Related papers: Complexity of Projected Gradient Methods for Stron…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
We consider gradient descent with constant stepsizes and derive exact worst-case convergence rates on the minimum gradient norm of the iterates. Our analysis covers all possible stepsizes and arbitrary upper/lower bounds on the curvature of…
In this paper, we consider conditional gradient methods. These are methods that use a linear minimization oracle, which, for a given vector $p \in \mathbb{R}^n$, computes the solution of the subproblem $$\arg \min_{x\in X}{\langle p,x…
The proximal inertial gradient descent is efficient for the composite minimization and applicable for broad of machine learning problems. In this paper, we revisit the computational complexity of this algorithm and present other novel…
In this paper, we study the problem of maximizing continuous submodular functions that naturally arise in many learning applications such as those involving utility functions in active learning and sensing, matrix approximations and network…
We present a novel class of projected gradient (PG) methods for minimizing a smooth but not necessarily convex function over a convex compact set. We first provide a novel analysis of the constant-stepsize PG method, achieving the…
In this paper, we propose a new inexact version of the projected subgradient method to solve nondifferentiable constrained convex optimization problems. The method combine $\epsilon$-subgradient method with a procedure to obtain a feasible…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can…
We introduce a notion of inexact model of a convex objective function, which allows for errors both in the function and in its gradient. For this situation, a gradient method with an adaptive adjustment of some parameters of the model is…
This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending…
We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…
We focus on analyzing the classical stochastic projected gradient methods under a general dependent data sampling scheme for constrained smooth nonconvex optimization. We show the worst-case rate of convergence $\tilde{O}(t^{-1/4})$ and…
Frequently, when dealing with many machine learning models, optimization problems appear to be challenging due to a limited understanding of the constructions and characterizations of the objective functions in these problems. Therefore,…
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…
In this paper, we deal with multiobjective composite optimization problems, where each objective function is a combination of smooth and possibly non-smooth functions. We first propose a parameter-dependent conditional gradient method to…
We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…
In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…
We obtain a new lower bound on the information-based complexity of first-order minimization of smooth and convex functions. We show that the bound matches the worst-case performance of the recently introduced Optimized Gradient Method,…
In this paper, we provide the universal first-order methods of Composite Optimization with new complexity analysis. It delivers some universal convergence guarantees, which are not linked directly to any parametric problem class. However,…