Related papers: Improved Algorithms for Convex-Concave Minimax Opt…
In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity bound of $\mathcal{O}(|\log(\epsilon)|)$…
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…
We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy…
We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…
A lot of effort has been invested into characterizing the convergence rates of gradient based algorithms for non-linear convex optimization. Recently, motivated by large datasets and problems in machine learning, the interest has shifted…
This paper studies bilinear saddle point problems $\min_{\bf{x}} \max_{\bf{y}} g(\bf{x}) + \bf{x}^{\top} \bf{A} \bf{y} - h(\bf{y})$, where the functions $g, h$ are smooth and strongly-convex. When the gradient and proximal oracle related to…
We consider a class of popular distributed non-convex optimization problems, in which agents connected by a network $\mathcal{G}$ collectively optimize a sum of smooth (possibly non-convex) local objective functions. We address the…
In this paper we study a class of constrained minimax problems. In particular, we propose a first-order augmented Lagrangian method for solving them, whose subproblems turn out to be a much simpler structured minimax problem and are…
In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we…
Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning, neural architecture search, and meta-learning. A common goal in bilevel optimization is to minimize a…
We extend the traditional worst-case, minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. Our main result gives function-specific lower and upper bounds on the…
This paper introduces a new extragradient-type algorithm for a class of nonconvex-nonconcave minimax problems. It is well-known that finding a local solution for general minimax problems is computationally intractable. This observation has…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
This work presents a universal accelerated first-order primal-dual method for affinely constrained convex optimization problems. It can handle both Lipschitz and H\"{o}lder gradients but does not need to know the smoothness level of the…
We construct a family of functions suitable for establishing lower bounds on the oracle complexity of first-order minimization of smooth strongly-convex functions. Based on this construction, we derive new lower bounds on the complexity of…
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…
We focus on analyzing the classical stochastic projected gradient methods under a general dependent data sampling scheme for constrained smooth nonconvex optimization. We show the worst-case rate of convergence $\tilde{O}(t^{-1/4})$ and…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
We study structured convex optimization problems, with additive objective $r:=p + q$, where $r$ is ($\mu$-strongly) convex, $q$ is $L_q$-smooth and convex, and $p$ is $L_p$-smooth, possibly nonconvex. For such a class of problems, we…