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Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
This paper considers a convex composite optimization problem with affine constraints, which includes problems that take the form of minimizing a smooth convex objective function over the intersection of (simple) convex sets, or regularized…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
This paper investigates a general class of problems in which a lower bounded smooth convex function incorporating $\ell_{0}$ and $\ell_{2,0}$ regularization is minimized over a box constraint. Although such problems arise frequently in…
We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…
We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
This paper focuses on stochastic methods for solving smooth non-convex strongly-concave min-max problems, which have received increasing attention due to their potential applications in deep learning (e.g., deep AUC maximization,…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
This paper develops the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of minimization problems (subproblems). We show that the sequence of approximations to the solutions of the…
Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…
This paper investigates the convex optimization problem with general convex inequality constraints. To cope with this problem, a discrete-time algorithm, called augmented primal-dual gradient algorithm (Aug-PDG), is studied and analyzed. It…
We analyze the complexity of single-loop quadratic penalty and augmented Lagrangian algorithms for solving nonconvex optimization problems with functional equality constraints. We consider three cases, in all of which the objective is…
We propose a new first-order optimisation algorithm to solve high-dimensional non-smooth composite minimisation problems. Typical examples of such problems have an objective that decomposes into a non-smooth empirical risk part and a…
In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…
In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity bound of $\mathcal{O}(|\log(\epsilon)|)$…
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…