A remark on self-adjoint problems in the optimization of non-linear models
Abstract
This article considers optimization problems under non-linear partial differential equation (p.d.e.) constraints. It is assumed that the p.d.e. arises from minimizing a convex energy. We prove that the optimization problem is self-adjoint when the objective function is the dual energy. In other words, the differential of the objective function with respect to the optimization variable does not involve any adjoint state. This result generalizes the well-known fact that the so-called compliance is self-adjoint in the linear case. We also prove that in a large class of objective functions the dual energy is the only one which is self-adjoint.
Fields of Study & Subjects
Advanced Control Systems Optimization
Publication details
- Journal / source
- Journal of Optimization Theory and Applications
- Publisher
- Springer Science and Business Media LLC
- Volume
- 208
- Issue
- 3
- Publication date
- 18 February 2026
- Language
- EN