Monotonicity of metric projections onto positive cones of ordered Euclidian spaces




G. Isac
Departement de Mathbmatique College Militaire Royal St-Jean, Qurbec, Canada JOJ IRO

A.B. Nemeth
Institutul de Matematica, Cluj-Napoca Romania (ICTP)


metric projection; positive cone; ordered Euclidean space.


[1] YA. I. AL’BER, Recurrence relations and variational inequalities. Dokl. Akad. Nauk USSR 270, 511-517 (1983).
[2] Y. C. CI-IEN~, On the gradient-projection method for solving the nonsymmetric linear complementarity problem. J. Optim. Theory Appl. 43, 527-541 (1984).
[3] E. M. GAFNI and D. P. BERTSEKAS, Two-metric projection method for constrained optimization. SIAM J. Control Optim. 22, 936-964 (1984).
[4] R. B. HOLMES, Geometric functional analysis and its applications. New York-HeidelbergBerlin 1975.
[5] P. J. LAtn~ENT, Approximation et optimization. Paris 1972.
[6] E. S. LEVmN and B. T. POLJAK, Constrained minimization problems. USSR Comput. Math. and Math. Phys. 6, 1-50 (1966).
[7] M. G. KREIN and M. A. RUTMAN, Linear operators leaving invariant a cone in a Banach space. Uspehi Mat. Nauk SSSR 3, 3-95 (1948); also Amer. Math. Soc. Transl. 26 (1950).
[8] J.-J. MOREAU, Drcomposition orthogonale d’un espace hilbertien selon deux c6nes mutuellement polaires. C. R. Acad. Sci. 255, 238-240 (1962).
[9] F. Rmsz, Sur quelques notions fondamentales dans la throrie grnerale des op&ations lineaires. Mat. Termrszett. l~rtes. 56, 1-45 (1937); also Ann. of Math. 41, 174-206 (1940).
[10] H. H. SCrI~d~FER, Topological vector spaces. New York 1966.
[11] B. SZ6KEFALVI NAGY, Sur les lattis linraires de dimension finie. Comment Math. Helv. 17, 209-213 (1944-45).
[12] A. P. WmRZBICVd and A. HATKO, Computational methods in Hilbert space for optimal control problems with delays. Proc. of 5th IFIP Conf. on Optimization Techniques, Rome; Berlin 1973.
[13] A. YOUDINE, Solution des deux probl+mes de la throrie des espaces semi-ordonnrs. C. R. Acad. Sci. URSS 27, 418-422 (1939).
[14] H. ZARANTANELLO, Projections on convex sets in Hilbert space and spectral theory. In Zarantanello (ed.): Contributions to nonlinear functional analysis, 237-421, New York-London 1971.
[15] S. STRASZEWICZ, Ober exponierte Punkte abgeschlossener Punktmengen. Fund. Math. 24, 139-143 (1935).

Paper coordinates

G. Isac, A.B. Nemeth, Monotonicity of metric projections onto positive cones of ordered euclidian spaces, Arch. Math., 46 (1986), 568-576



About this paper


Archiv der Mathematik

Publisher Name


Print ISSN


Online ISSN


Google Scholar Profile


Related Posts