First-order methods for solving convex optimization problems have been at the forefront of mathematical in last 20 years. The rapid development this important class algorithms is motivated by success stories reported various applications, including most importantly machine learning, signal processing, imaging and control theory. potential to provide low accuracy solutions computational complexi...

Abstract We explore whether quantum advantages can be found for the zeroth-order online convex optimization problem, which is also known as bandit with multi-point feedback. In this setting, given access to oracles (that is, loss function accessed a black box that returns value any queried input), player attempts minimize sequence of adversarially generated functions. This procedure described $...

We describe the proximal method for minimization of convex functions. We review classical results, recent extensions, and interpretations of the proximal method that work in online and stochastic optimization settings.

We introduce the Variational Hölder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference. Unlike VB which typically involves maximization of a non-convex lower bound with respect to the variational parameters, the VH bound involves minimization of a convex upper bound to the intractable integral with respect to the variational parameters. Minimization of the...

Deployment is a critical issue affecting the quality of service of camera networks. The deployment aims at adopting the least number of cameras to cover the whole scene, which may have obstacles to occlude the line of sight, with expected observation quality. This is generally formulated as a non-convex optimization problem, which is hard to solve in polynomial time. In this paper, we propose a...