Ali Mohammad-Nezhad

Quadratic convergence to the optimal solution of second-order conic optimization without strict complementarity

  • Ali Mohammad-Nezhad
  • Tamás Terlaky
    • Categories Second-Order Cone Programming

    Under primal and dual nondegeneracy conditions, we establish the quadratic convergence of Newton’s method to the unique optimal solution of second-order conic optimization. Only very few approaches have been proposed to remedy the failure of strict complementarity, mostly based on nonsmooth analysis of the optimality conditions. Our local convergence result depends on the optimal partition … Read more

    A rounding procedure for semidefinite optimization

  • Ali Mohammad-Nezhad
  • Tamás Terlaky
    • Categories Semi-definite Programming Tags , , ,

    Recently, Mohammad-Nezhad and Terlaky studied the identification of the optimal partition for semidefinite optimization. An approximation of the optimal partition was obtained from a bounded sequence of solutions on, or in a neighborhood of the central path. Here, we use the approximation of the optimal partition in a rounding procedure to generate an approximate maximally … Read more

    On the identification of optimal partition for semidefinite optimization

  • Ali Mohammad-Nezhad
  • Tamás Terlaky
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming, Semi-definite Programming

    The concept of the optimal partition was originally introduced for linear optimization and linear complementarity problems and subsequently extended to semidefinite optimization. For linear optimization and sufficient linear complementarity problems, from a central solution sufficiently close to the optimal set, the optimal partition and a maximally complementary optimal solution can be identified in strongly polynomial … Read more

    A polynomial primal-dual affine scaling algorithm for symmetric conic optimization

  • Ali Mohammad-Nezhad
  • Tamás Terlaky
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    The primal-dual Dikin-type affine scaling method was originally proposed for linear optimization and then extended to semidefinite optimization. Here, the method is generalized to symmetric conic optimization using the notion of Euclidean Jordan algebras. The method starts with an interior feasible but not necessarily centered primal-dual solution, and it features both centering and reducing the … Read more