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Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
The Heavy Ball Method, proposed by Polyak over five decades ago, is a first-order method for optimizing continuous functions. While its stochastic counterpart has proven extremely popular in training deep networks, there are almost no known…
We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the…
The paper presents a review of the state-of-the-art of subgradient and accelerated methods of convex optimization, including in the presence of disturbances and access to various information about the objective function (function value,…
The optimal allocation of resources for maximizing influence, spread of information or coverage, has gained attention in the past years, in particular in machine learning and data mining. But in applications, the parameters of the problem…
In this paper we consider the solvability of a non-convex regular polynomial vector optimization problem on a nonempty closed set. We introduce regularity conditions for the polynomial vector optimization problem and study properties and…
The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local…
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
We study nonconvex optimization landscapes for learning overcomplete representations, including learning (i) sparsely used overcomplete dictionaries and (ii) convolutional dictionaries, where these unsupervised learning problems find many…
Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…
This paper investigates the stochastic distributed nonconvex optimization problem of minimizing a global cost function formed by the summation of $n$ local cost functions. We solve such a problem by involving zeroth-order (ZO) information…
This paper investigates the optimality conditions for characterizing the local minimizers of the constrained optimization problems involving an $\ell_p$ norm ($0<p<1$) of the variables, which may appear in either the objective or the…
We consider the problem of maximizing an unknown function over a compact and convex set using as few observations as possible. We observe that the optimization of the function essentially relies on learning the induced bipartite ranking…
We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that…
In this article, we work with set-valued optimization problems in locally convex topological vector spaces. We prove the equivalencies of some definitions of generalized convex maps introduced by Jeyakumar, Yang, Yang & Yang & Chen, as well…
Decentralized minimax optimization has been actively studied in the past few years due to its application in a wide range of machine learning models. However, the current theoretical understanding of its convergence rate is far from…
We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain…
The paper is devoted to the existence of global optimal solutions for a general class of nonsmooth problems of constrained vector optimization without boundedness assumptions on constraint sets. The main attention is paid to the two major…