Variable metric gradient projection method and replicator equation

Proceedings of the IEEE International Conference on Systems, Man and Cybernetics

Volumn 3, Issue , 1999, Pages

  Horie, R ^a   Aiyoshi, E ^a  

^a KEIO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICAL SEARCHING MODEL; POPULATION GENETICS; VARIABLE METRIC GRADIENT PROJECTION METHODS;

COMPUTATIONAL METHODS; CONSTRAINT THEORY; MATHEMATICAL MODELS; MATHEMATICAL PROGRAMMING; MAXIMUM PRINCIPLE;

OPTIMIZATION;

EID: 0033345435     PISSN: 08843627     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (19)

1. P. Schuster and K. Sigmund, "Replicator Dynamics", J. Theo. Biol., Vol. 100, 1983, pp.533-538.
2. R. A. Fisher, The Geneiical Theory of Natural Selection, Oxford, Claredon Press, 1930.
3. S. Shahshahni, "A new mathematical framework for the study of linkage and selection," Memories Am. Math. Soc, Vol. 17, No. 211, Jan. 1979.
4. K. Sigmund, "The Maximum Principle for Replicator Equations," in:Lotka-Volterra Approach to Dynamical Systems, M. Peschel, ed., Berlin, Akademie Verlag, 1985, pp.63-71.
5. K. Sigmund, "Game Dynamics, Mixed Strategies, and Gradient Systems," Theor. Population Biol., Vol. 32, 1987, pp. 114-126.
6. E. Akin, "The differential Geometry of Population Genetics and Evolutionary Games," in:Mathematical and Statistical Developments of Evolutionary Theory, S. Lessard ed., Kluwer Academic, 1990, pp. 1-93.
7. J. B. Rosen, "The Gradient Projection Method for Nonlinear Programming, Part I, Linear Constraints," SIAM J. Applied Mathmaiics, Vol. 8, 1960, pp. 181-217.
8. S. Amari, "Natural Gradient Works Efficiently in Learning," Neural Computation, Vol 10, 1998, pp. 251-276.
9. R. Horie and E. Aiyoshi, "Neural Networks Realization of Searching Models for Nash Equilibrium Points and Their Application to Associative Memories," SMC'98 Conference Proceedings, 1998, pp.1886-1891.
10. D. Goldfarb, "Extension of Davidon's Variable Metric Method to Maximization Under Linear Inequality and Equality Constraints," SIAM J. Applied Mathmatics, Vol. 17, 1969, pp. 739-764.
11. D. A. Bayer and J. C. Lagarias, "The Nonlinear Geometry of Linear Programming I. Affine and Projective Scaling Trajectories," Transactions of the American Mathematical Society, Vol. 314, No. 2, Aug. 1989, pp. 499-526.
12. N. Karmarkar, "Riemannian Geometry Underlying Interior-Point Methods for Linear Programming," Contemporary Mathematics, Vol. 114, 1990, pp. 51-75.
13. M. Vidyasagar, "Dynamical System, Gradient Flows and Optimization," System Control and Information, Vol. 39, No. 1, 1995, pp. 22-28.
14. N. Karmarkar, "A New Polynomial-Time Algorithm for Linear Programming," Combinatorica, Vol. 4, No. 4, 1984, pp. 373-395.
15. I. I. Dikin, "Iterative Solution of Problems of Linear and Quadratic Programming", Soviet Math. Dokl., Vol.8, No.3, 1967, pp.674-675.
16. H. Garcke, B. Nestler and B. Stoth, "On anisotropic order parameter models for multi-phase systems and their sharp interface limits," Phisica D, Vol.115, 1998, pp.87-108.
17. P. D. Taylor and L. B. Jonker, "Evolutionarily Stable Strategies and Game Dynamics," Mathematical Biosciences, Vol. 40, 1978, pp.145-156.
18. J. Maynard Smith, Evolutionary Game theory, Cambridge Univ. Press, 1982.
19. T. Chawanya, "A New Type of Irregular Motion in a Class of Game Dynamics Systems," Phisica D, Vol.109, 1997, pp.201-241.