A projected gradient method for αℓ 1 − βℓ 2 sparsity regularization

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...

Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints

Regularization of ill-posed linear inverse problems via l1 penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an l1 penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to l1-constraints, using a gradient method, with projection on l1-balls. The correspondin...

Inexact projected gradient method for vector optimization

In this work, we propose an inexact projected gradient-like method for solving smooth constrained vector optimization problems. In the unconstrained case, we retrieve the steepest descent method introduced by Graña Drummond and Svaiter. In the constrained setting, the method we present extends the exact one proposed by Graña Drummond and Iusem, since it admits relative errors on the search dire...

Spectral projected gradient method for stochastic optimization

We consider the Spectral Projected Gradient method for solving constrained optimization porblems with the objective function in the form of mathematical expectation. It is assumed that the feasible set is convex, closed and easy to project on. The objective function is approximated by a sequence of Sample Average Approximation functions with different sample sizes. The sample size update is bas...

Strong Convergence of a Projected Gradient Method