Speaker: Prof.Defeng
Sun
Time： 15:50-16:50,June 9, 2015
Room： X2511, XiPu Campus
Profile：
Defeng Sun is a professor at Department of
Mathematics, National University of Singapore. He received his PhD in
Operations Research and Control Theory from the Institute of Applied
Mathematics, Chinese Academy of Sciences, China in 1995. He completed his
post-doctoral training at the University of New South Wales, Australia. His
research interests are mainly on Optimization, a subject of studying best decision-making
with limited resources, with side interest in financial risk management. He
served as the past editor-in-chief to Asia-Pacific Journal of Operational
Research and currently serves as associate editor to Mathematical Programming
(Series A and Series B), SIAM Journal on Optimization and Journal of China
Operations Research Society.
Topic：An Efficient Inexact
ABCD Method for Least Squares Semidefinite Programming
Abstract: We consider least squares semidefinite programming (LSSDP)
where the primal matrix variable must satisfy given linear equality and
inequality constraints, and must also lie in the intersection of the cone of
symmetric positive semidefinite matrices and a simple polyhedral set. We
propose an inexact accelerated block coordinate descent (ABCD) method for
solving LSSDP via its dual, which can be reformulated as a convex composite
minimization problem whose objective is the sum of a coupled quadratic function
involving four blocks of variables and two separable non-smooth functions
involving only the first and second block, respectively. Our inexact ABCD
method has the attractive O(1/k^2) iteration complexity if the subproblems are
solved progressively more accurately. The design of our ABCD method relies on
recent advances in the symmetric Gauss-Seidel technique for solving a convex
minimization problem whose objective is the sum of a multi-block quadratic
function and a non-smooth function involving only the first block. Extensive
numerical experiments on various classes of over 600 large scale LSSDP problems
demonstrate that our proposed ABCD method not only can solve the problems to
high accuracy, but it is also far more efficient than (a) the well known BCD
(block coordinate descent) method, (b) the eARBCG (an enhanced version of the
accelerated randomized block coordinate gradient) method, and (c) the APG
(accelerated proximal gradient) method.
