intrinsic core

Duality assertions in vector optimization w.r.t. relatively solid convex cones in real linear spaces

  • Christian Günther
  • Bahareh Khazayel
  • Christiane Tammer
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization Tags , , , , , , ,

    We derive duality assertions for vector optimization problems in real linear spaces based on a scalarization using recent results concerning the concept of relative solidness for convex cones (i.e., convex cones with nonempty intrinsic cores). In our paper, we consider an abstract vector optimization problem with generalized inequality constraints and investigate Lagrangian type duality assertions … Read more

    Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces

  • Christian Günther
  • Bahareh Khazayel
  • Christiane Tammer
    • Categories Convex and Nonsmooth Optimization, Other Topics Tags , , , , , , ,

    In vector optimization, it is of increasing interest to study problems where the image space (a real linear space) is preordered by a not necessarily solid (and not necessarily pointed) convex cone. It is well-known that there are many examples where the ordering cone of the image space has an empty (topological / algebraic) interior, … Read more

    On the intrinsic core of convex cones in real linear spaces

  • Ali P. Farajzadeh
  • Christian Günther
  • Christiane Tammer
  • Bahareh Khazayel
    • Categories Convex Optimization, Multi-Criteria Optimization Tags , , , , , , ,

    Convex cones play an important role in nonlinear analysis and optimization theory. In particular, specific normal cones and tangent cones are known to be convex cones, and it is a crucial fact that they are useful geometric objects for describing optimality conditions. As important applications (especially, in the fields of optimal control with PDE constraints, … Read more