Community Detection by a Riemannian Projected Proximal Gradient Method

A cyclic projected gradient method

In recent years, convex optimization methods were successfully applied for various image processing tasks and a large number of first-order methods were designed to minimize the corresponding functionals. Interestingly, it was shown recently in [25] that the simple idea of so-called “superstep cycles” leads to very efficient schemes for time-dependent (parabolic) image enhancement problems as w...

extremal region detection guided by maxima of gradient magnitude

a problem of computer vision applications is to detect regions of interest under dif- ferent imaging conditions. the state-of-the-art maximally stable extremal regions (mser) detects affine covariant regions by applying all possible thresholds on the input image, and through three main steps including: 1) making a component tree of extremal regions’ evolution (enumeration), 2) obtaining region ...

Scalable Nuclear-norm Minimization by Subspace Pursuit Proximal Riemannian Gradient

Trace-norm regularization plays a vital role in many learning tasks, such as low-rank matrix recovery (MR), and low-rank representation (LRR). Solving this problem directly can be computationally expensive due to the unknown rank of variables or large-rank singular value decompositions (SVDs). To address this, we propose a proximal Riemannian gradient (PRG) scheme which can efficiently solve tr...

Strong Convergence of a Projected Gradient Method

Solving semi-infinite programs by smoothing projected gradient method

In this paper, we study a semi-infinite programming (SIP) problem with a convex set constraint. Using the value function of the lower level problem, we reformulate SIP problem as a nonsmooth optimization problem. Using the theory of nonsmooth Lagrange multiplier rules and Danskin’s theorem, we present constraint qualifications and necessary optimality conditions. We propose a new numerical meth...