strict feasibility

Superlinear convergence of an interior point algorithm on linear semi-definite feasibility problems with application to linear matrix inequalities

  • Chee-Khian Sim
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , , ,

    In the literature, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual and the NT direction, to solve semi-definite programs (SDPs) can be shown by (i) assuming that the given SDP is nondegenerate and modifying these algorithms [10], or (ii) considering special classes of SDPs, such … Read more

    Local Analysis of the Feasible Primal-Dual Interior-Point Method

  • R. Silva
  • Luis Nunes Vicente
  • J. Soares
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In this paper we analyze the rate of local convergence of the Newton primal-dual interior-point method when the iterates are kept strictly feasible with respect to the inequality constraints. It is shown under the classical conditions that the rate is q-quadratic when the functions associated to the inequality constraints define a locally concave feasible region. … Read more