Related papers: Denoising Using Projection Onto Convex Sets (POCS)…

In this paper, we present a new framework for reducing the computational complexity of geometric vision problems through targeted reweighting of the cost functions used to minimize reprojection errors. Triangulation - the task of estimating…

In image denoising problems, one widely-adopted approach is to minimize a regularized data-fit objective function, where the data-fit term is derived from a physical image acquisition model. Typically the regularizer is selected with two…

We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence…

In this paper, we propose a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the…

Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…

This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…

It is possible to solve unbounded convex vector optimization problems (CVOPs) in two phases: (1) computing or approximating the recession cone of the upper image and (2) solving the equivalent bounded CVOP where the ordering cone is…

We show that a broad range of convex optimization algorithms, including alternating projection, operator splitting, and multiplier methods, can be systematically derived from the framework of subspace correction methods via convex duality.…

The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…

We solve the image denoising problem with a dictionary learning technique by writing a convex functional of a new form. This functional contains beside the usual sparsity inducing term and fidelity term, a new term which induces similarity…

The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods…

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

In a recent paper, Parikh and Boyd describe a method for solving a convex optimization problem, where each iteration involves evaluating a proximal operator and projection onto a subspace. In this paper we address the critical practical…

We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…

In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…

In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be written as the difference of two convex…

This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…

In this article, we consider the problem of unconstrained time-varying convex optimization, where the cost function changes with time. We provide an in-depth technical analysis of the problem and argue why freezing the cost at each time…

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…

Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total…