Zhou Wei — Page 2 | Searcharxiv

arXiv2013

Nonsmooth Steepest Descent Method by Proximal Subdifferentials in Hilbert Spaces

In this paper, we first study nonsmooth steepest descent method for nonsmooth functions defined on Hilbert space and establish the corresponding algorithm by proximal subgradients. Then, we use this algorithm to find stationary points for those functions satisfying prox-regularity and Lipschitzian continuity. As one application, the established algorithm is used to search the minimizer of lower semicontinuous and convex functions on finite-dimensional space. The convergent theorem, as one extension and improvement of the existing converging result for twice continuously differentiable convex functions, is also presented therein.

math.OC↗

arXiv2013

Normal property, Jamenson property, CHIP and linear regularity for an infinite system of convex sets in Banach spaces

In this paper, we study different kinds of normal properties for infinite system of arbitrarily many convex sets in a Banach space and provide the dual characterization for the normal property in terms of the extended Jamenson property for arbitrarily many weak*-closed convex cones in the dual space. Then, we use the normal property and the extended Jamenson property to study CHIP, strong CHIP and linear regularity for the infinite case of arbitrarily many convex sets and establish equivalent relationship among these properties. In particular, we extend main results in [3] on normal property, Jamenson property, CHIP and linear regularity for finite system of convex sets in a Hilbert space to the infinite case of arbitrarily many convex sets in Banach space setting.

math.OC↗