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A New Approach to Solve Convex Infinite-Dimensional Bilevel Problems: Application to the Pollution Emission Price Problem

Author

Listed:
  • Antonino Maugeri

    (University of Catania)

  • Laura Scrimali

    (University of Catania)

Abstract

This paper presents a new approach to studying bilevel programming problems in infinite-dimensional spaces, based on infinite-dimensional duality and evolutionary variational inequalities. The result is applied to the evolutionary emission price problem. In our model, the government chooses the optimal price of pollution emissions, with consideration to firms’ response to the price. Moreover, firms choose the optimal quantities of production to maximize their profits, given the price of pollution emissions. Finally, we provide a numerical example to show the feasibility of our approach.

Suggested Citation

  • Antonino Maugeri & Laura Scrimali, 2016. "A New Approach to Solve Convex Infinite-Dimensional Bilevel Problems: Application to the Pollution Emission Price Problem," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 370-387, May.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:2:d:10.1007_s10957-016-0894-1
    DOI: 10.1007/s10957-016-0894-1
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    References listed on IDEAS

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    1. Patrizia Daniele & Sofia Giuffrè & Antonino Maugeri & Fabio Raciti, 2014. "Duality Theory and Applications to Unilateral Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 718-734, September.
    2. Amouzegar, Mahyar A. & Moshirvaziri, Khosrow, 1999. "Determining optimal pollution control policies: An application of bilevel programming," European Journal of Operational Research, Elsevier, vol. 119(1), pages 100-120, November.
    3. Boris S. Mordukhovich & Nguyen Mau Nam & Hung M. Phan, 2012. "Variational Analysis of Marginal Functions with Applications to Bilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 557-586, March.
    4. Beckmann, Martin J & Wallace, James P, 1969. "Continuous Lags and the Stability of Market Equilibrium," Economica, London School of Economics and Political Science, vol. 36(141), pages 58-68, February.
    5. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
    6. A. Maugeri & F. Raciti, 2010. "Remarks on infinite dimensional duality," Journal of Global Optimization, Springer, vol. 46(4), pages 581-588, April.
    7. Laura Scrimali, 2012. "Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 258-277, July.
    8. P. Daniele & A. Maugeri & W. Oettli, 1999. "Time-Dependent Traffic Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 543-555, December.
    9. Patrizia Daniele, 2006. "Dynamic Networks and Evolutionary Variational Inequalities," Books, Edward Elgar Publishing, number 3516.
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