We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide the first theoretical convergence analysis for both algorithms. An efficient implementation using a tailored linesearch scheme is also proposed. We demonstrate our methods’ computational e...

Three-dimensional reconstructions of icosahedral viruses from cryoelectron microscope images have reached resolutions where the microscope depth of field is a significant resolution-limiting factor. An analytical treatment presented here shows how the depth of field limitation can be understood as an envelope function which gradually attenuates the signal, starting well before the numerical dep...

although many methods exist for intensity modulated radiotherapy (imrt) fluence map optimization for crisp data, based on clinical practice, some of the involved parameters are fuzzy. in this paper, the best fluence maps for an imrt procedure were identifed as a solution of an optimization problem with a quadratic objective function, where the prescribed target dose vector was fuzzy. first, a d...

Projection methods are a popular class of methods for solving the incompressible Navier-Stokes equations. If a cell-centered grid is chosen, in order to use highresolution methods for the advection terms, performing the projection exactly is problematic. An attractive alternative is to use an approximate projection, in which the velocity is required to be only approximately discretely divergenc...

An efficient gradient-based method to solve the volume constrained topology optimization problems is presented. Each iterate of this algorithm is obtained by the projection of a Barzilai-Borwein step onto the feasible set consisting of box and one linear constraints (volume constraint). To ensure the global convergence, an adaptive nonmonotone line search is performed along the direction that i...

This paper presents a new iterative equalization algorithm that maximizes capacity for discrete multitone (DMT) systems. The research modifies a previously proposed criterion and applies an appropriate transformation to map the objective function and the constraint set into a canonical region. The resulting constraint set exhibits an identifiable geometric characteristic. Using the gradient pro...

In this paper we study smooth convex programming problems where the decision variables vector is split into several blocks of variables. We analyze the block coordinate gradient projection method in which each iteration consists of performing a gradient projection step with respect to a certain block taken in a cyclic order. Global sublinear rate of convergence of this method is established and...