An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) function nor logarithmic barrier function, the primaldual IPMs based on this kernel function enjoy the worst case iteration bound O (√ n log n log n/ϵ ) for the large-update methods with the special choice of its parameters. This bound coincides to the so far best known complexity results obtained from SR kernel functions for linear and semidefinite optimization problems. Finally, some numerical issues regarding the practical performance of the new proposed kernel function are reported.