Related papers: A parameterized proximal point algorithm for separ…

Sparse Principal Component Analysis (SPCA) is a fundamental technique for dimensionality reduction, and is NP-hard. In this paper, we introduce a randomized approximation algorithm for SPCA, which is based on the basic SDP relaxation. Our…

Friedlander, Mac\^{e}do, and Pong recently introduced the projected polar proximal point algorithm (P4A) for solving optimization problems by using the closed perspective transforms of convex objectives. We analyse a generalization (GP4A)…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

Convergence of a projected stochastic gradient algorithm is demonstrated for convex objective functionals with convex constraint sets in Hilbert spaces. In the convex case, the sequence of iterates ${u_n}$ converges weakly to a point in the…

We propose a variable smoothing algorithm for solving nonconvexly constrained nonsmooth optimization problems. The target problem has two issues that need to be addressed: (i) the nonconvex constraint and (ii) the nonsmooth term. To handle…

In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal…

Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…

In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish…

We explore the connection between outlier-robust high-dimensional statistics and non-convex optimization in the presence of sparsity constraints, with a focus on the fundamental tasks of robust sparse mean estimation and robust sparse PCA.…

We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…

We address the minimization of a smooth objective function under an $\ell_0$-constraint and simple convex constraints. When the problem has no constraints except the $\ell_0$-constraint, some efficient algorithms are available; for example,…

We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the $\ell_0$ norm. Specifically, the $\ell_0$ model has an objective function that is the sum of a convex fidelity term and a…

We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…

In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…

The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $s\leq s^*\gamma$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $\gamma\geq 1$ is an…

We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a…