American Institute of Mathematical Sciences

Advanced
April  2007, 3(2): 233-255. doi: 10.3934/jimo.2007.3.233

Existence of closed graph, maximal, cyclic pseudo-monotone relations and revealed preference theory

A. C. Eberhard 1, and  J-P. Crouzeix 2,

1. 

School of Mathematical and Geospatial Sciences, Royal Melbourne Institute of Technology, G.P.O. Box 2476V, Melbourne, Australia 3001, Australia
2. 

LIMOS, Université Blaise Pascal, Boite Postale 206, F-63174 AUBIERE Cedex, France

Received  August 2006 Revised  October 2006 Published  April 2007

We investigate a multifunction $x$→Ñ f $(x)$ derived via normal cones to the level sets Š $(x)$ := { $x^$' | $f(x^$') $ < f(x)$} for an important class of pseudo--convex functions. It is shown that $x$→Ñ f $(x)$ is simultaneously both a maximally cyclically pseudo--monotone and a maximally pseudo-monotone relation within neighbourhoods on which $f$ is nonconstant. The relevance of this work to the problem of construction of a utility function from observations of revealed preferences of a consumer is discussed.
Keywords: revealed preferences., cyclic quasi/pseudo-monotonicity, utility functions, normal cone mappings.
Mathematics Subject Classification: Primary: 47H05, 90A40, 26A51; Secondary: 90A10, 52A0.
Citation: A. C. Eberhard, J-P. Crouzeix. Existence of closed graph, maximal, cyclic pseudo-monotone relations and revealed preference theory. Journal of Industrial & Management Optimization, 2007, 3 (2) : 233-255. doi: 10.3934/jimo.2007.3.233
[1]

Azam Chaudhry, Rehana Naz. Closed-form solutions for the Lucas-Uzawa growth model with logarithmic utility preferences via the partial Hamiltonian approach. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 643-654. doi: 10.3934/dcdss.2018039
[2]

Huiyan Xue, Antonella Zanna. Generating functions and volume preserving mappings. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 1229-1249. doi: 10.3934/dcds.2014.34.1229
[3]

Carlo Alabiso, Mario Casartelli. Quasi Normal modes in stochastic domains. Conference Publications, 2003, 2003 (Special) : 21-29. doi: 10.3934/proc.2003.2003.21
[4]

Peng Huang, Xiong Li, Bin Liu. Invariant curves of smooth quasi-periodic mappings. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 131-154. doi: 10.3934/dcds.2018006
[5]

Piotr Pokora, Tomasz Szemberg. Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone. Electronic Research Announcements, 2014, 21: 126-131. doi: 10.3934/era.2014.21.126
[6]

Kanat Abdukhalikov, Sihem Mesnager. Explicit constructions of bent functions from pseudo-planar functions. Advances in Mathematics of Communications, 2017, 11 (2) : 293-299. doi: 10.3934/amc.2017021
[7]

Zhenguo Bai, Tingting Zhao. Spreading speed and traveling waves for a non-local delayed reaction-diffusion system without quasi-monotonicity. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4063-4085. doi: 10.3934/dcdsb.2018126
[8]

Lam Quoc Anh, Nguyen Van Hung. Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems. Journal of Industrial & Management Optimization, 2018, 14 (1) : 65-79. doi: 10.3934/jimo.2017037
[9]

S. S. Dragomir, I. Gomm. Some new bounds for two mappings related to the Hermite-Hadamard inequality for convex functions. Numerical Algebra, Control & Optimization, 2012, 2 (2) : 271-278. doi: 10.3934/naco.2012.2.271
[10]

Fernando Hernando, Tom Høholdt, Diego Ruano. List decoding of matrix-product codes from nested codes: An application to quasi-cyclic codes. Advances in Mathematics of Communications, 2012, 6 (3) : 259-272. doi: 10.3934/amc.2012.6.259
[11]

Yanqin Bai, Pengfei Ma, Jing Zhang. A polynomial-time interior-point method for circular cone programming based on kernel functions. Journal of Industrial & Management Optimization, 2016, 12 (2) : 739-756. doi: 10.3934/jimo.2016.12.739
[12]

Masao Fukushima. A class of gap functions for quasi-variational inequality problems. Journal of Industrial & Management Optimization, 2007, 3 (2) : 165-171. doi: 10.3934/jimo.2007.3.165
[13]

JIAO CHEN, WEI DAI, GUOZHEN LU. $L^p$ boundedness for maximal functions associated with multi-linear pseudo-differential operators. Communications on Pure & Applied Analysis, 2017, 16 (3) : 883-898. doi: 10.3934/cpaa.2017042
[14]

Byung-Soo Lee. A convergence theorem of common fixed points of a countably infinite family of asymptotically quasi-$f_i$-expansive mappings in convex metric spaces. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 557-565. doi: 10.3934/naco.2013.3.557
[15]

Svetlana Bunimovich-Mendrazitsky, Yakov Goltser. Use of quasi-normal form to examine stability of tumor-free equilibrium in a mathematical model of bcg treatment of bladder cancer. Mathematical Biosciences & Engineering, 2011, 8 (2) : 529-547. doi: 10.3934/mbe.2011.8.529
[16]

Yuhong Dai, Nobuo Yamashita. Convergence analysis of sparse quasi-Newton updates with positive definite matrix completion for two-dimensional functions. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 61-69. doi: 10.3934/naco.2011.1.61
[17]

Gerard Gómez, Josep–Maria Mondelo, Carles Simó. A collocation method for the numerical Fourier analysis of quasi-periodic functions. I: Numerical tests and examples. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 41-74. doi: 10.3934/dcdsb.2010.14.41
[18]

Gerard Gómez, Josep–Maria Mondelo, Carles Simó. A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: Analytical error estimates. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 75-109. doi: 10.3934/dcdsb.2010.14.75
[19]

Haisen Zhang. Clarke directional derivatives of regularized gap functions for nonsmooth quasi-variational inequalities. Mathematical Control & Related Fields, 2014, 4 (3) : 365-379. doi: 10.3934/mcrf.2014.4.365
[20]

Shaolin Ji, Xiaomin Shi. Recursive utility optimization with concave coefficients. Mathematical Control & Related Fields, 2018, 8 (3&4) : 753-775. doi: 10.3934/mcrf.2018033

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences