Convergence of non-smooth descent methods using the Kurdyka-\L ojasiewicz inequality.

Dominikus Noll (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We investigate convergence of subgradient-oriented descent methods in non-smooth non-convex optimization. We prove convergence in the sense of subsequences for functions with a strict standard model, and we show that convergence to a single critical point may be guaranteed, if the strong Kurdyka-Łojasiewicz condition is added. We show by way of an example that the Kurdyka-Łojasiewicz inequality alone is not sufficient to prove convergence to critical points.

Mots clés: subgradient-oriented descent method; Non-smooth non-convex optimization; upper C 1 function; lower C 1 function; Kurdyka-Łojasiewicz inequality; model; strict

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Dominikus Noll. Convergence of non-smooth descent methods using the Kurdyka-\L ojasiewicz inequality.. Journal of Optimization Theory and Applications, 2014, 160 (2), pp.553-572. ⟨10.1007/s10957-013-0391-8⟩. ⟨hal-01868363⟩