geometric conic optimization problem

Exact SDP relaxations for a class of quadratic programs with finite and infinite quadratic constraints

  • Naohiko Arima
  • Sunyoung Kim
  • Masakazu Kojima
    • Categories Cone Programming, Semi-definite Programming Tags , , ,

    We investigate exact semidefinite programming (SDP) relaxations for the problem of minimizing a nonconvex quadratic objective function over a feasible region defined by both finitely and infinitely many nonconvex quadratic inequality constraints (semi-infinite QCQPs). Sufficient conditions for the exactness of SDP relaxations for QCQPs with finitely many constraints have been extensively studied, notably by Argue … Read more

    Further Development in Convex Conic Reformulation of Geometric Nonconvex Conic Optimization Problems

  • Naohiko Arima
  • Sunyoung Kim
  • Masakazu Kojima
    • Categories Global Optimization, Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , , , ,

    A geometric nonconvex conic optimization problem (COP) was recently proposed by Kim, Kojima and Toh asa unified framework for convex conic reformulation of a class of quadratic optimization problems and polynomial optimization problems. The nonconvex COP minimizes a linear function over the intersection of a nonconvex cone K, a convex subcone J of the convex … Read more