Semi–definite programming for the nearest circulant semi–definite matrix problem

Positive semi–definite circulant matrices arise in many important applications. The problem arises in various applications where the data collected in a matrix do not maintain the specified structure as is expected in the original system.The task is to retrieve useful information while maintaining the underlying physical feasibility often necessitates search for a good structured approximation of the data matrix. This paper construct structured circulant positive semi–definite matrix that is nearest to a given data matrix. The problem is converted into a semi–definite programming problem as well as a problem comprising a semi–defined program and second-order cone problem. The duality and optimality conditions are obtained and the primal-dual algorithm is outlined. Some of the numerical issues involved will be addressed including unsymmetrical of the problem.Computational results are presented.