Event № 360
We focus on convergence of numerical schemes for non-smooth non-convex optimization in finite dimension. In this realm, most results are given for "prox-friendly" data: the non-smooth part is simple enough to be handled through efficiently computable operators. This excludes many applications for which dedicated methods have been proposed. We focus on Sequential Quadratic Programming ideas (SQP) for general Non-Linear Programs (NLP). Despite their widespread usage, these methods lack satisfactory convergence analysis. This work constitutes a step toward obtaining such theoretical guarantees.The core algorithmic feature is the sequential minimization of tractable "tangent" upper-approximation models. This is typical of the SQP framework. Under semialgebraicity of the data, we propose an original convergence analysis for such processes. This is applied to analyze asymptotic properties of the Moving Ball Method (Auslender-Shefi-Teboulle 2010) and the Extended Sequential Quadratic Method (Auslender 2013). This work was conducted in collaboration with Jerome Bolte (Toulouse 1, France). The presentation is based on the preprint http://arxiv.org/pdf/1409.8147.pdf.