Value Function Calculus and Applications

In this paperIto, K. the sensitivity analysis is discussed for the parameter-dependent optimization and constraint optimization. The sensitivity of the optimality value function with respect to the change in parameters plays a significant role in the inverse problems and the optimization theory, including economics, finance, the Hamilton–Jacobi theory, the inf-sup duality and the topological design and the bi-level optimization. We develop the calculus for the value function and present its applications in the variational calculus, the bi-level optimization and the optimal control and optimal design, shape calculus and inverse problems.