Dynamical systems which solve optimization problems with linear constraints

IMA Journal of Mathematical Control and Information

Volumn 8, Issue 2, 1991, Pages 135-149

  Faybusovich, L ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001708712     PISSN: 02650754     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamci/8.2.135     Document Type: Article

References (10)

1. Bayer, D. A., & Lagarias, J. C. 1989 The nonlinear geometry of linear programming I, II. Trans. Amer. Math. Soc. 314, 499-580.
2. Brockett, R. W. 1988 Dynamical systems that sort lists and solve linear programming problems (In: Proceedings 27th Conference on Decision and Control. Pp. 799-803). Linear Algebra and its Applies. 146, 79-91.
3. Cooke, G. E. & Finney, R. L. 1967 Homology of Cell Complexes. Princeton University Press, Princeton.
4. Faybusovich, L. 1983 The simplex-method in coordinate-free formulation. Cybernetics 19, 247-52.
5. Faybusovich, L. 1990 Simplex method and groups generated by reflections. Acta Appl. Math. 20, 231-45.
6. Faybusovich, L. 1991 Hamiltonian structure of dynamical systems which solve linear programming problems. To appear in Physica D.
7. Karmarkar, N. 1984 A new polynomial-time algorithm for linear programming. Combinatorica 4, 373-95.
8. Meggido, N., & Shub, M. 1989 Boundary behavior of interior point algorithms in linear programming. Math, of Ops Res. 14, 97-146.
9. Smale, S. 1987 Algorithms for solving equations. In: Proceedings of the International Congress of Mathematicians, 1986. Pp. 172-95.
10. Warner, F. 1971 Foundations of Differentiable Manifolds and Lie Groups. Scott, Foresman and Company, Glenview.