MOOSE Optimization Module: Physics-constrained Optimization

The MOOSE Optimization Module integrates optimization capabilities within the MOOSE framework, enabling efficient and accurate physics-constrained optimization. This module leverages automatic differentiation to compute Jacobians and employs an automatic adjoint formulation for gradient computation, significantly simplifying the implementation of optimization algorithms. The primary goal of this software is to provide a platform where analysts and researchers can rapidly prototype and explore new optimization algorithms tailored to their complex multiphysics problems without requiring them to be computational experts. By handling the aspects of adjoint problem formulation and gradient computation, the module allows users to focus on the optimization problem itself, thereby accelerating the development of more efficient designs and solutions.