Convergence Analysis of an Inexact Infeasible Interior Point Method for Semidefinite Programming

Authors:
Stefania Bellavia;Sandra Pieraccini
Affiliations:
Dipartimento di Energetica “S. Stecco”, University of Florence, via C. Lombroso 6/17, 50134 Florence, Italy. stefania.bellavia@unifi.it;Dipartimento di Matematica, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129 Torino, Italy. sandra.pieraccini@polito.it
Venue:
Computational Optimization and Applications
Year:
2004

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Abstract

In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima, Megiddo and Mizuno (A primal-dual infeasible-interior-point algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use of inexact search directions; i.e., the linear systems defining the search directions can be solved with an accuracy that increases as the solution is approached. A convergence analysis is carried out and the global convergence of the method is proved.