does the sequence converge strongly? This was resolved in the negative by Guder. Consequently, several authors over the years, proposed various involved modifications of the proximal point algorithm to obtain strong convergence. In this talk, we present our new iterative algorithm, recently introduced which is totally different from the proximal point algorithm or any of its modifications, and yields strong convergence to a zero of a maximal monotone map even in real Banach spaces much more general than real Hilbert spaces. Finally, we present numerical examples to illustrate the strong convergence of the sequence of our algorithm.

Biographical sketch

Charles Ejike Chidume received his PhD degree in Mathematics from The Ohio State University, Columbus, Ohio. He returned immediately to his home country, Nigeria and worked at the University of Nigeria, Nsukka, for six years during which he rose to the rank of full professor of Mathematics. He then moved, on invitation, to join the International Centre for Theoretical Physics (ICTP) of IAEA and UNESCO of the United Nations, in Trieste, Italy, where he worked as the coordinator of the Postgraduate Diploma Program (Mathematics) and Research Mathematician. In 2009, Professor Chidume, on invitation, joined the African University of Science and Technology (AUST), a Nelson Mandela Institution offering only Postgraduate programs, located in Abuja, Nigeria. He is currently at this University serving as the Department Head of Pure and Applied Mathematics, Director of the Mathematics Institute, and Acting President of the University.

Professor Chidume has supervised 19 PhD theses and over 80 MSc and Postgraduate Diploma of the ICTP thesis. He publishes copiously and is an Associate Editor in several top journals.

Faculty host: Geraldo de Souza, Professor Emeritus