Extending Mehrotra and Gondzio Higher Order Methods to
Mixed Semidefinite-Quadratic-Linear Programming
Jean-Pierre Haeberly, Madhu Nayakkankuppam and Michael Overton
We discuss extensions of Mehrotra's higher order corrections
scheme and Gondzio's multiple centrality corrections scheme tomixed semidefinite-quadratic-linear programming (SQLP).
These extensions have been included in a solver forSQLP written in C and based on LAPACK.
The code implements a primal--dual path--following algorithm for
solving SQLP problems based on the XZ+ZX search direction and
Mehrotra's predictor--corrector method.
We present benchmarks showing that the use of the higher orderschemes yields substantial reductions in both the number of
iterations and the running time of the algorithm, and also
improves its robustness.
To appear in Optimization Methods and Software.