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In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…

This paper proposes a receding horizon active learning and control problem for dynamical systems in which Gaussian Processes (GPs) are utilized to model the system dynamics. The active learning objective in the optimization problem is…

In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…

We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…

We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy…

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…

We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact…

We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose less restrictive assumptions on the composite objective functional considering…

Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…

We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…

We investigate the convergence properties of a class of iterative algorithms designed to minimize a potentially non-smooth and noisy objective function, which may be algebraically intractable and whose values may be obtained as the output…

Min-max saddle point games appear in a wide range of applications in machine leaning and signal processing. Despite their wide applicability, theoretical studies are mostly limited to the special convex-concave structure. While some recent…

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…

We propose a family of optimization methods that achieve linear convergence using first-order gradient information and constant step sizes on a class of convex functions much larger than the smooth and strongly convex ones. This larger…

In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…

In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…

We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…

In this paper we deal with a general second order continuous dynamical system associated to a convex minimization problem with a Fr\`echet differentiable objective function. We show that inertial algorithms, such as Nesterov's algorithm,…