no code implementations • 23 Mar 2023 • Hengyue Liang, Buyun Liang, Le Peng, Ying Cui, Tim Mitchell, Ju Sun
Taking advantage of PWCF and other existing numerical algorithms, we further explore the distinct patterns in the solutions found for solving these optimization problems using various combinations of losses, perturbation models, and optimization algorithms.
no code implementations • 3 Oct 2022 • Buyun Liang, Tim Mitchell, Ju Sun
Imposing explicit constraints is relatively new but increasingly pressing in deep learning, stimulated by, e. g., trustworthy AI that performs robust optimization over complicated perturbation sets and scientific applications that need to respect physical laws and constraints.
no code implementations • 2 Oct 2022 • Hengyue Liang, Buyun Liang, Ying Cui, Tim Mitchell, Ju Sun
Empirical evaluation of deep learning models against adversarial attacks entails solving nontrivial constrained optimization problems.
1 code implementation • 27 Nov 2021 • Buyun Liang, Tim Mitchell, Ju Sun
GRANSO is among the first optimization solvers targeting general nonsmooth NCVX problems with nonsmooth constraints, but, as it is implemented in MATLAB and requires the user to provide analytical gradients, GRANSO is often not a convenient choice in machine learning (especially deep learning) applications.
no code implementations • 4 Mar 2021 • Manuela Hund, Tim Mitchell, Petar Mlinarić, Jens Saak
In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad class of parametric linear time-invariant systems.
Optimization and Control Numerical Analysis Systems and Control Systems and Control Numerical Analysis 15A24, 46N10, 65K05, 65Y20, 93A15, 93B40
no code implementations • 2 Oct 2019 • Tim Mitchell
Divide-and-conquer techniques have been proposed that reduce the work complexity to $\mathcal{O}(n^4)$ on average and $\mathcal{O}(n^5)$ in the worst case, but these variants are nevertheless still very expensive and can be numerically unreliable.
Optimization and Control Numerical Analysis Numerical Analysis