Related papers: Projected Subgradient Minimization versus Superior…
We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…
We propose first order algorithms for convex optimization problems where the feasible set is described by a large number of convex inequalities that is to be explored by subgradient projections. The first algorithm is an adaptation of a…
In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The…
We consider a convex unconstrained optimization problem that arises in a network of agents whose goal is to cooperatively optimize the sum of the individual agent objective functions through local computations and communications. For this…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
We propose the superiorization of incremental algorithms for tomographic image reconstruction. The resulting methods follow a better path in its way to finding the optimal solution for the maximum likelihood problem in the sense that they…
We present a computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS). CS theory requires solving a convex constrained minimization problem. We…
We identify and analyze a fundamental limitation of the classical projected subgradient method in nonsmooth convex optimization: the inevitable failure caused by the absence of valid subgradients at boundary points. We show that, under…
In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes. At a…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective…
Classical extragradient schemes and their stochastic counterpart represent a cornerstone for resolving monotone variational inequality problems. Yet, such schemes have a per-iteration complexity of two projections onto a convex set and…
This work is concerned with applying iterative image reconstruction, based on constrained total-variation minimization, to low-intensity X-ray CT systems that have a high sampling rate. Such systems pose a challenge for iterative image…
Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…
The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint…
We consider a distributed multi-agent network system where the goal is to minimize a sum of convex objective functions of the agents subject to a common convex constraint set. Each agent maintains an iterate sequence and communicates the…
In this paper we consider a problem, called convex projection, of projecting a convex set onto a subspace. We will show that to a convex projection one can assign a particular multi-objective convex optimization problem, such that the…
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…
Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not…