Implementation in Java of Algorithms for Semidefinite Optimization

Abstract

Abstract We discuss the possibility of solving the semidefinite optimization problem using interior-point algorithms. We present the primal and dual semidefinite programming problems, and then determine the interior-point condition and the optimality criteria. We analyze the central path system and the modification of this, using the method of algebraically equivalent transformation. We use the Nesterov-Todd scaling technique to obtain the proper search directions. We give a modified version of the Nesterov-Todd step interior-point algorithm based on the implementation point of view. We present some numerical results based on a code implemented in the Java programming language. We compare the results obtained for the identity map and the square root function within the framework of the algebraically equivalent transformation technique.