large sparse problems

A Stable Iterative Method for Linear Programming

  • Maria Gonzalez-Lima
  • Hua Wei
  • Henry Wolkowicz
    • Categories Linear Programming Tags , ,

    This paper studies a new primal-dual interior/exterior-point method for linear programming. We begin with the usual perturbed primal-dual optimality equations $F_\mu(x,y,z)=0$. Under nondegeneracy assumptions, this nonlinear system is well-posed, i.e. it has a nonsingular Jacobian at optimality and is not necessarily ill-conditioned as the iterates approach optimality. We use a simple preprocessing step to eliminate … Read more

    Simple Efficient Solutions for Semidefinite Programming

  • Henry Wolkowicz
    • Categories Combinatorial Optimization, Nonlinear Systems and Least-Squares, Semi-definite Programming Tags , , , , ,

    This paper provides a simple approach for solving a semidefinite program, SDP\@. As is common with many other approaches, we apply a primal-dual method that uses the perturbed optimality equations for SDP, $F_\mu(X,y,Z)=0$, where $X,Z$ are $n \times n$ symmetric matrices and $y \in \Re^n$. However, we look at this as an overdetermined system of … Read more