An abstract extremal principle with applications to welfare economics

Journal of Mathematical Analysis and Applications

Volumn 251, Issue 1, 2000, Pages 187-216

  Mordukhovich, Boris S ^a  

^a WAYNE STATE UNIVERSITY   (United States)

Author keywords

Prenormal and normal structures; Banach spaces; variational analysis; normal cones and subdifferentials; extremal principle; Pareto optimality; welfare economics

Indexed keywords

EID: 0034311162     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7041     Document Type: Article

References (35)

1. Abramovich Y. A., Aliprantis C. D., Burkinshaw O. Positive operators on Krein spaces. Acta Appl. Math. 27:1992;1-22.
2. Arrow K. J., Hahn F. H. General Competitive Analysis. 1971;Holden-Day, San Francisco.
3. Bonnisseau J.-M., Cornet B. Valuation equilibrium and Pareto optimum. J. Math. Econom. 17:1988;293-308.
4. Borwein J. M., Jofré A. A nonconvex separation property in Banach spaces. Math. Methods Oper. Res. 48:1998;169-179.
5. J. M. Borwein, Y. Lucet, and, B. S. Mordukhovich, Compactly epi-Lipschitzian convex sets and functions in normed spaces, J. Convex Anal, in press.
6. Borwein J. M., Mordukhovich B. S., Shao Y. On the equivalence of some basic principles in variational analysis. J. Math. Anal. Appl. 229:1999;228-257.
7. Borwein J. M., Strojwas H. M. Tangential approximations. Nonlinear Anal. 9:1985;1347-1366.
8. Borwein J. M., Zhu Q. J. Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity. SIAM J. Control Optim. 34:1996;1568-1591.
9. Clarke F. H. Optimization and Nonsmooth Analysis. 1983;Wiley, New York.
10. B. Cornet, The Second Welfare Theorem in Nonconvex Economies, CORE, Discussion Paper, No. 8630, 1986.
11. Cornet B. Marginal cost pricing and Pareto optimality. Champsaur P., Essays in Honor of Edmond Malinvaud. 1990;14-53 MIT Press, Cambridge.
12. Debreu G. Theory of Value. 1959;Wiley, New York.
13. S. D. Flåm, and, A. Jourani, Prices and Pareto optima, preprint, 2000.
14. Guesnerie R. Pareto optimality in non-convex economies. Econometrica. 43:1975;1-29.
15. Ioffe A. D. Approximate subdifferential and applications. III. The metric theory. Mathematika. 36:1989;1-38.
16. Ioffe A. D. Fuzzy principles and characterization of trustworthiness. Set-Valued Anal. 6:1998;265-276.
17. Ioffe A. D. Codirectional compactness, metric regularity and subdifferential calculus. Théra M., Experimental, Constructive and Nonlinear Analysis. Canad. Math. Soc. Conf. Proceed. 27:2000.
18. Jofré A. A second welfare theorem in nonconvex economies. Théra M., Experimental, Constructive and Nonlinear Analysis. Canad. Math. Soc. Conf. Proceed. 27:2000.
19. A. Jofré, and, J. Rivera, A nonconvex separation property and some applications, Math. Programming, in press.
20. Khan M. A. Ioffe's normal cone and the foundations of welfare economics: The infinite dimensional theory. J. Math. Anal. Appl. 161:1991;284-298.
21. Khan M. A. The Mordukhovich normal cone and the foundations of welfare economics. J. Public Econ. Theory. 1:1999;309-338.
22. Kruger A. Y., Mordukhovich B. S. Extremal points and the Euler equation in nonsmooth optimization. Dokl. Akad. Nauk BSSR. 24:1980;684-687.
23. G. G. Malcolm, and, B. S. Mordukhovich, The Extremal Principle and Pareto Optimality in Nonconvex Economies, Department of Mathematics, Research Report No. 1, Wayne State University, 2000.
24. Mas-Colell A. The Theory of General Economic Equilibrium: A Differentiable Approach. 1985;Cambridge Univ. Press, London.
25. Mordukhovich B. S. Maximum principle in problems of time optimal control with nonsmooth constraints. J. Appl. Math. Mech. 40:1976;960-969.
26. Mordukhovich B. S. Approximation Methods in Problems of Optimization and Control. 1988;Nauka, Moscow.
27. Mordukhovich B. S. Generalized differential calculus for nonsmooth and set-valued mappings. J. Math. Anal. Appl. 183:1994;250-288.
28. B. S. Mordukhovich, The extremal principle and its applications to optimization and economics, in, Optimization and Related Topics, (, A. M. Rubinov, Ed.), Kluwer Academic, Dordrecht, in press.
29. Mordukhovich B. S., Shao Y. Extremal characterizations of Asplund spaces. Proc. Amer. Math. Soc. 124:1996;197-205.
30. Mordukhovich B. S., Shao Y. Nonsmooth sequential analysis in Asplund spaces. Trans. Amer. Math. Soc. 348:1996;1235-1280.
31. Mordukhovich B. S., Shao Y. Nonconvex differential calculus for infinite-dimensional multifunctions. Set-Valued Anal. 4:1996;205-236.
32. Phelps R. R. Convex Functions, Monotone Operators and Differentiability. 1993;Springer-Verlag, Berlin.
33. Rockafellar R. T. Generalized directional derivatives and subgradients of nonconvex functions. Canad. J. Math. 32:1980;257-280.
34. Rockafellar R. T., Wets R. J.-B. Variational Analysis. 1998;Springer-Verlag, Berlin.
35. Zhu Q. J. The equivalence of several basic theorems for subdifferentials. Set-Valued Anal. 6:1998;171-185.