Georg Still

Genericity in linear algebra and analysis with applications to optimization

  • Georg Still
    • Categories Nonlinear Optimization Tags ,

    This report gives a concise overview into genericity results for sets of matrices, linear and nonlinear equations as well as for unconstrained and constrained optimization problems. We present the generic behavior of non-parametric problems and parametric families of problems. The genericity analysis is based on results from differential geometry, in particular transversality theorems. ArticleDownload View … Read more

    Lectures on Parametric Optimization: An Introduction

  • Georg Still
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , ,

    The report aims to provide an overview over results from Parametric Optimization which could be called classical results on the subject. Parametric Optimization considers optimization problems depending on a parameter and describes how the feasible set, the value function, and the local or global minimizers of the program depend on changes in the parameter. After … Read more

    The Slater condition is generic in linear conic programming

  • Mirjam Dür
  • Georg Still
  • Bolor Jargalsaikhan
    • Categories Linear, Cone and Semidefinite Programming, Semi-infinite Programming

    We call a property generic if it holds for almost all problem instances. For linear conic problems, it has been shown in the literature that properties like uniqueness, strict complementarity or nondegeneracy of the optimal solution are generic under the assumption that Slater’s condition is fulfilled. The possibility that Slater’s condition generically fails has not … Read more