Abstract
In this paper 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.
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Ito, K. (2020). Value Function Calculus and Applications. In: Cheng, J., Lu, S., Yamamoto, M. (eds) Inverse Problems and Related Topics. ICIP2 2018. Springer Proceedings in Mathematics & Statistics, vol 310. Springer, Singapore. https://doi.org/10.1007/978-981-15-1592-7_13
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DOI: https://doi.org/10.1007/978-981-15-1592-7_13
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