Infeasible Start Semidefinite Programming Algorithms Via Self-Dual Embeddings

The development of algorithms for semide nite programming is an active research area, based on extensions of interior point methods for linear programming. As semide nite programming duality theory is weaker than that of linear programming, only partial information can be obtained in some cases of infeasibility, nonzero optimal duality gaps, etc. Infeasible start algorithms have been proposed which yield di erent kinds of information about the solution. In this paper a comprehensive treatment of a speci c initialization strategy is presented, namely self-dual embedding, where the original primal and dual problems are embedded in a larger problem with a known interior feasible starting point. A framework for infeasible start algorithms with the best obtainable complexity bound is thus presented. The information that can be obtained in case of infeasibility, unboundedness, etc., is stated clearly. Important unresolved issues are discussed. iii

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