A primal-dual potential reduction method for problems involving matrix inequalities

  title={A primal-dual potential reduction method for problems involving matrix inequalities},
  author={Lieven Vandenberghe and Stephen P. Boyd},
  journal={Math. Program.},
We describe a potential reduction method for convex optimization problems involving matrix inequalities. The method is based on the theory developed by Nesterov and Nemirovsky and generalizes Gonzaga and Todd's method for linear programming. A worst-case analysis shows that the number of iterations grows as the square root of the problem size, but in practice it appears to grow more slowly. As in other interior-point methods the overall computational effort is therefore dominated by the least… CONTINUE READING
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