Kevin Sturm - First-order differentiability properties of a class of equality constrained optimal value functions with applications

jnsao:6034 - Journal of Nonsmooth Analysis and Optimization, December 17, 2020, Volume 1 - https://doi.org/10.46298/jnsao-2020-6034
First-order differentiability properties of a class of equality constrained optimal value functions with applications

Authors: Kevin Sturm

In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to the parameter. Target applications are nonconvex objective functions with equality constraints arising in optimal control and shape optimisation. The theorem makes use of the averaged adjoint approach in conjunction with the variational approach of Kunisch, Ito and Peichl. We provide two examples of our abstract result: (a) a shape optimisation problem involving a semilinear partial differential equation which exhibits infinitely many solutions, (b) a finite dimensional quadratic function subject to a nonlinear equation.


Volume: Volume 1
Section: Original research articles
Published on: December 17, 2020
Submitted on: January 16, 2020
Keywords: Mathematics - Optimization and Control


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