Related papers: An Optimal Algorithm for Strongly Convex Minimizat…
This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic…
Modern power systems are now in continuous process of massive changes. Increased penetration of distributed generation, usage of energy storage and controllable demand require introduction of a new control paradigm that does not rely on…
We develop refined Karush-Kuhn-Tucker (KKT) and Fritz-John (FJ)-type optimality conditions for nonsmooth, nonconvex mathematical pro\-gra\-mming problems. We pay special attention in the case that the functional constraint belongs to a…
Online optimization covers problems such as online resource allocation, online bipartite matching, adwords (a central problem in e-commerce and advertising), and adwords with separable concave returns. We analyze the worst case competitive…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
We give a simple and natural method for computing approximately optimal solutions for minimizing a convex function $f$ over a convex set $K$ given by a separation oracle. Our method utilizes the Frank--Wolfe algorithm over the cone of valid…
This paper introduces and studies the convergence properties of a new class of explicit $\epsilon$-subgradient methods for the task of minimizing a convex function over the set of minimizers of another convex minimization problem. The…
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 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…
We present two parallel optimization algorithms for a convex function $f$. The first algorithm optimizes over linear inequality constraints in a Hilbert space, $\mathbb H$, and the second over a non convex polyhedron in $\mathbb R^n$. The…
The convergence rate of various first-order optimization algorithms is a pivotal concern within the numerical optimization community, as it directly reflects the efficiency of these algorithms across different optimization problems. Our…
In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…
A popular approach to minimize a finite-sum of convex functions is stochastic gradient descent (SGD) and its variants. Fundamental research questions associated with SGD include: (i) To find a lower bound on the number of times that the…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…
In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…
We consider the misspecified optimization problem of minimizing a convex function $f(x;\theta^*)$ in $x$ over a conic constraint set represented by $h(x;\theta^*) \in \mathcal{K}$, where $\theta^*$ is an unknown (or misspecified) vector of…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
In this paper, we use composite optimization algorithms to solve sigmoid networks. We equivalently transfer the sigmoid networks to a convex composite optimization and propose the composite optimization algorithms based on the linearized…
Gradient-based minimax optimal algorithms have greatly promoted the development of continuous optimization and machine learning. One seminal work due to Yurii Nesterov [Nes83a] established $\tilde{\mathcal{O}}(\sqrt{L/\mu})$ gradient…