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Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…
Separable multi-block convex optimization problem appears in many mathematical and engineering fields. In the first part of this paper, we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes…
For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives…
In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study,…
Assume that f is a strict convex function with a unique minimum in R^n. We divide the vector of n-variables to d groups of vector subvariables with d at least two. We assume that we can find the partial minimum of f with respect to each…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…
We study two log-concave sampling problems: constrained sampling and composite sampling. First, we consider sampling from a target distribution with density proportional to $\exp(-f(x))$ supported on a convex set $K \subset \mathbb{R}^d$,…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
Population risk is always of primary interest in machine learning; however, learning algorithms only have access to the empirical risk. Even for applications with nonconvex nonsmooth losses (such as modern deep networks), the population…
An explicit algorithm for the minimization of an $\ell_1$ penalized least squares functional, with non-separable $\ell_1$ term, is proposed. Each step in the iterative algorithm requires four matrix vector multiplications and a single…
A class of second-order algorithms is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps in an iteration-dependent subspace. In most cases, the Hessian matrix is…
We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation…
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
We introduce an optimal and nearly parameter-free algorithm for minimizing piecewise smooth (PWS) convex functions under the quadratic growth (QG) condition, where the locations and structure of the smooth regions are entirely…
We present a novel statistical inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a…