convex conic programming

Duality aspects in convex conic programming

  • Mária Trnovská
  • Jakub Hrdina
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    In this paper we study strong duality aspects in convex conic programming over general convex cones. It is known that the duality in convex optimization is linked with specific theorems of alternatives. We formulate and prove strong alternatives to the existence of the relative interior point in the primal (dual) feasible set. We analyze the … Read more

    An inexact proximal bundle method with applications to convex conic programming

  • Chek Beng Chua
  • Huiling Lin
    • Categories Convex and Nonsmooth Optimization, Global Optimization Tags , , , ,

    We present an inexact bundle method for minimizing an unconstrained convex sup-function with an open domain. Under some mild assumptions, we reformulate a convex conic programming problem as such problem in terms of the support function. This method is a first-order method, hence it requires much less computational cost in each iteration than second-order approaches … Read more