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Finite-difference methods are a class of algorithms designed to solve black-box optimization problems by approximating a gradient of the target function on a set of directions. In black-box optimization, the non-smooth setting is…
Distributed optimization advances centralized machine learning methods by enabling parallel and decentralized learning processes over a network of computing nodes. This work provides an accelerated consensus-based distributed algorithm for…
This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
We consider the problem of finding critical points of functions that are non-convex and non-smooth. Studying a fairly broad class of such problems, we analyze the behavior of three gradient-based methods (gradient descent, proximal update,…
The stochastic gradient descent has been widely used for solving composite optimization problems in big data analyses. Many algorithms and convergence properties have been developed. The composite functions were convex primarily and…
We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with…
In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…
We consider the task of minimizing the sum of convex functions stored in a decentralized manner across the nodes of a communication network. This problem is relatively well-studied in the scenario when the objective functions are smooth, or…
Implicit bias induced by gradient-based algorithms is essential to the generalization of overparameterized models, yet its mechanisms can be subtle. This work leverages the Normalized Steepest Descent} (NSD) framework to investigate how…
Operator splitting methods have been successfully used in computational sciences, statistics, learning and vision areas to reduce complex problems into a series of simpler subproblems. However, prevalent splitting schemes are mostly…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster…
Gradient descent algorithms perform well in convex optimization but can get tied for finding local minima in non-convex optimization. A robust method that combines a spectral approach with nonmonotone line search strategy for solving…
This paper investigates new families of compositional optimization problems, called $\underline{\bf n}$on-$\underline{\bf s}$mooth $\underline{\bf w}$eakly-$\underline{\bf c}$onvex $\underline{\bf f}$inite-sum $\underline{\bf c}$oupled…
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…
We consider an unconstrained problem of minimizing a smooth convex function which is only available through noisy observations of its values, the noise consisting of two parts. Similar to stochastic optimization problems, the first part is…
Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain…
It is well-known that given a smooth, bounded-from-below, and possibly nonconvex function, standard gradient-based methods can find $\epsilon$-stationary points (with gradient norm less than $\epsilon$) in $\mathcal{O}(1/\epsilon^2)$…