An iterative approach to quadratic optimization

Journal of Optimization Theory and Applications

Volumn 116, Issue 3, 2003, Pages 659-678

  Xu, H K ^a  

^a UNIVERSITY OF KWAZULU NATAL   (South Africa)

Author keywords

convex feasibility problems; Hilbert spaces; Iterative algorithms; nonexpansive mappings; quadratic optimization

Indexed keywords

EID: 0037269525     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023073621589     Document Type: Article

References (16)

1. DEUTSCH, F., and YAMADA, I., Minimizing Certain Convex Functions over the Intersection of the Fixed-Point Sets of Nonexpansive Mappings, Numerical Functional Analysis and Optimization, Vol. 19, pp. 33-56, 1998.
2. GOEBEL, K., and KIRK, W. A., Topics on Metric Fixed-Point Theory, Cambridge University Press, Cambridge, England, 1990.
3. GOEBEL, K., and REICH, S., Uniform Convexity, Hyperbolic Geometry, and Non-expansive Mappings, Marcel Dekker, New York, NY, 1984.
4. HALPERN, B., Fixed Points of Nonexpanding Maps, Bulletin of the American Mathematical Society, Vol. 73, pp. 957-961, 1967.
5. LIONS, P. L., Approximation de Points Fixes de Contractions, Comptes Rendus de l'Academie des Sciences, Serie I-Mathematique, Vol. 284, pp. 1357-1359, 1997.
6. WITTMANN, R., Approximation of Fixed Points of Nonexpansive Mappings, Archiv der Mathematik, Vol. 58, pp. 486-491, 1992.
7. BAUSCHKE, H. H., The Approximation of Fixed Points of Compositions of Non-expansive Mappings in Hilbert Spaces, Journal of Mathematical Analysisis and Applications, Vol. 202, pp. 150-159, 1996.
8. REICH, S., Approximating Fixed Points of Nonexpansive Mappings, Panamerican Mathematical Journal, Vol. 4, pp. 23-28, 1994.
9. ATTOUCH, H., Viscosity Solutions of Minimization Problems, SIAM Journal on Optimization, Vol. 6, pp. 769-806, 1996.
10. BAUSCHKE, H. H., and BORWEIN, J. M., On Projection Algorithms for Solving Convex Feasibility Problems, SIAM Reviews, Vol. 38, pp. 367-426, 1996.
11. COMBETTES, P. L., Hilbertian Convex Feasibility Problem: Convergence of Projection Methods, Applied Mathematics and Optimization, Vol. 35, pp. 311-330, 1997.
12. ODEN, J. T., Qualitative Methods on Nonlinear Mechanics, Prentice-Hall, Englewood Cliffs, New Jersey, 1986.
13. O'HARA, J. G., PILLAY, P., and XU, H. K., Iterative Approaches to Finding Nearest Common Fixed Points in Hilbert Spaces, Nonlinear Analysis (to appear).
14. YAMADA, I., The Hybrid Steepest Descent Method for Variational Inequality Problems over the Intersection of the Fixed-Point Sets of Nonexpansive Mappings, Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, Edited by D. Butnariu, Y. Censor, and S. Reich, North-Holland, Amsterdam, Holland, pp. 473-504, 2001.
15. XU, H. K., and KIM, T. W., Convergence of Hybrid Steepest Descent Methods for Variational Inequalities, Preprint, 2003.
16. HIRIART-URRUTY, J. B., Conditions for Global Optimality 2, Journal of Global Optimization, Vol. 13, pp. 349-367, 1998.