Parametric Nonlinear Optimization: Stability of Stationary Solutions and Some Applications
Diethard Klatte · 1992
For perturbed nonlinear programs (NLP) with twice continuously differentiable data, there is a well-developed theory of solution stability based on second-order conditions (SOC), cf., e.g., [2,3,9,11,12]. Motivations for this theory are manifold. For example, convergence analysis of optimization methods, the study of incorrect models, decomposition techniques, semi-infinite programming and input-output modelling lead to the question whether a stationary solution or a local/global minimizer of a NLP behaves stable in some sense. In the following, we give 2nd-order sufficient stability conditions for NLP, allowing some non-smoothness of initial data. The applications mentioned in the title particulary concern iterated local minimization and semi-infinite programming. For brevity of presentation, we refer in this connection only to the recent papers [5] and [6]. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.