Publications


Submitted Papers and Preprints

  1. 'Exposed extreme rays of the SONC cone'
    with H. Liao and V. Roshchina; see arXiv:2512.00348, submitted for publication.


Published and Accepted Papers

  1. 'Least multivariate Chebyshev polynomials on diagonally determined domains'
    with S. Foucart, M. Joldes, E. de Klerk, J.-B. Lasserre, and Y. Xu; SIAM Journal of Applied Algebra and Geometry 10 (2026), no. 2, 450-466; see arXiv:2405.19219.

  2. 'Multiple typical ranks in matrix completion'
    with R. Krone; Linear Algebra and its Applications 710 (2025), 165-182; see arXiv:2010.09777.

  3. 'Douglas-Rachford is the best projection method in its family'
    with M. Dao, H. Liao, and V. Roshchina; Optimization, 1-23 (2024); see arXiv:2310.17077.

  4. 'Optimization-Aided Construction of Multivariate Chebyshev Polynomials' with S. Foucart, M. Joldes, E. de Klerk, J.-B. Lasserre, and Y. Xu; Journal of Approximation Theory 305 (2025), Paper No. 106116; see arXiv:2405.10438 and supplement.

  5. 'Study of the Cone of Sums of Squares plus Sums of Nonnegative Circuit Forms' with S. Kuhlmann and M. Schick; Advances in Geometry 25 (2025), no. 1, 127-146; see arXiv:2305.14848.

  6. 'Time-Varying Semidefinite Programming: Path Following a Burer-Monteiro Factorization'
    with A. Bellon, V. Kungurtsev, J. Mareček, and A. Uschmajew; SIAM Journal on Optimization, 34 (2024), no. 1, 1-26; see arXiv:2210.08387.

  7. 'Kronecker Product Approximation of Operators in Spectral Norm via Alternating SDP'
    with A. Uschmajew and V. Chandrasekaran; SIAM Journal on Matrix Analysis and Applications, 44 (2023), no. 4, 1693-1708; see arXiv:2207.03186.

  8. 'Algebraic Optimization of Sequential Decision Problems'
    with M. Garrote-López, G. Montúfar, J. Müller, and K. Rose; Journal of Symbolic Computation 121 (2024), Paper No. 102241, 19 pp; see the online published version here and see arXiv:2211.09439.
    Was accepted for a talk at "MEGA 2022".

  9. 'Algebraic Perspectives on Signomial Optimization'
    with R. Murray; SIAM Journal of Applied Algebra and Geometry 6 (2022), no. 4, 650-684; see arXiv:2107.00345.

  10. 'Fostering Proving Skills in Upper-Division Mathematics Classes through Peer Feedback Assignments'
    with A. Knop, L. Klement, and P. Hadjipieris; Transformative Dialogues: Teaching and Learning Journal, 14 (3), (2022); see Review Paper.

  11. 'Separability of Hermitian Tensors and PSD Decompositions'
    with J. Nie and Z. Yang; Linear and Multilinear Algebra 70 (2022), no. 21, 6581-6608; see arXiv:2011.08132.

  12. 'Optimization over the Boolean Hypercube via Sums of Nonnegative Circuit Polynomials'
    with A. Kurpisz and T. de Wolff; Foundations of Computational Mathematics 22 (2022), no. 2, 365-387; see arXiv:1802.10004.

  13. 'Real Zeros of SONC Polynomials'
    Journal of Pure and Applied Algebra 225 (2021), no. 7, Paper No. 106602, 23 pp; (special issue of the "Arctic Applied Algebra Conference"); see the online published version here and see arXiv:1909.06707.

  14. 'The dual cone of sums of nonnegative circuit polynomials'
    with H. Naumann and T. Theobald; Advances in Geometry 21 (2021), no. 2, 227-236; see arXiv:1809.07648.
    Was accepted for a talk at "MEGA 2019".

  15. 'An Approach to Constrained Polynomial Optimization via Nonnegative Circuit Polynomials and Geometric Programming'
    with S. Iliman and T. de Wolff; Journal of Symbolic Computation 91 (2019), 149-172; (special issue of "MEGA 2017"); see arXiv:1602.06180.

  16. 'A Positivstellensatz for Sums of Nonnegative Circuit Polynomials'
    with S. Iliman and T. de Wolff; SIAM Journal of Applied Algebra and Geometry 1 (2017), no. 1, 536-555; see arXiv:1607.06010.
    Was accepted for a talk at "MEGA 2017".


Conference Publications

  1. 'Global Optimization via the Dual SONC Cone and Linear Programming'
    with J. Heuer, H. Naumann, and T. de Wolff; Proceedings of ISSAC 2020, Kalamata, Greece, July 20-23, 2020 (virtual conference due to COVID-19) (I. Z. Emiris, and L. Zhi (eds.)), ACM, (2020),138 - 145; see arXiv:2002.09368.
    Was also accepted for a talk at "MTNS 2020".

  2. 'Optimization over the Boolean Hypercube via Sums of Nonnegative Circuit Polynomials'
    with A. Kurpisz and T. de Wolff; 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, Liverpool, UK, August 27-31, 2018, (I. Potapov, P. G. Spirakis, and J. Worrell, eds.), LIPIcs, 117, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, (2018), 82:1-82:17; see arXiv:1802.10004.
    Was also accepted for a talk at "FLoC '18".


Reports

  1. 'Theoretical and Practical Applications of Signomial Rings to Polynomial Optimization'
    Oberwolfach Reports, vol. 21, no. 3, 2024; for the workshop "Polynomial Optimization for Nonlinear Dynamics: Theory, Algorithms, and Applications".

  2. 'Algebraic Perspectives on Signomial Optimization'
    Oberwolfach Reports, vol. 20, no. 1, 2023; for the workshop "Real Algebraic Geometry with a View toward Koopman Operator Methods".

  3. 'Global Optimization via the Dual SONC Cone and Linear Programming'
    Oberwolfach Reports, vol. 17, no. 1, 2020; for the workshop "Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability".


Theses