Lucas Gamertsfelder

Lucas Gamertsfelder

Researcher in applied mathematics

Talks and presentations

The Effective Countable Generalized Moment Problem

October 08, 2025

Talk, Real Algebraic Geometry and Interactions, Nice, France

This talk presented recent convergence rates for the moment-SOS relaxations Generalized Moment Problem (GMP). Under Archimedean, S-fullness, and dual attainment conditions, one derives geometry-adaptive bounds for GMPs with countable moment constraints. The results ensure convergence of optimal values, feasibility sets in Hausdorff distance, and optimizers in the weak* topology. Applications of these relaxations to symmetric tensor decomposition were presented.

Moment-SoS relaxations of the generalized moment problem and applications

November 13, 2024

Talk, AROMATH Annual Workshop 2024, Sophia Antipolis, France

This talk described an upcoming work on the application of moment-SOS hierarchies to the generalized moment problem. In particular, we recover the convergence rates of the hierarchies of relaxations in both the optima and the feasibility sets. Applications in minimal symmetric tensor decomposition and long-run optimal control were presented.

Convergence of occupational measures sets of discrete-time stochastic control systems, with applications to averaging of hybrid systems

January 20, 2022

Talk, Inria Sophia Antipolis, NEO Team Workshop, Sophia Antipolis, France

This talk concerned recent results showing that the set of random occupational measures generated by the state-control trajectories of a discrete-time stochastic system as well as the set of their mathematical expectations converge to a non-random, convex and compact set. We apply these results to the averaging a hybrid system with a slow continuous-time component and a fast discrete-time component. It is shown that the solutions of the hybrid system are approximated by the solutions of a differential inclusion. The novelty of our results is that we allow the state-control space of the fast component to be non-denumerable. See the corresponding article here.

LP Based Bounds for Cesaro and Abel Limits of the Optimal Values in Non-Ergodic Stochastic Systems

June 29, 2021

Talk, European Control Conference, Virtual

In this talk, we discussed asymptotic properties of problems of control of stochastic discrete time systems (also known as Markov decision processes) with time averaging and time discounting optimality criteria. It demonstrated recent results that the Cesaro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinite-dimensional linear programming problem and its dual. See the corresponding article here.

LP Based Bounds for Cesaro and Abel Limits of the Optimal Values in Non-Ergodic Stochastic Systems

December 10, 2020

Talk, 64th Annual AustMS Meeting, Virtual

In this talk, we discussed asymptotic properties of problems of control of stochastic discrete time systems (also known as Markov decision processes) with time averaging and time discounting optimality criteria. It demonstrated recent results that the Cesaro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinite-dimensional linear programming problem and its dual. See the corresponding article here.