IMPLEMENTATION OF INTERIOR POINT METHODSIMPLEMENTATION OF INTERIOR POINT METHODS FOR SECOND ORDER CONIC OPTIMIZATION

This thesis deals with the implementation of interior point methods for second order conic optimization (SOCO) problems. In an SOCO, we minimize a linear function subject to the intersection of an affine set, and product of second order cones. SOCO problems have a variety of applications in engineering, including antenna array design and truss design. We first introduce a primal-dual interior point algorithm that is based on selfregular search directions. This algorithm employs the homogeneous self-dual embedding model, with Nesterov-Todd scaling, and the Mehrotra predictor-corrector technique. Then we discuss efficient implementation of search directions and step length with MATLAB and Watson Sparse Matrix Package. We also introduce an adaptive strategy that is used to choose the barrier parameter to define the self-regular search directions. We test the algorithm on a variety of problems from the DIMACS set, and compare these results with state of the art software like SeDuMi. Numerical testin