In this study, we focus on solving the nonlinear fractional optimization problem in which numerator is smooth convex and denominator concave. To achieve goal, develop an algorithm called adaptive projection gradient method. The main advantage of method that it allows computations for gradients considered functions metric to take place separately. Moreover, interesting property distinguishes pro...

A new active set algorithm (ASA) for large-scale box constrained optimization is introduced. The algorithm consists of a nonmonotone gradient projection step, an unconstrained optimization step, and a set of rules for switching between the two steps. Numerical experiments and comparisons are presented using box constrained problems in the CUTEr and MINPACK test problem libraries. keywords: Nonm...

A weighted Bregman-Gradient Projection denoising method, based on the Bregman iterative regularization (BIR) method and Chambolle's Gradient Projection method (or dual denoising method) is established. Some applications to image denoising on a 1-dimensional curve, 2-dimensional gray image and 3-dimensional color image are presented. Compared with the main results of the literatures, the present...

Algorithm 3 details the process for incrementally computing term (13) for all xk. (The process for computing (14) is similar.) Computation of the full gradient is thus also an O(nm) operation. Using this technique, we can apply full-gradient first-order methods efficiently, including gradient projection and Frank-Wolfe. With an appropriate line-search method, gradient projection is guaranteed t...