Nonlinear Error Bounds via a Change of Function

Dominique Azé (1) , Jean-Noël Corvellec (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations

This work can be seen as a sequel to our previous paper, which dealt with local nonlinear error bounds for lower semicontinuous functions on complete metric spaces, based on estimates of the strong slope of the function through the distance to a sublevel set. Here, we consider estimates of the strong slope through the values of the function, and we provide characterizations of nonlinear local and global error bounds that are again obtained by a reduction to the linear case. Our main tool is a simple chain rule for the strong slope. We provide several examples showing that recent results in the literature can be recaptured from our general framework.

Mots clés: Asymptotically well-behaved functions; Descent methods in optimization; Nonlinear error bounds

Domaines: Mathématiques [math]

Dominique Azé, Jean-Noël Corvellec. Nonlinear Error Bounds via a Change of Function. Journal of Optimization Theory and Applications, 2016, pp.9-32. ⟨10.1007/s10957-016-1001-3⟩. ⟨hal-01368648⟩