quantum information

A more efficient reformulation of complex SDP as real SDP

  • Jie Wang
    • Categories Global Optimization Theory, Semi-definite Programming Tags , , , ,

    This note proposes a novel reformulation of complex semidefinite programs (SDPs) as real SDPs. As an application, we present an economical reformulation of complex SDP relaxations of complex polynomial optimization problems as real SDPs and derive some further reductions by exploiting structure of the complex SDP relaxations. Various numerical examples demonstrate that our new reformulation … Read more

    Conic Geometric Programming

  • Venkat Chandrasekaran
  • Parikshit Shah
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , , , , , ,

    We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as linear programs (LPs) and semidefinite programs (SDPs). A CGP consists of a linear objective function that is to be minimized subject to affine constraints, convex conic constraints, and upper bound constraints … Read more