Distributed Optimisation with Linear Equality and Inequality Constraints using PDMM

In this article, we consider the problem of distributed optimisation of a separable convex cost function over a graph, where every edge and node in the graph could carry both linear equality and/or inequality constraints. We show how to modify the primal-dual method of multipliers (PDMM), originally designed for linear equality constraints,...

Covering grids with multiplicity

Given a finite grid in R², how many lines are needed to cover all but one point at least k times? Problems of this nature have been studied for decades, with a general lower bound having been established by Ball and Serra. We solve this problem for various types of grids, in particular showing the tightness of the Ball–Serra bound...

Safety Certification for Stochastic Systems via Neural Barrier Functions

Providing non-trivial certificates of safety for non-linear stochastic systems is an important open problem. One promising solution to address this problem is the use of barrier functions. Barrier functions are functions whose composition with the system forms a Martingale and enable the computation of the probability that the system stays...

Generalized Models of Sequential Decision-Making under Uncertainty

Sequential decision-making under uncertainty is an important branch of artificial intelligence research with a plethora of real-life applications. In this thesis, we generalize two fundamental properties of the decision-making process. First, we show that the theory on planning methods for finite spaces can be extended to infinite but countable...

Efficient reduction techniques for a large-scale Transmission Expansion Planning problem

The aim of Transmission Expansion Planning (TEP) studies is to decide which, where, and when new grid elements should be built in order to minimize the total system cost. The lumpiness of the investment decisions, together with the large size of the problem, make the problem very hard to solve. Consequently, methods should be put in place to...

An innovative design for left turn bicycles at continuous flow intersections

To improve the practical capacity of the continuous flow intersections (CFI)<br/>and eliminate the conflict between left-turn bicycles and through vehicles,<br/>an optimization design method for left-turn bicycles was proposed.<br/>The pre-stop line for through vehicles and the crossing passage for leftturn<br/>bicycles were set at the pre...

Maximum entropy estimation via Gauss-LP quadratures

We present an approximation method to a class of parametric integration problems that naturally appear when solving the dual of the maximum entropy estimation problem. Our method builds up on a recent generalization of Gauss quadratures via an infinite-dimensional linear program, and utilizes a convex clustering algorithm to compute an...