The inverse problem in convex optimization with linear constraints
Aloqeili, Marwan1
1 Department of Mathematics, Birzeit University, P.O. Box 14 Birzeit, Palestine.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 71-94.

In this paper, we solve an inverse problem arising in convex optimization. We consider a maximization problem under m linear constraints. We characterize the solutions of this kind of problems. More precisely, we give necessary and sufficient conditions for a given function in R n to be the solution of a multi-constraint maximization problem. The conditions we give here extend well-known results in microeconomic theory.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2015040
Classification : 90C45, 49N45
Mots-clés : Inverse problem, multi-constraint maximization, value function, Slutsky relations
Aloqeili, Marwan 1

1 Department of Mathematics, Birzeit University, P.O. Box 14 Birzeit, Palestine. 
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Aloqeili, Marwan. The inverse problem in convex optimization with linear constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 71-94. doi : 10.1051/cocv/2015040. http://www.numdam.org/articles/10.1051/cocv/2015040/

M. Aloqeili, Utilisation du calcul différentiel exteriur en théorie du consommateur. Ph.D thesis, Université Paris Dauphine (2000).

M. Aloqeili, Characterizing demand functions with price dependent income. Math. Fin. Econ. 8 (2014) 135–151. | DOI | MR | Zbl

M. Aloqeili, The Generalized Slutsky Relations. J. Math. Econ. 40/1-2 (2004) 71-91. | MR | Zbl

R. Bryant, S. Chern, R. Gardner, H. Goldschmidt, and P. Griffiths, Exterior Differential Systems. In vol. 18. MSRI Publications. Springer-Verlag (1991). | MR | Zbl

P.A. Chiappori and I. Ekeland, The micro economics of group behavior: General characterization. J. Econ. Theory 130 1–26. | DOI | MR | Zbl

P.A. Chiappori and I. Ekeland, The Economics and Mathematics of Aggregation: Formal Models of Efficient Group Behavior. Now Publishers Inc. Hanover (2010). | Zbl

P.A. Chiappori and I. Ekeland, Exterior differential calculus and aggregation theory: a presentation and some new results. CEREMADE, Université Paris-Dauphine.

I. Ekeland and N. Djitté, An inverse problem in the economic theory of demand. Ann. Inst. Henri Poincaré, Non Lin. Anal. 23 (2016) 269–281. | DOI | Numdam | MR | Zbl

I. Ekeland and L. Nirenberg, A Convex Darboux Theorem. Methods Appl. Anal. 9 (2002) 329–344. | DOI | MR | Zbl

L.G. Epstein, Generalized duality and integrability. Econometrica 49 (1981) 655–678. | DOI | MR | Zbl

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