Some optimization problems in multivariate statistics

Journal of Global Optimization

Volumn 28, Issue 2, 2004, Pages 217-228

  Rapcsak T ^a  

^a INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

Multivariate statistics; Quadratic equality constraints; Smooth optimization; Stiefelmanifolds

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LAGRANGE MULTIPLIERS; MATRIX ALGEBRA; PRINCIPAL COMPONENT ANALYSIS; PROBLEM SOLVING; STATISTICAL METHODS; SYSTEM STABILITY; THEOREM PROVING;

MULTIVARIATE STATISTICS; QUADRATIC FUNCTION; SINGULAR VALUE DECOMPOSITION; STIEFEL MANIFOLDS;

GLOBAL OPTIMIZATION;

EID: 1542375790     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOGO.0000015312.57436.28     Document Type: Article

References (19)

1. Bellmann, R. (1960), Introduction to Matrix Analysis, McGraw-Hill Book Company, New York, Toronto, London.
2. Bolla, M., Michaletzky, Gy., Tusnády, G. and Ziermann, M. (1998) Extrema of sums of heterogeneous quadratic forms, Linear Algebra and Applications 269, 331-365.
3. Byrnes, C.I. and Willems, J C. (1986), Least-squares estimation, linear programming, and momentum: a geometric parametrization of local minima, IMA Journal of Mathematical Control & Information 3, 103-118.
4. Eckart, C. and Young, G. (1936), The approximation of one matrix by another of lower rank, Psychometrika 1, 211-218.
5. Edelman, A., Arias, T.A. and Smith, S.T. (1998), The geometry of algorithms with orthogonality constraints, SIAM Journal on Matrix Analysis and Applications 20, 303-353.
6. Fang, K.T., Hickernell, F.J. and Winker, P. (1996), Some global optimization algorithms in statistics, in: D.Z. Du, X.S. Zhang and Cheng K. (eds.) Lecture Notes in Operations Research World Publishing Corporation, pp. 14-24.
7. Gabriel, K.R. (1971), The biplot-graphic display of matrices with application to principal components analysis, Biometrika 58, 453-467.
8. Gabriel, K.R. (1981), Biplot display of multivariate matrices for inspection of data and diagnosis, in: V. Barnett (ed.) Interpreting Multivariate Data, Wiley, Chichester, UK pp. 147-174.
9. Golub, G.H. and Kahan, W. (1965), Calculating the singular values and pseudoinverse of a matrix, SIAM Journal on Numerical Analysis 2, 205-224.
10. Greenacre, M.J. (1984), Theory and Applications of Correspondence Analysis, Academic Press, London, Orlando.
11. Helmke, U. and Moore, J.B. (1994), Optimization and Dynamical Systems, Springer-Verlag.
12. Kennedy, W.J. and Gentle, J.E. (1980), Statistical Computing, Marcel Dekker, New York, Basel.
13. Mareschal, B. and Brans, J.-P. (1988), Geometrical representations for MCDA, European Journal of Operational Research 34, 69-77.
14. Rao, C.R. (1993) (ed.), Computational Statistics, in: Handbook of Statistics 9.
15. n, Kluwer Academic Publishers, Boston, London, Dordrecht.
16. Rapcsák, T. (2001), On minimization of sums of heterogeneosu quadratic functions on Stiefel manifolds. In: Migdalas, A., Pardalos, P. and Varbrand, P. (eds.), From local to global optimization, Dordrecht-Boston-London, Kluwer Academic Publishers, 277-290.
17. Rapcsák, T. (2002), On minimization on Stiefel manifolds, European Journal of Operational Research. 143, 365-376.
18. Stiefel, E. (1935/6), Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten, Commentarii Mathematici Helvetici 8, 305-353.
19. Young, F.W, Faldowski, R.A. and McFarlane, M.M. (1993), Multivariate statistical visualization, in: C.R. Rao (ed.) Handbook of Statistics: Elsevier Science Publishers, Amsterdam, pp. 959-998.