Abstract
The concluding chapter of the book is devoted to applications of advanced constructions and techniques of variational analysis to economic modeling.
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References
C. D. Aliprantis and K. C. Border (2006), Infinite Dimensional Analysis: A Hitchhiker’s Guide, Springer, Berlin.
T. Q. Bao and B. S. Mordukhovich (2010), Set-valued optimization in welfare economics, Adv. Math. Econ. 13, 114–153.
T. Q. Bao and B. S. Mordukhovich (2011), Refined necessary conditions in multiobjective optimization with applications to microeconomic modeling, Discrete Contin. Dyn. Syst. 31, 1069–1096.
T. Q. Bao and B. S. Mordukhovich (2012), Extended Pareto optimality in multiobjective problems, in Recent Developments in Vector Optimization, edited by Q. H. Ansari and J.-C. Yao, pp. 467–515, Springer, Berlin.
T. Q. Bao and C. Tammer (2012), Lagrange necessary conditions for Pareto minimizers in Asplund spaces and applications, Nonlinear Anal. 75, 1089–1103.
S. Bellaassali and A. Jourani (2008), Lagrange multipliers for multiobjective programs with a general preference, Set-Valued Anal. 16, 229–243.
J.-M. Bonnisseau, B. Cornet and M.-O. Czarnecki (2007), The marginal pricing rule revisited, Econom. Theory 33, 579–589.
J.-M. Bonnisseau and O. Lachiri (2006), About the second theorem of welfare economics with stock markets, Pac. J. Optim. 2, 469–485.
B. Cornet (1990), Marginal cost pricing and Pareto optimality, in Essays in Honor of Edmond Malinvaud, edited by P. Champsaur, Vol. 1, pp. 14–53, MIT Press, Cambridge, Massachusetts.
S. Dempe and J. Dutta (2012), Is bilevel programming a special case of mathematical programming with complementarity constraints?, Math. Program. 131, 37–48.
S. D. Flåm (2006), Upward slopes and inf-convolutions, Math. Oper. Res. 31, 188–198.
S. D. Flåm, J.-B. Hiriart-Urruty and A. Jourani (2009), Feasibility in finite time, J. Dyn. Contr. Syst. 15, 537–555.
M. Florenzano, P. Gourdel and A. Jofré (2006), Supporting weakly Pareto optimal allocations in infinite-dimensional nonconvex economies, J. Economic Theory 29, 549–564.
A. Habte and B. S. Mordukhovich (2011), Extended second welfare theorem for nonconvex economies with infinite commodities and public goods, Adv. Math. Econ. 14, 93–126.
A. Jofré (2000), A second welfare theorem in nonconvex economies, in Constructive, Experimental, and Nonlinear Analysis, edited by M. Théra, pp. 175–184, American Mathematical Society, Providence, Rhode Island.
A. Jofré and A. Jourani (2015), Characterizations of the free disposal condition for nonconvex economies on infinite dimensional commodity spaces, SIAM J. Optim. 25 (2015), 699–712.
A. Jofré and J. Rivera Cayupi (2006), A nonconvex separation property and some applications, Math. Program. 108 (2006), 37–51.
A. A. Khan, C. Tammer and C. Zălinescu (2015), Set-Valued Optimization. An Introduction with Applications, Springer, Berlin.
M. A. Khan (1991), Ioffe’s normal cone and the foundation of welfare economics: the infinite-dimensional theory, J. Math. Anal. Appl. 161, 284–298.
M. A. Khan (1999), The Mordukhovich normal cone and the foundations of welfare economics, J. Public Econ. Theory 1, 309–338.
G. G. Malcolm and B. S. Mordukhovich (2001), Pareto optimality in nonconvex economies with infinite-dimensional commodity spaces, J. Global Optim. 20, 323–346.
A. Mas-Colell (1985), Pareto optima and equilibria: the finite-dimensional case, in Advances in Equilibrium Theory, edited by C. D. Aliprantis, O. Burkinshaw and N. J. Rothman, Lecture Notes in Econom. Math. Systems 244, pp. 25–42, Springer, Berlin.
A. Mas-Collel, M. D. Whinston and J. R. Green (1995), Mircoeconomic Theory, Oxford University Press, Oxford, United Kingdom.
B. S. Mordukhovich (2000), Abstract extremal principle with applications to welfare economics, J. Math. Anal. Appl. 251, 187–216.
B. S. Mordukhovich (2005), Nonlinear prices in nonconvex economies with classical Pareto and strong Pareto optimal allocations, Positivity 9, 541–568.
B. S. Mordukhovich (2006), Variational Analysis and Generalized Differentiation, I: Basic Theory, Springer, Berlin.
B. S. Mordukhovich (2006), Variational Analysis and Generalized Differentiation, II: Applications, Springer, Berlin.
A. Uderzo (2014), Localizing vector optimization problems with application to welfare economics, Set-Valued Var. Anal. 22, 483–501.
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Mordukhovich, B.S. (2018). Set-Valued Optimization and Economics. In: Variational Analysis and Applications. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-92775-6_10
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DOI: https://doi.org/10.1007/978-3-319-92775-6_10
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