Alternating Projections on Manifolds

References

• Auslender L.Differential Geometry (1967) (Harper and Row, New York) Google Scholar
• Bauschke H. H., Borwein J. M. On the convergence of von Neumann's alternating projection algorithm for two sets. Set Valued Anal. (1993) 1(2):185–212Crossref, Google Scholar
• Bauschke H. H., Borwein J. M. On projection algorithms for solving convex feasibility problems. SIAM Rev. (1996) 38(3):367–426Crossref, Google Scholar
• Bauschke H. H., Combettes P. L., Luke D. R. Phase retrieval, error reduction algorithm, and Fienup variants: A view from convex optimization. J. Optical Soc. Amer. (2002) 19(7):1334–1345Crossref, Google Scholar
• Borwein J. M., Lewis A. S.Convex Analysis and Nonlinear Optimization (2005) 2nd ed.(Springer-Verlag, New York) Google Scholar
• Chen X., Chu M. T. On the least squares solution of inverse eigenvalue problems. SIAM J. Numer. Anal. (1996) 33:2417–2430Crossref, Google Scholar
• Cheney W., Goldstein A. Proximity maps for convex sets. Proc. Amer. Math. Soc. (1959) 10(3):448–450Crossref, Google Scholar
• Chu M. T. Constructing a Hermitian matrix from its diagonal entries and eigenvalues. SIAM J. Matrix Anal. Appl. (1995) 16:207–217Crossref, Google Scholar
• Chu M. T., Driessel K. R. The projected gradient method for least squares matrix approximations with spectral constraints. SIAM J. Numer. Anal. (1990) 27:1050–1060Crossref, Google Scholar
• Combettes P. L. Signal recovery by best feasible approximation. IEEE Trans. Image Processing (1993) 2(2):269–271Crossref, Google Scholar
• Combettes P. L., Trussell H. J. Method of successive projections for finding a common point of sets in metric spaces. J. Optim. Theory Appl. (1990) 67(3):487–507Crossref, Google Scholar
• Dennis J. E., Schnabel R. B.Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1983) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
• Deutsch F., Singh S. P. The angle between subspaces of a Hilbert space. Approximation Theory, Wavelets and Applications (1995) (Kluwer, Dordrecht, Netherlands) 107–130Crossref, Google Scholar
• Deutsch F.Best Approximation in Inner Product Spaces (2001) (Springer, New York) Crossref, Google Scholar
• Dontchev A. L., Lewis A. S., Rockafellar T. The radius of metric regularity. Trans. Amer. Math. Soc. (2003) 355(2):493–517Crossref, Google Scholar
• Facchinei F., Pang J.-S.Finite-Dimensional Variational Inequalities and Complementarity Problems (2003) II(Springer, New York) Google Scholar
• Friedricks K. On certain inequalities and characteristic value problems for analytic functions and for functions of two variables. Trans. Amer. Math. Soc. (1937) 41:321–364Crossref, Google Scholar
• Golub G. H., Van Loan C. F.Matrix Computations (1995) 3rd ed.(Johns Hopkins University Press, Baltimore) Google Scholar
• Grigoriadis K. M., Beran E. Alternating projection algorithms for linear matrix inequalities problems with rank constraints. Adv. Linear Matrix Inequality Methods in Control (2000) (SIAM, Philadelphia) 251–267Crossref, Google Scholar
• Grigoriadis K. M., Skelton R. E. Low-order control design for LMI problems using alternating projection methods. Automatica (1996) 32:1117–1125Crossref, Google Scholar
• Hardy G. H., Littlewood J. E., Pólya G.Inequalities (1952) (Cambridge University Press, Cambridge, UK) Google Scholar
• Higham N. Computing a nearest symmetric correlation matrix: A problem from finance. IMA J. Numer. Anal. (2002) 22(3):329–343Crossref, Google Scholar
• Holmes R. B. Smoothness of certain metric projections on Hilbert space. Trans. Amer. Math. Soc. (1973) 184:87–100Crossref, Google Scholar
• Horn R. A., Johnson Ch. R.Matrix Analysis (1989) New ed. 1999(Cambridge University Press, Cambridge, UK) Google Scholar
• Lewis A. S. Convex analysis on the Hermitian matrices. SIAM J. Optim. (1996) 6:164–177Crossref, Google Scholar
• Lewis A. S. Group invariance and convex matrix analysis. SIAM J. Matrix Anal. Appl. (1996) 17:927–949Crossref, Google Scholar
• Lewis A. S., Luke D. R., Malick J. Local linear convergence of alternating and averaged projections. (2007) . Preprint, Cornell University School of ORIE, Ithaca, NYGoogle Scholar
• Nesterov Y. E., Nemirovskii A. S.Interior-Point Polynomial Algorithms in Convex Programming (1994) (SIAM, Philadelphia) Crossref, Google Scholar
• Nocedal J., Wright S. J.Numerical Optimization (1999) (Springer Verlag, New York) Crossref, Google Scholar
• Orsi R. Numerical methods for solving inverse eigenvalue problems for nonnegative matrices. SIAM J. Matrix Anal. Appl. (2006) 28:190–212Crossref, Google Scholar
• Orsi R., Helmke U., Moore J. A Newton-like method for solving rank constrained linear matrix inequalities. Automatica (2006) 42:1875–1882Crossref, Google Scholar
• Oustry F. A second-order bundle method to minimize the maximum eigenvalue function. Math. Programming (2000) 89:1–34Crossref, Google Scholar
• Poliquin R. A., Rockafellar R. T., Thibault L. Local differentiability of distance functions. Trans. Amer. Math. Soc. (2000) 352:5231–5249Crossref, Google Scholar
• Robinson S. B. Constraint nondegeneracy in variational analysis. Math. Oper. Res. (2003) 28:201–232Link, Google Scholar
• Rockafellar R. T., Wets R. J.-B.Variational Analysis (1998) (Springer Verlag, Heidelberg, Germany) Crossref, Google Scholar
• Smith K. T., Solomon D. C., Wagner S. L. Practical and mathematical aspects of the problem of reconstructing objects from radiographs. Bull. Amer. Math. Soc. (1977) 83:1227–1270Crossref, Google Scholar
• Tropp J. A., Dhillon I. S., Heath R. W., Strohmer T. Designing structured tight frames via an alternating projection method. IEEE Trans. Inform. Theory (2005) 51:188–209Crossref, Google Scholar
• von Neumann J. Some matrix inequalities and metrization of matric-space. Tomsk University Rev. (1937) 1:286–300Collected Works, Vol. IV. Pergamon, Oxford, UK, 1962, 205–218Google Scholar
• von Neumann J. Functional operators, Vol. II. The geometry of orthogonal spaces. Annals of Mathematical Studies (1950) 22(Princeton University Press, Princeton, NJ) . [Reprint of mimeographed notes first distributed in 1933.]Google Scholar
• Weber C. A., Allebach J. P. Reconstruction of frequency-offset Fourier data by alternating projection on constraint sets. Proc. 24th Allerton Conf. Comm., Control and Comput. (1986) Monticello, IL:194–203Google Scholar
• Widrow B., Wallach E.Adaptive Inverse Control (1996) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
• Yang K., Orsi R. Generalized pole placement via static output feedback: A methodology based on projections. Automatica (2006) 42:2143–2150Crossref, Google Scholar