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Under the strongly convex assumption, several recent works studied the global linear convergence rate of the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of a large number of smooth component functions and a…
This paper deals with subsampled spectral gradient methods for minimizing finite sum. Subsample function and gradient approximations are employed in order to reduce the overall computational cost of the classical spectral gradient methods.…
We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates…
Proximal gradient methods are popular in sparse optimization as they are straightforward to implement. Nevertheless, they achieve biased solutions, requiring many iterations to converge. This work addresses these issues through a suitable…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
The goal of this paper is to reduce the total complexity of gradient-based methods for two classes of problems: affine-constrained composite convex optimization and bilinear saddle-point structured non-smooth convex optimization. Our…
This letter presents a fast distributed algorithm for aggregating a large number of households with mixed-integer variables and intricate couplings between devices. The proposed fast distributed gradient algorithm is applied to the double…
We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we…
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…
This paper considers a generic convex minimization template with affine constraints over a compact domain, which covers key semidefinite programming applications. The existing conditional gradient methods either do not apply to our template…
Online and stochastic gradient methods have emerged as potent tools in large scale optimization with both smooth convex and nonsmooth convex problems from the classes $C^{1,1}(\reals^p)$ and $C^{1,0}(\reals^p)$ respectively. However to our…
Discrete gradient methods are geometric integration techniques that can preserve the dissipative structure of gradient flows. Due to the monotonic decay of the function values, they are well suited for general convex and nonconvex…
When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…
Gradient sampling (GS) has proved to be an effective methodology for the minimization of objective functions that may be nonconvex and/or nonsmooth. The most computationally expensive component of a contemporary GS method is the need to…
A stochastic conjugate gradient method for approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method…
In this paper we consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a…
We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…
The stochastic composition optimization proposed recently by Wang et al. [2014] minimizes the objective with the compositional expectation form: $\min_x~(\mathbb{E}_iF_i \circ \mathbb{E}_j G_j)(x).$ It summarizes many important applications…
We study the solution of minimax problems $\min_x \max_y G(x) + \langle K(x),y\rangle - F^*(y)$ in finite-dimensional Hilbert spaces. The functionals $G$ and $F^*$ we assume to be convex, but the operator $K$ we allow to be non-linear. We…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…