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In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…
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We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
Learning to optimize (L2O) has recently emerged as a promising approach to solving optimization problems by exploiting the strong prediction power of neural networks and offering lower runtime complexity than conventional solvers. While L2O…
We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…
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In existing distributed stochastic optimization studies, it is usually assumed that the gradient noise has a bounded variance. However, recent research shows that the heavy-tailed noise, which allows an unbounded variance, is closer to…
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In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…
Coordinate-type subgradient methods for addressing nonsmooth optimization problems are relatively underexplored due to the set-valued nature of the subdifferential. In this work, our study focuses on nonsmooth composite optimization…
Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…
Federated learning enables training on a massive number of edge devices. To improve flexibility and scalability, we propose a new asynchronous federated optimization algorithm. We prove that the proposed approach has near-linear convergence…
This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can be written as an infimal convolution…