An Interior Point-Proximal Method of Multipliers for Linear Positive Semi-Definite Programming

Abstract In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in Pougkakiotis and Gondzio (Comput Optim Appl 78:307–351, 2021. 10.1007/s10589-020-00240-9 ) for solution linear positive Semi-Definite Programming (SDP) problems, allowing inexactness associated Newton systems. particular, combine an infeasible Point (IPM) with Proximal (PMM) interpret algorithm as a primal-dual regularized IPM, suitable solving SDP problems. We apply some iterations IPM to each sub-problem PMM until satisfactory is found. then update parameters, form new neighbourhood, repeat process. Given framework, prove polynomial complexity algorithm, under mild assumptions, without requiring exact computations directions. furthermore provide necessary condition lack strong duality, which can be used basis constructing detection mechanisms identifying pathological cases within IP-PMM.