Related papers: Convex Optimization on Functionals of Probability …
We resolve the min-max complexity of distributed stochastic convex optimization (up to a log factor) in the intermittent communication setting, where $M$ machines work in parallel over the course of $R$ rounds of communication to optimize…
The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by…
In this paper, we investigate mutual information as a cost function for clustering, and show in which cases hard, i.e., deterministic, clusters are optimal. Using convexity properties of mutual information, we show that certain formulations…
Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a…
We propose decentralized primal-dual methods for cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the…
In this paper we consider the problem of minimizing area subject to a volume constraint in a given convex set.
Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…
We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and…
Conservation laws are usually studied in the context of sufficient regularity conditions imposed on the flux function, usually $C^{2}$ and uniform convexity. Some results are proven with the aid of variational methods and a unique minimizer…
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…
Convex programming with linear constraints plays an important role in the operation of a number of everyday systems. However, absent any additional protections, revealing or acting on the solutions to such problems may reveal information…
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
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…
Optimization in machine learning typically deals with the minimization of empirical objectives defined by training data. However, the ultimate goal of learning is to minimize the error on future data (test error), for which the training…
We establish that the min-sum message-passing algorithm and its asynchronous variants converge for a large class of unconstrained convex optimization problems.
State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization,…
Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we focus on checking local optimality in hidden…