A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces
Published Online:1 May 2001https://doi.org/10.1287/moor.26.2.248.10558
References
- A mesh-independence principle for operator equations and their discretizations. SIAM J. Numer. Anal. (1986) 23:160–169Crossref, Google Scholar
- The asymptotic mesh independence principle for inexact Newton-Galerkin-like methods. Pure Math. Appl. (1997) 8:169–194Google Scholar
- A norm convergence result on random products of relaxed projections in Hilbert space. Trans. Amer. Math. Soc. (1995) 347:1365–1373Crossref, Google Scholar
- On projection algorithms for solving convex feasibility problems. SIAM Rev. (1996) 38:367–426Crossref, Google Scholar
- The method of cyclic projections for closed convex sets in Hilbert space. Contemp. Math. (1997) 204:1–38Crossref, Google Scholar
- Examples of convex functions and classifications of Banach spaces. J. Convex Anal. (1994) 1:61–73Google Scholar
- Krasnoselski-Mann iterations in normed spaces. Canad. Math. Bull. (1992) 35:21–28Crossref, Google Scholar
- The method of successive projection for finding a common point of convex sets. Soviet Math. Dokl. (1965) 6:688–692Google Scholar
- Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert (1973) (North-Holland/Elsevier, New York) Google Scholar
- Produits infinis de résolvantes. Israel J. Math. (1978) 29:329–345Crossref, Google Scholar
- Convergence theorems for sequences of nonlinear operators in Banach spaces. Math. Z. (1967) 100:201–225Crossref, Google Scholar
- Nonexpansive projections and resolvents of accretive operators in Banach spaces. Houston J. Math. (1977) 3:459–470Google Scholar
- Construction d'un point fixe commun à une famille de contractions fermes. C. R. Acad. Sci. Paris Sér. I Math. (1995) 320:1385–1390Google Scholar
- , Hawkes P. The convex feasibility problem in image recovery. Advances in Imaging and Electron Physics (1996) 95(Academic Press, New York) 155–270Google Scholar
- Hilbertian convex feasibility problem: Convergence of projection methods. Appl. Math. Optim. (1997) 35:311–330Crossref, Google Scholar
- Strong convergence of block-iterative outer approximation methods for convex optimization. SIAM J. Control Optim. (2000) 38:538–565Crossref, Google Scholar
- , Floudas C. A., Pardalos P. M. Fejér monotonicity in convex optimization. Encyclopedia of Optimization (2001) (Kluwer, Boston, MA) Google Scholar
- Mathematical Analysis and Numerical Methods for Science and Technology (1988-1993) 1–6(Springer-Verlag, New York) Crossref, Google Scholar
- On the Mann iterative process. Trans. Amer. Math. Soc. (1970) 149:65–73Crossref, Google Scholar
- Infinite–Dimensional Optimization and Control Theory (1999) (Cambridge University Press, Cambridge) Crossref, Google Scholar
- An example concerning fixed points. Israel J. Math. (1975) 22:81–86Crossref, Google Scholar
- Topics in Metric Fixed Point Theory (1990) (Cambridge University Press, Cambridge, U.K.) Crossref, Google Scholar
- The method of projections for finding the common point of convex sets. USSR Comput. Math. Math. Phys. (1967) 7:1–24Crossref, Google Scholar
- On the convergence of the proximal point algorithm for convex minimization. SIAM J. Control Optim. (1991) 29:403–419Crossref, Google Scholar
- Sur les inéquations variationnelles et la minimisation de fonctionnelles convexes. (1968) . Thèse, Université de Paris, Paris, FranceGoogle Scholar
- Khan M. A., Yannelis N. C.Equilibrium Theory in Infinite Dimensional Spaces (1991) (Springer-Verlag, New York) Crossref, Google Scholar
- Surrogate projection methods for finding fixed points of firmly nonexpansive mappings. SIAM J. Optim. (1997) 7:1084–1102Crossref, Google Scholar
- Une méthode d'éclatement des opérateurs et des contraintes en calcul des variations. C. R. Acad. Sci. Paris Sér. A Math. (1966) 263:563–565Google Scholar
- Régularisation d'inéquations variationnelles par approximations successives. Rev. Française Inform. Rech. Opér. (1970) 4:154–158Google Scholar
- The solution by iteration of nonlinear equations in Hilbert spaces. Proc. Amer. Math. Soc. (1977) 63:69–73Crossref, Google Scholar
- Un cas de convergence des itérées d'une contraction d'un espace hilbertien. C. R. Acad. Sci. Paris Sér. A Math (1978) 286:143–144Google Scholar
- Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings. J. Math. Anal. Appl. (1973) 43:459–497Crossref, Google Scholar
- Minimization of unsmooth functionals. USSR Comput. Math. Math. Phys. (1969) 9:14–29Crossref, Google Scholar
- A class of iterative methods with Fejér-monotone sequences. Eesti NSV Tead. Akad. Toimetised Füüs.-Mat. (1969) 18:22–26Google Scholar
- On infinite products of resolvents. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. ser. VIII (1977) 63:338–340Google Scholar
- Monotone operators and the proximal point algorithm. SIAM J. Control Optim. (1976) 14:877–898Crossref, Google Scholar
- Forcing strong convergence of proximal point iterations in a Hilbert space. Math. Programming (2000) 87:189–202Crossref, Google Scholar
- Optical Signal Processing (1992) (Wiley, New York) Google Scholar

