Computational Aspects for Gradient-Based Optimization Methods for Sensitivity Analysis or Optimal Control Problems
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In gradient-based optimization of nonlinear dynamical systems, the dominant computational burden arises from gradient evaluation. Optimization packages usually provide gradients via numerical differentiation - usually determined by finite differences. The complex-step alternative can be used to mitigate issues with very small perturbations. Both numerical approaches require an additional solution of the system for each gradient entry. Analytical gradients avoid this cost but require more extensive derivation and implementation. Direct differentiation and the adjoint method are two widely applied analytical techniques. Existing comparative studies for different gradient computation strategies remain limited and formulation-dependent. This work aims to compare computational times and function-evaluation counts and to clarify the optimal application domains for the various gradient computation strategies across different formulations and parametrization.
