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We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our…
Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…
This paper addresses an online convex optimization problem where the cost function at each step depends on a history of past decisions (i.e., memory), and the decision maker has access to limited predictions of future cost values within a…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
Recently, there were introduced important classes of relatively smooth, relatively continuous, and relatively strongly convex optimization problems. These concepts have significantly expanded the class of problems for which optimal…
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…
The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence ($V_T$) and/or the path-length of the minimizer sequence after $T$ rounds. For strongly convex and smooth…
This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…
It is well-known that accelerated gradient first order methods possess optimal complexity estimates for the class of convex smooth minimization problems. In many practical situations, it makes sense to work with inexact gradients. However,…
In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…
In the past few years, Online Convex Optimization (OCO) has received notable attention in the control literature thanks to its flexible real-time nature and powerful performance guarantees. In this paper, we propose new step-size rules and…
We consider online convex optimization with time-varying stage costs and additional switching costs. Since the switching costs introduce coupling across all stages, multi-step-ahead (long-term) predictions are incorporated to improve the…
We present an adaptive online gradient descent algorithm to solve online convex optimization problems with long-term constraints , which are constraints that need to be satisfied when accumulated over a finite number of rounds T , but can…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
In this paper, we consider the composite optimization problem, where the objective function integrates a continuously differentiable loss function with a nonsmooth regularization term. Moreover, only the function values for the…
We investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
We consider the problem of controlling an unknown linear dynamical system under adversarially changing convex costs and full feedback of both the state and cost function. We present the first computationally-efficient algorithm that attains…
Many techniques for online optimization problems involve making decisions based solely on presently available information: fewer works take advantage of potential predictions. In this paper, we discuss the problem of online convex…
Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…