Subgradient Methods in Infinite Dimensional Hilbert Spaces

Thời gian: 930-10h30 Thứ Tư, ngày 19/7/2013

Địa điểm: Phòng 612, nhà A6

Tóm tắt: Subgradient methods, introduced by Shor and developed by Albert, Iusem, Nesterov, Polyak, Soloov, and many others, are used to solve nondifferentiable optimization problems. The major differences from the gradient descent methods (or projection-gradient methods) for differentiable optimization problems lie in the selection manners of the step-sizes. For instance, constant step-sizes for differen-tiable objective functions no longer work for nondifferentiable objective functions; for the latter case, diminishing step-sizes must however be adopted. In this talk, we will first review some existing projected subgradient methods and the main purpose is to discuss weak and strong convergence of projected subgradient methods in an infinite-dimensional Hilbert space. Some regularization techniques for strong convergence of projected subgradient methods will particu-larly be presented. Extension to the proximal-subgradient method for minimizing the sum of two nondifferentiable convex functions will also be discussed.