An Analysis of the EM Algorithm and Entropy-Like Proximal Point Methods

References

• Ash R. B.Real Analysis and Probability (1972) (Academic Press, New York) Google Scholar
• Auslender A., Teboulle M., Ben-Tiba S. A. Interior proximal and multiplier methods based on second order homogeneous kernels. Math. Oper. Res. (1999) 24:645–668Link, Google Scholar
• Ben-Tal A., Zibulevsky M. Penalty/barrier multiplier methods for convex programming problems. SIAM J. Optim. (1997) 7:347–366Crossref, Google Scholar
• Bertsekas D. P.Nonlinear Programming (1999) 2nd ed.(Athena Scientific, Belmont, MA) Google Scholar
• Censor Y., Zenios S. A.Parallel Optimization: Theory, Algorithms, and Applications (1997) (Oxford University Press, New York and Oxford) Google Scholar
• Chrétien S., Hero A. O. Generalized proximal point algorithms. (2000) . Report, Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MIGoogle Scholar
• Csiszár I. Information-type measures of difference of probability distributions and indirect observations. Studia Sci. Math. Hungarica (1967) 2:299–318Google Scholar
• Csiszár I., Tusnády G. Information geometry and alternating minimization procedures. Statist. Decisions Suppl. (1984) 1:205–237Google Scholar
• Dempster A. P., Laird N. M., Rubin D. B. Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. (1977) 39:1–38Google Scholar
• Horng S. C. Examples of sublinear convergence of the EM algorithm. Proc. Statist. Comput. Section (1987) (American Statistical Association, Alexandria, VA) 266–271Google Scholar
• Iusem A. N., Teboulle M. A regularized dual-based iterative method for a class of image reconstruction problems. Inverse Problems (1993) 9:679–696Crossref, Google Scholar
• Iusem A. N., Teboulle M. Convergence rate analysis of nonquadratic proximal methods for convex and linear programming. Math. Oper. Res. (1995) 20:657–677Link, Google Scholar
• Kaplan A., Tichatschke R. Proximal point methods and nonconvex optimization. J. Global Optim. (1998) 13:389–406Crossref, Google Scholar
• Kiwiel K. C. Proximal minimization methods with generalized Bregman functions. SIAM J. Control Optim. (1997) 35:1142–1168Crossref, Google Scholar
• Luo Z-Q., Tseng P. Error bounds and convergence analysis of feasible descent methods: A general approach. Ann. Oper. Res. (1993) 46:157–178Crossref, Google Scholar
• Martinet B. Regularisation d'inéquations variationelles par approximations successives. Rev. Française d'Automatique Inform. Rech. Opér. (1970) 4:154–159Google Scholar
• Martinet B. Determination approchée d'un point fixe d'une application pseudo-contractante. C. R. Acad. Sci. Paris (1972) 274:163–165Google Scholar
• McLachlan G. J., Krishnan T.The EM Algorithm and Extensions (1997) (Wiley, New York) Google Scholar
• Neal R. M., Hinton G. E., Jordan M. I. A view of the EM algorithm that justifies incremental, sparse, and other variants. Learning in Graphical Models (1998) (Kluwer Academic Publishers, Dordrecht, The Netherlands) 355–368also available from http://www.cs.toronto.edu/∼radford/papers-online.htmlCrossref, Google Scholar
• Polyak R., Teboulle M. Nonlinear rescaling and proximal-like methods in convex optimization. Math. Programming (1997) 76:265–284Crossref, Google Scholar
• Ortega J. M., Rheinboldt W. C.Iterative Solution of Nonlinear Equations in Several Variables (1970) (Academic Press, New York) Google Scholar
• Pennanen T. Local convergence of the proximal point algorithm and multiplier methods without monotonicity. Math. Oper. Res. (2002) 27:170–191Link, Google Scholar
• Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Rockafellar R. T. Monotone operators and the proximal point algorithm. SIAM J. Control Optim. (1976a) 14:877–898Crossref, Google Scholar
• Rockafellar R. T. Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math. Oper. Res. (1976b) 1:97–116Link, Google Scholar
• Rockafellar R. T., Wets R. J-B.Variational Analysis (1998) (Springer-Verlag, New York) Crossref, Google Scholar
• Silva P. J., Eckstein J., Humes C. Rescaling and stepsize selection in proximal method using separable generalized distances. (1999) . RUTCOR Research Report 35-99, Rutgers University, Piscataway, NJGoogle Scholar
• Teboulle M. Entropic proximal mapping with applications to nonlinear programming. Math. Oper. Res. (1992) 17:670–690Link, Google Scholar
• Teboulle M. Convergence of proximal-like algorithms. SIAM J. Optim. (1997) 7:1069–1083Crossref, Google Scholar
• Tseng P. Convergence of block coordinate descent method for nondifferentiable minimization. J. Optim. Theory Appl. (2001) 109:473–492Crossref, Google Scholar
• Tseng P., Bertsekas D. P. On the convergence of the exponential multiplier method for convex programming. Math. Programming (1993) 60:1–19Crossref, Google Scholar
• Vardi Y., Shepp L. A., Kaufman L. A statistical model for positron emission tomography. J. Amer. Statist. Assoc. (1985) 80:8–37Crossref, Google Scholar
• Wu J. C. F. On the convergence properties of the EM algorithm. Ann. Statist. (1983) 11:95–103Crossref, Google Scholar