Related papers: Convergence Rates of Inexact Proximal-Gradient Met…
In this paper, we use Proximal Cubic regularized Newton Methods (PCNM) to optimize the sum of a smooth convex function and a non-smooth convex function, where we use inexact gradient and Hessian, and an inexact subsolver for the cubic…
We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our…
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…
The sum of ratios problem has a variety of important applications in economics and management science, but it is difficult to globally solve this problem. In this paper, we consider the minimization problem of a sum of a number of…
In this paper, we propose a proximal stochasitc gradient algorithm (PSGA) for solving composite optimization problems by incorporating variance reduction techniques and an adaptive step-size strategy. In the PSGA method, the objective…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
In this paper, we find the special case of the subgradient method minimizing a one-dimensional real-valued function, which we term the specular gradient method, that converges root-linearly without any additional assumptions except the…
In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…
We consider the problem of minimizing a finite sum of convex functions subject to the set of minimizers of a convex differentiable function. In order to solve the problem, an algorithm combining the incremental proximal gradient method with…
We develop model-based methods for solving stochastic convex optimization problems, introducing the approximate-proximal point, or aProx, family, which includes stochastic subgradient, proximal point, and bundle methods. When the modeling…
In many modern machine learning applications, structures of underlying mathematical models often yield nonconvex optimization problems. Due to the intractability of nonconvexity, there is a rising need to develop efficient methods for…
In this paper, we consider a nonsmooth convex finite-sum problem with a conic constraint. To overcome the challenge of projecting onto the constraint set and computing the full (sub)gradient, we introduce a primal-dual incremental gradient…
We consider minimizing a function consisting of a quadratic term and a proximable term which is possibly nonconvex and nonsmooth. This problem is also known as scaled proximal operator. Despite its simple form, existing methods suffer from…
One of the most popular and important first-order iterations that provides optimal complexity of the classical proximal gradient method (PGM) is the "Fast Iterative Shrinkage/Thresholding Algorithm" (FISTA). In this paper, two inexact…
We consider the problem of minimizing a function, which is the sum of a linear function and a composition of a strongly convex function with a linear transformation, over a compact polyhedral set. Jaggi and Lacoste-Julien [14] showed that…
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
We propose several adaptive algorithmic methods for problems of non-smooth convex optimization. The first of them is based on a special artificial inexactness. Namely, the concept of inexact ($ \delta, \Delta, L$)-model of objective…
Due to the non-smoothness of optimization problems in Machine Learning, generalized smoothness assumptions have been gaining a lot of attention in recent years. One of the most popular assumptions of this type is $(L_0,L_1)$-smoothness…