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math.OC2026
Nested Extremum Seeking Converges to Stackelberg Equilibrium
Brad Ratto, Alan Williams, Miroslav KrstiÄ +2
The nested Extremum Seeking (nES) algorithm is a model-free optimization method that has been shown to converge to a neighborhood of a Nash equilibrium. In this work, we demonstrat…
math.OC2025
Generalized Multi-Constraint Extremum Seeking
Alan Williams, Jorge Cortés, Alexander Scheinker
We generalize the Safe Extremum Seeking algorithm to address the minimization of an unknown objective function subject to multiple unknown inequality and equality constraints, rely…
math.OC2024
QP Based Constrained Optimization for Reliable PINN Training
Alan Williams, Christopher Leon, Alexander Scheinker
Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for integrating physics-based constraints and data to address forward and inverse problems in machine learn…