Penalty/Barrier Multiplier Algorithm for Semidefinite Programming: Dual Bounds and Implementation

Leonid Mosheyev and Michael Zibulevsky

We present generalization of penalty/barrier and Augmented Lagrangian algorithms for semidefinite programming. It allows to use, among others, logarithmic, shifted logarithmic, exponential and a very effective quadratic-logarithmic penalty/barrier functions. We show correspondence between the suggested Augmented Lagrangian algorithm for Semidefinite Programming and its dual counterpart, resulting in a proximal-like maximization algorithm with nonquadratic prox-kernel. In addition to we present dual bounds and report computational results for Robust Control and Stable Truss Topology Design problems.

Research Report #1/96, Optimization Laboratory, Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technolologygy