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In this paper we consider finite sum composite convex optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…
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…
Many applications in vision require estimation of thin structures such as boundary edges, surfaces, roads, blood vessels, neurons, etc. Unlike most previous approaches, we simultaneously detect and delineate thin structures with sub-pixel…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…
In this paper we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable…
We consider a minimization problem whose objective function is the sum of a fidelity term, not necessarily convex, and a regularization term defined by a positive regularization parameter $\lambda$ multiple of the $\ell_0$ norm composed…
In compressed sensing one uses known structures of otherwise unknown signals to recover them from as few linear observations as possible. The structure comes in form of some compressibility including different notions of sparsity and low…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…
Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…
Distributed consensus optimization has received considerable attention in recent years; several distributed consensus-based algorithms have been proposed for (nonsmooth) convex and (smooth) nonconvex objective functions. However, the…
We propose an extended forward-backward algorithm for approximating a zero of a maximal monotone operator which can be split as the extended sum of two maximal monotone operators. We establish the weak convergence in average of the sequence…
High-order tensor methods that employ Taylor-based local models (of degree $p\ge 3$) within adaptive regularization frameworks have been recently proposed for both convex and nonconvex optimization problems. They have been shown to have…
This article presents a discussion of optimization problems where the objective function f(x) has parameters that are constrained by some scaling, so that q(x) = constant, where this function q() involves a sum of the parameters, their…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…
Learning with a {\it convex loss} function has been a dominating paradigm for many years. It remains an interesting question how non-convex loss functions help improve the generalization of learning with broad applicability. In this paper,…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
This paper describes a new efficient conjugate subgradient algorithm which minimizes a convex function containing a least squares fidelity term and an absolute value regularization term. This method is successfully applied to the inversion…