self-dual embedding

Solving conic optimization problems via self-dual embedding and facial reduction: a unified approach

  • Erling D. Andersen
  • Henrik A. Friberg
  • Frank Permenter
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    We establish connections between the facial reduction algorithm of Borwein and Wolkowicz and the self-dual homogeneous model of Goldman and Tucker when applied to conic optimization problems. Specifically, we show the self-dual homogeneous model returns facial reduction certificates when it fails to return a primal-dual optimal solution or a certificate of infeasibility. Using this observation, … Read more

    On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization

  • Robert M. Freund
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , , , ,

    There is a natural norm associated with a starting point of the homogeneous self-dual (HSD) embedding model for conic convex optimization. In this norm two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of epsilon-optimal solutions, and (ii) the maximum distance of epsilon-optimal solutions to the … 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