Johannes Milz

Assistant Professor

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  • Johannes Milz Google Scholar

Education

  • Ph.D. Applied Mathematics (2021), Technical University of Munich
  • M.S. Mathematics in Science and Engineering (2017), Technical University of Munich
  • B.S. Applied Mathematics (2015), Technical University of Munich

Expertise

  • Optimization

About

Johannes Milz is an Assistant Professor in the H. Milton Stewart School of Industrial and Systems Engineering. His research focuses on optimization under uncertainty and optimal control of uncertain systems, with a strong emphasis on sustainability applications. By addressing large-scale optimization challenges in physics-based models under uncertainty, he aims to contribute to the development of sustainable energy systems, such as renewable tidal energy farms. Dr. Milz is also dedicated to open science; he develops reproducible numerical simulations and shares them publicly, making his results accessible to a broad group of researchers and practitioners. Prior to joining ISyE, he was a postdoctoral researcher at the Technical University of Munich, where he earned his Ph.D. in Applied Mathematics in 2021. He is a Brook Byers Institute for Sustainable Systems (BBISS) Faculty Fellow for 2025--2027.

Research

Dr. Milz develops reliable optimization methods for decision-making under uncertainty, with an emphasis on complex, physics-based models. His work spans risk-aware formulations, scalable algorithms for PDE- and dynamical-system constraints, and theory that links modeling and discretization error to optimization performance, with an emphasis on reproducible software.

Teaching

Dr. Milz teaches deterministic, nonlinear, and advanced optimization. He emphasizes model formulation, principled algorithmic understanding, and computation, using case-study openings, guided materials, and frequent low-stakes assessments to support learning.

Representative Publications

  • Olena Melnikov and Johannes Milz. Risk-averse optimization using randomized quasi-Monte Carlo methods. J. Optim. Theory Appl., 206(1):14, 2025. doi:10.1007/s10957-025-02693-6
  • Danlin Li and Johannes Milz. Criticality measure-based error estimates for infinite dimensional optimization. SIAM J. Numer. Anal., 63(1):193–213, 2025. doi:10.1137/24M1647023
  • Johannes Milz. Consistency of sample-based stationary points for infinite-dimensional stochastic optimization. SIAM J. Optim., 35(1):42–61, 2025. doi:10.1137/23M1600608
  • Johannes Milz and Thomas M. Surowiec. Asymptotic consistency for nonconvex risk-averse stochastic optimization with infinite dimensional decision spaces. Math. Oper. Res., 49(3):1403–1418, 2024. doi:10.1287/moor.2022.0200
  • Johannes Milz and Michael Ulbrich. Sample size estimates for risk-neutral semilinear PDE-constrained optimization. SIAM J. Optim., 34(1):844–869, 2024. doi:10.1137/22M1512636
  • Johannes Milz. Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs. SIAM/ASA J. Uncertain. Quantif., 11(4):1139–1163, 2023. doi:10.1137/22M1503889
  • Johannes Milz. Consistency of Monte Carlo estimators for risk-neutral PDE-constrained optimization. Appl. Math. Optim., 87(57), 2023. doi:10.1007/s00245-023-09967-3
  • Johannes Milz. Sample average approximations of strongly convex stochastic programs in Hilbert spaces. Optim. Lett., 17:471–492, 2023. doi:10.1007/s11590-022-01888-4
  • Johannes Milz and Michael Ulbrich. An approximation scheme for distributionally robust PDE-constrained optimization. SIAM J. Control Optim., 60(3):1410–1435, 2022. doi:10.1137/20M134664X
  • Johannes Milz and Michael Ulbrich. An approximation scheme for distributionally robust nonlinear optimization. SIAM J. Optim., 30(3):1996–2025, 2020. doi:10.1137/19M1263121