Related papers: A Coordinate-wise Optimization Algorithm for Spars…
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
We consider variants of a recently-developed Newton-CG algorithm for nonconvex problems \citep{royer2018newton} in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on…
Recent results in homotopy and solution paths demonstrate that certain well-designed greedy algorithms, with a range of values of the algorithmic parameter, can provide solution paths to a sequence of convex optimization problems. On the…
Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…
In this paper, the sparse sensor placement problem for least-squares estimation is considered, and the previous novel approach of the sparse sensor selection algorithm is extended. The maximization of the determinant of the matrix which…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
In this paper, we use composite optimization algorithms to solve sigmoid networks. We equivalently transfer the sigmoid networks to a convex composite optimization and propose the composite optimization algorithms based on the linearized…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
Matching pursuit, especially its orthogonal version (OMP) and variations, is a greedy algorithm widely used in signal processing, compressed sensing, and sparse modeling. Inspired by constrained sparse signal recovery, this paper proposes a…
Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we…
Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
The data-compatibility approach to constrained optimization, proposed here, strives to a point that is "close enough" to the solution set and whose target function value is "close enough" to the constrained minimum value. These notions can…
Coordinate descent methods usually minimize a cost function by updating a random decision variable (corresponding to one coordinate) at a time. Ideally, we would update the decision variable that yields the largest decrease in the cost…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…