Continuous differentiability of the signum function and Newton's method for bang-bang control

2025/09/29 by Wachsmuth, Daniel, Wachsmuth, Gerd
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2509.24829

Abstract

We investigate bang-bang control problems and the possibility to apply Newton's method to solve such kind of problems numerically. To this end, we show that the signum function is Fréchet differentiable between appropriate function spaces. Numerical experiments show the applicability of the resulting method.

Citations

• Adaptive finite element method for an unregularized semilinear optimal control problem
• A globalized inexact semismooth Newton method for strongly convex optimal control problems
• A posteriori error estimates for a bang-bang optimal control problem
• No-gap second-order conditions for minimization problems in spaces of measures
• On fast convergence rates for generalized conditional gradient methods with backtracking stepsize
• Variational discretization of a control-constrained parabolic bang-bang optimal control problem
• Tikhonov regularization of control-constrained optimal control problems
• Sobolev embeddings, extensions and measure density condition
• Analytic extensions of differentiable functions defined in closed sets

Related

• Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems
• Solving Bang-Bang Problems Using The Immersed Interface Method and Integer Programming
• Stability for Bang-Bang Control Problems of Partial Differential\n Equations
• Typical dynamics of Newton's method
• Stability and genericity of bang-bang controls in affine problems