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Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and…
A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the "Thermodynamic Field Theory" (TFT). The aim of the work was to determine the nonlinear…
Understanding the feasible power flow region is of central importance to power system analysis. In this paper, we propose a geometric view of the power system loadability problem. By using rectangular coordinates for complex voltages, we…
A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the…
The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To…
We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical…
A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the…
We identify incompressible planar linear flows that are generalizations of the well known one-parameter family characterized by the ratio of in-plane extension to (out-of-plane) vorticity. The latter `canonical' family is classified into…
Fluid flow past one or more solid bodies is a fundamental problem of much practical importance. Standard solutions of simplified problems involving incompressible inviscid irrotational flow past common geometries such as circular cylinders…
To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along…
This work addresses the problem of risk-sensitive control for nonlinear systems with imperfect state observations, extending results for the linear case. In particular, we derive an algorithm that can compute local solutions with…
The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It…
The common linear optimal power flow (LOPF) formulation that underlies most transmission expansion planning (TEP) formulations uses bus voltage angles as auxiliary optimization variables to describe Kirchhoff's voltage law. As well as…
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
In the following article we consider the numerical approximation of the non-linear filter in continuous-time, where the observations and signal follow diffusion processes. Given access to high-frequency, but discrete-time observations, we…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…
This paper investigates the control of nonlinear systems using a piecewise linear approximation framework. The proposed approach combines a PID controller with locally linearized models obtained by partitioning the nonlinear function into…
We consider transport processes that are modeled by first order hyperbolic partial differential equations. Our goal is to find a full state feedback that makes a given reference profile locally asymptotically stable. To accomplish this we…
In this paper, we consider the problem of optimally coordinating the response of a group of distributed energy resources (DERs) in distribution systems by solving the so-called optimal power flow (OPF) problem. The OPF problem is concerned…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…