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In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…

This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…

We present a preconditioner for saddle point problems. The proposed preconditioner is extracted from a stationary iterative method which is convergent under a mild condition. Some properties of the preconditioner as well as the eigenvalues…

In this paper, we propose two new algorithms for transduction with Matrix Completion (MC) problem. The joint MC and prediction tasks are addressed simultaneously to enhance the accuracy, i.e., the label matrix is concatenated to the data…

This paper studies the primal-dual convergence and iteration-complexity of proximal bundle methods for solving nonsmooth problems with convex structures. More specifically, we develop a family of primal-dual proximal bundle methods for…

Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…

We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…

This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…

Maximization of submodular functions under various constraints is a fundamental problem that has been studied extensively. A powerful technique that has emerged and has been shown to be extremely effective for such problems is the…

In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable…

We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a…

We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…

Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…

We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

In this paper we propose a primal-dual dynamical approach to the minimization of a structured convex function consisting of a smooth term, a nonsmooth term, and the composition of another nonsmooth term with a linear continuous operator. In…

A decision rule is epsilon-minimax if it is minimax up to an additive factor epsilon. We present an algorithm for provably obtaining epsilon-minimax solutions for a class of statistical decision problems. In particular, we are interested in…

We present a novel accelerated primal-dual (APD) method for solving a class of deterministic and stochastic saddle point problems (SPP). The basic idea of this algorithm is to incorporate a multi-step acceleration scheme into the…

In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…