Port-Hamiltonian Optimization

The energy-balance form provides diagnostics for noise, port work, and discretization defects. Classical gradient-based optimizers are reviewed through a port-Hamiltonian lens. The continuous-time template includes canonical coupling, learned skew dynamics, learned positive semidefinite dissipation, and bounded port input. The local Hamiltonian combines the base objective, shaped potential, and kinetic energy. The implementation uses a semi-implicit first-order update for momentum and then position. The port-Hamiltonian structure separates landscape shaping, energy transport, dissipation, and active energy injection.