×

zbMATH — the first resource for mathematics

Decomposition through formalization in a product space. (English) Zbl 0523.49022

MSC:
49M27 Decomposition methods
52A40 Inequalities and extremum problems involving convexity in convex geometry
90C25 Convex programming
52A07 Convex sets in topological vector spaces (aspects of convex geometry)
49M25 Discrete approximations in optimal control
49M30 Other numerical methods in calculus of variations (MSC2010)
65K05 Numerical mathematical programming methods
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] A. Auslender, ”Etude numérique des problèmes d’optimisation avec contraintes”, Doctoral thesis, University of Grenoble (Grenoble, 1969). · Zbl 0213.17301
[2] A. Auslender,Optimisation, méthodes numériques (Masson, Paris, 1976).
[3] J. Baranger and T. Dumont ”Decomposition and projection for nonlinear boundary value problems”, Discussion paper, UER de Mathématiques, University of Lyon I (Lyon, September 1980).
[4] A. Bensoussan and P. Kenneth, ”Sur l’analogie entre les méthodes de régularisation et de pénalisation”,Revue d’Informatique et de Recherche Opérationnelle 13-R3 (1968) 13–25.
[5] J. Cea,Optimisation (Dunod, Paris, 1971).
[6] J. Dumont, ”Décomposition par projection de certains problèmes elliptiques non linéaires”, 3rd C. Thesis, University of Lyon (Lyon 1978).
[7] I. Ekeland and R. Temam,Analyse convexe et problèmes variationnels (Dunod, Paris, 1974). · Zbl 0281.49001
[8] W. Findeisen, ”Parametric optimization by primal method in multilevel systems”,IEEE Transactions on Systems Science and Cybernetics 4 (1968) 155–164. · Zbl 0181.16501
[9] N. Gastinel,Analyse numérique linéaire (Hermann, Paris, 1966).
[10] L. G. Gubin, B.T. Polyak and E.V. Raik, ”The method of projections for finding the common point of convex sets”,USSR Computational Mathematics and Mathematical Physics 7 (1967) 1–24 (Translation of theZhurnal vychislitelnoj Matematiki i matematicheskoj Fiziki). · Zbl 0199.51002
[11] Y. Haugazeau, ”Sur les inéquations variationnelles et la minimisation de fonctionnelles convexes”, Doctoral thesis, University of Paris (Paris 1968).
[12] A.A. Kaplan, ”Determination of the extremum of a linear function of a convex set”,Soviet Mathematics Doklady 9 (1968) 269–271 (Translation of the Pure Mathematics Section of the Doklady Akademii Nauk SSSR) · Zbl 0186.23704
[13] J.E. Kelley, ”The cutting plane method for solving convex programs”,Journal of the Society for Industrial and Applied Mathematics 6 (1958) 15–22. · Zbl 0084.15804
[14] P.J. Laurent and B. Martinet, ”Méthodes duales pour le calcul du minimum d’une fonction convexe sur une intersection de convexes”, in: A. V. Balakrishnan, M. Contensou, B.F. de Veubeke, P. Krée, J. L. Lions and N.N. Moiseev, eds,Lecture Notes in Mathematics 132 (Springer, Berlin, 1970) pp. 159–180. · Zbl 0243.90034
[15] J.L. Lions and R. Temam, ”Eclatement et décentralisation en calcul des variations”, in: A.V. Balakrishnan, M. Contensou, B.F. de Veubeke, P. Krée, J.L. Lions and N.N. Moiseev, eds.,Lecture Notes in Mathématics 132 (Springer, Berlin, 1970) pp. 196–217. · Zbl 0223.49033
[16] J.L. Lions and G.I. Marchouk,Sur les méthodes numériques en sciences physiques et économiques (Dunod, Paris, 1974). · Zbl 0332.65040
[17] L. McLinden, ”Symmetrized separable convex programming”,Transactions of the American Mathematical Society 247 (1979) 1–44. · Zbl 0431.90064
[18] B. Martinet, ”Algorithmes pout la résolution des problèmes d’optimisation et de minimax”, Doctoral thesis, University of Grenoble (Grenoble, 1972).
[19] B. Martinet and A. Auslander, ”Méthodes de décomposition pour la minimisation d’une fonction sur un espace produit”,SIAM Journal on Control 12 (1974) 635–642. · Zbl 0302.49025
[20] Y.I. Merzlyakov, ”On a relaxation method of solving systems of linear inequalities”USSR Computational Mathematics and Mathematical Physics 2 (1962) 482–487 (Translation of the Zhurnal vychislitelnoj Matematiki i matematicheskoj Fiziki). · Zbl 0123.11204
[21] M. D. Mesarovic, D. Macko and Y. Takahara,Theory of hierarchical multilevel systems (Academic Press, New York, 1970). · Zbl 0224.93005
[22] J.J. Moreau, ”Proximité et dualité dans un espace hilbertien”,Bulletin de la Société Mathématique de France 93 (1965) 273–299.
[23] W. Oettli, ”An iterative method, having a linear rate of convergence, for solving a pair of dual linear programs”,Mathematical Programming 3 (1972) 302–311. · Zbl 0259.90019
[24] E.L. Peterson, ”Generalization and symmetrization of duality in geometric programming”, Discussion paper, Northwestern University, [Evanston, 1972].
[25] G. Pierra, ”Eclatement de contraintes en parallèle pour la minimisation d’une forme quadratique” in: J. Cea, ed.,Lecture Notes in Computer Science 41 (Springer, Berlin, 1976) pp. 200–218. · Zbl 0346.49032
[26] G. Pierra, ”Crossing of algorithms in decomposition methods”, in: G. Gardabassi and A. Locatelli, eds.,Large Scale Systems theory and applications (ISA, Pittsburg, 1976) pp. 309–319.
[27] G. Pierra, ”Méthodes de décomposition et croisement d’algorithmes pour des problèmes d’optimisation”, Doctoral thesis, University of Grenoble (Grenoble 1976).
[28] R. T. Rockafellar, ”Monotone operators and the proximal point algorithm”,SIAM Journal on Control 14 (1976) 877–898. · Zbl 0358.90053
[29] R. Temam, ”Quelques méthodes de décomposition en analyse numérique”, in:Actes, Congrès International des Mathématiciens 1970 (Gauthier-Villars, Paris, 1971) pp. 311–319.
[30] N.N. Yanenko,Méthode à pas fractionnaires (Armand Colin, Paris, 1968).
[31] R.S. Varga,Matrix iterative analysis (Prentice Hall, Englewood Cliffs, N.J., 1962). · Zbl 0133.08602
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.