Related papers: A Second-Order Method for Convex $\ell_1$-Regulari…
In this paper, we propose new accelerated methods for smooth convex optimization, called contracting proximal methods. At every step of these methods, we need to minimize a contracted version of the objective function augmented by a…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix. Iteratively, our variant only requires access to…
Interesting theoretical associations have been established by recent papers between the fields of active learning and stochastic convex optimization due to the common role of feedback in sequential querying mechanisms. In this paper, we…
We study the optimization of (strongly) quasar-convex functions, a class that arises naturally in many machine learning and data science applications due to its favorable properties. The fundamental properties of this class are first…
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…
An important method to optimize a function on standard simplex is the active set algorithm, which requires the gradient of the function to be projected onto a hyperplane, with sign constraints on the variables that lie in the boundary of…
We present a simple scheme for restarting first-order methods for convex optimization problems. Restarts are made based only on achieving specified decreases in objective values, the specified amounts being the same for all optimization…
We introduce the concept of strong high-order approximate minimizers for nonconvex optimization problems. These apply in both standard smooth and composite non-smooth settings, and additionally allow convex or inexpensive constraints. An…
We consider the problem of active learning in the context of spatial sampling for level set estimation (LSE), where the goal is to localize all regions where a function of interest lies above/below a given threshold as quickly as possible.…
In this paper, we study the problem of noisy, convex, zeroth order optimisation of a function $f$ over a bounded convex set $\bar{\mathcal X}\subset \mathbb{R}^d$. Given a budget $n$ of noisy queries to the function $f$ that can be…
Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…
This paper develops and analyzes an accelerated proximal descent method for finding stationary points of nonconvex composite optimization problems. The objective function is of the form $f+h$ where $h$ is a proper closed convex function,…
We consider the proximal-gradient method for minimizing an objective function that is the sum of a smooth function and a non-smooth convex function. A feature that distinguishes our work from most in the literature is that we assume that…
We present an algorithm for the minimization of a nonconvex quadratic function subject to linear inequality constraints and a two-sided bound on the 2-norm of its solution. The algorithm minimizes the objective using an active-set method by…
Owing to their statistical properties, non-convex sparse regularizers have attracted much interest for estimating a sparse linear model from high dimensional data. Given that the solution is sparse, for accelerating convergence, a working…
In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to…
Most systems and learning algorithms optimize average performance or average loss -- one reason being computational complexity. However, many objectives of practical interest are more complex than simply average loss. This arises, for…
We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…