Related papers: Submodular Maximization through the Lens of Linear…
We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy…
Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
Convex relaxations based on different hierarchies of linear/semi-definite programs have been used recently to devise approximation algorithms for various optimization problems. The approximation guarantee of these algorithms improves with…
In this paper, we consider the unconstrained submodular maximization problem. We propose the first algorithm for this problem that achieves a tight $(1/2-\varepsilon)$-approximation guarantee using $\tilde{O}(\varepsilon^{-1})$ adaptive…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
We study parallel algorithms for the problem of maximizing a non-negative submodular function. Our main result is an algorithm that achieves a nearly-optimal $1/2 -\epsilon$ approximation using $O(\log(1/\epsilon) / \epsilon)$ parallel…
This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input…
A fundamental task underlying many important optimization problems, from influence maximization to sensor placement to content recommendation, is to select the optimal group of $k$ items from a larger set. Submodularity has been very…
This article provides a comprehensive exploration of submodular maximization problems, focusing on those subject to uniform and partition matroids. Crucial for a wide array of applications in fields ranging from computer science to systems…
A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size $n$ subject to cardinality constraint $k$; the algorithm is based upon the idea of interlacing two…
The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint…
Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain.…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
This paper considers scheduling on identical machines. The scheduling objective considered in this paper generalizes most scheduling minimization problems. In the problem, there are $n$ jobs and each job $j$ is associated with a…