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Value function calculus and applications. (English) Zbl 1437.90150
Cheng, Jin (ed.) et al., Inverse problems and related topics. Extended versions of papers based on the international conference on inverse problems, Shanghai, China, October 12–14, 2018. In honor of Masahiro Yamamoto on the occasion of his 60th anniversary. Singapore: Springer. Springer Proc. Math. Stat. 310, 275-306 (2020).
Summary: 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.
For the entire collection see [Zbl 1442.35004].
MSC:
90C31 Sensitivity, stability, parametric optimization
49Q10 Optimization of shapes other than minimal surfaces
65J22 Numerical solution to inverse problems in abstract spaces
65K05 Numerical mathematical programming methods
49J35 Existence of solutions for minimax problems
49J40 Variational inequalities
Software:
PLCP; SQPlab
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References:
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