self-concordant barrier functions

Dual certificates of primal cone membership

  • Joonyeob Lee
  • Dávid Papp
  • Anita Varga
    • Categories Cone Programming, Convex Optimization, Semi-definite Programming Tags , , , , ,

    We discuss optimization problems over convex cones in which membership is difficult to verify directly. In the standard theory of duality, vectors in the dual cone \(K^*\) are associated with separating hyperplanes and interpreted as certificates of non-membership in the primal cone \(K\). Complementing this perspective, we develop easily verifiable certificates of membership in \(K\) … Read more

    A New Self-Dual Embedding Method for Convex Programming

  • Shuzhong Zhang
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    In this paper we introduce a conic optimization formulation for inequality-constrained convex programming, and propose a self-dual embedding model for solving the resulting conic optimization problem. The primal and dual cones in this formulation are characterized by the original constraint functions and their corresponding conjugate functions respectively. Hence they are completely symmetric. This allows for … Read more