Applied Mathematics, Optimization
Office: TA-3, Bldg 1690, Room 125
Mail Stop: B258
Phone: (505) 667-1078
The Power of Moments
For more information on this see here.
- Moments have incredible modeling power.
- Non Linearities become linear in the moment space.
- Positive polynomials can be used to compute moments efficiently.
- Information about the measure can be recovered from the knowledge of finitly many of its moments.
- since 2018 - Postdoc at T-5/CNLS, Los Alamos National Laboratory.
- 2015-2018 - Ph.D. at LAAS-CNRS and University Toulouse 3 Paul Sabatier, Toulouse, France.
- 2008-2016 - Staatsexamen (teaching degree), University of Konstanz, Germany.
- 2011-2015 - Diplom (M.S. Mathematics), University of Konstanz, Germany.
My research interests are focussing around algorithms and applications of the Generarlized Moment Problem (GMP) and Positive Polynomials.
The GMP is an infinite dimensional linear optimization problem on the space of (fintie, positive) Borel measures and has an incredible modelling power: to name only two recent applications, the GMP can describe solutions to hyperbolic PDEs as well as the probability of a semi-algebraic set. I love the flexibility of this problem formulation and am always keen on discovering new fields of application.
Positive Polynomials and more precisely Certificates for Non-Negativity are key to numerically approximate solutions to the GMP. Currently computing these certificates is quite costly and usually involves solving Semi-Definite Programs (SDP). In order to push forward applications of the GMP to real world applications, I investigate possibilities to reduce this computational burden by proposing alternative certificates that usually exploit some feature of the particular instance of the GMP such as algebraic or geometric properties.
Selected Recent Publications:
- Gopinath, S., Hijazi, H, Weisser, T., Nagarajan, H., Yetkin, M., Sundar, K., Bent, R.W., Towards Closing the AC-OPF Chapter, submitted, 2019.
- Weisser, T., Roald, L.A., Misra, S., Chance-Constrained Optimization for Non-Linear Network Flow Problems , submitted, 2018.
- Tacchi, M., Weisser, T., Lasserre, J.B., Henrion, D., Exploiting Sparsity for Semi-Algebraic Set Volume Computation , submitted, 2019.
- Marx, S., Pauwels, E., Weisser, T., Henrion, D. Lasserre, J.B., Tractable semi-algebraic approximation using Christoffel-Darboux kernel , submitted, 2019.
- Lasserre, J.B., Weisser, T., Representation of distributionally robust chance-constraints , Mathematical Programming, (),1-45, 2019.
- Marx, S., Weisser, T., Henrion, D., Lasserre, J.B., A moment approach for entropy solutions to nonlinear hyperbolic PDEs , Mathematical Control and Related Fields, 10(1), 113-140, 2020.
- Henrion D., Kruzik, M., Weisser, T., Optimal control problems with oscillations, concentrations and discontinuities , Automatica, 103, 159-165, 2019.
- Weisser, T., Lasserre, J.B., Toh, K.-C., Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity , Mathematical Programming Computation, 10, 1-32, 2018.
- Goerlach, P., Riener, C., Weisser, T., Deciding Positivity of Multisymmetric Polynomials , Journal of Symbolic Computation, 74, 603-616, 2015.
- MomentOpt: A julia package to model the Generalized Moment Problem
- BSOS: Polynomial Optimization with Bounded Sum-Of-Squares
- Weisser, T., Computing Approximations and Generalized Solutions using Moments and Positive Polynomials , Ph.D. thesis, University of Toulouse 3 Paul Sabatier, 2018.
- Weisser, T., Polynomial Inequalities arising from Triangles and Tetrahedra, Diploma thesis, University of Konstanz, 2014.