Mathematical optimization is one of the cornerstones of modern engineering research and
practice. Yet, throughout all application domains, mathematical optimization is, for the most …

This article considers the problem of designing a continuous-time dynamical system that
solves a constrained nonlinear optimization problem and makes the feasible set forward …

We consider unconstrained minimization of smooth convex functions. We propose a novel
variational perspective using forced Euler-Lagrange equation that allows for studying high …

We consider the problem of minimizing a non-convex function over a smooth manifold M.
We propose a novel algorithm, the Orthogonal Directions Constrained Gradient Method …

In this chapter, we identify fundamental geometric structures that underlie the problems of
sampling, optimization, inference, and adaptive decision-making. Based on this …

In distributed optimization (DO), the designed algorithms are expected to have a fast
convergence rate but less computation cost. Moreover, the boundedness of the control …

Global infrastructure robustness and local transport efficiency are critical requirements for
transportation networks. However, since passengers often travel greedily to maximize their …

In this paper, we develop a new algorithm, Annealed Skewed SGD-AskewSGD-for training
deep neural networks (DNNs) with quantized weights. First, we formulate the training of …

In many applications, learning systems are required to process continuous non-stationary
data streams. We study this problem in an online learning framework and propose an …

This paper considers the problem of designing a dynamical system to solve constrained
optimization problems in a distributed way and in an anytime fashion (ie, such that the …