6 papers · 1 filter
Variational Analysis in the Wasserstein Space
Nicolas Lanzetti, Antonio Terpin, Florian Dörfler
We study optimization problems whereby the optimization variable is a probability measure. Since the space of probability measures is not a vector space, many classical methods for…
Distributionally Robust Linear Quadratic Gaussian Regulator with Stationary Distributions
Alain Schöbi, Nicolas Lanzetti, Florian Dörfler +2
We study the Linear Quadratic Gaussian regulation problem in the face of worst-case noise distributions when these are mutually independent, zero-mean, stationary, and within a rad…
Sparse optimal control in the Wasserstein space
Enrico Sartor, Florian Dörfler, Nicolas Lanzetti
We study sparse optimal control of a non-local continuity equation, where the goal is to steer a distribution via finitely many controllable agents or actuators. This model arises…
Hedging against Black Swans in Day-Ahead Energy Markets
Liviu Aolaritei, Boubacar Bangoura, Saverio Bolognani +2
Renewable generators must commit to day-ahead market bids despite uncertainty in both production and real-time prices. While forecasts provide valuable guidance, rare and unpredict…
First-order Conditions for Optimization in the Wasserstein Space
Nicolas Lanzetti, Saverio Bolognani, Florian Dörfler
We study first-order optimality conditions for constrained optimization in the Wasserstein space, whereby one seeks to minimize a real-valued function over the space of probability…
Dynamic Programming in Probability Spaces via Optimal Transport
Antonio Terpin, Nicolas Lanzetti, Florian Dörfler
We study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the…