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Duality Theory and Applications to Unilateral Problems

Author

Listed:
  • Patrizia Daniele

    (Università di Catania)

  • Sofia Giuffrè

    (Mediterranean University of Reggio Calabria)

  • Antonino Maugeri

    (Università di Catania)

  • Fabio Raciti

    (Università di Catania)

Abstract

This paper is concerned with the problem of strong duality between an infinite dimensional convex optimization problem with cone and equality constraints and its Lagrange dual. A necessary and sufficient condition and sufficient conditions, really new, in order that the strong duality holds true are given. As an application, the existence of the Lagrange multiplier associated with the obstacle problem and to an elastic–plastic torsion problem, more general than the ones previously considered, is stated together with a characterization of the elastic–plastic torsion problem. This application is the main result of the paper. It is worth remarking that the usual conditions based on the interior, on the core, on the intrinsic core or on the strong quasi-relative interior cannot be used because they require the nonemptiness of the interior (and of the above mentioned generalized interior concepts) of the ordering cone, which is usually empty.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:3:d:10.1007_s10957-013-0512-4
    DOI: 10.1007/s10957-013-0512-4
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    References listed on IDEAS

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    1. R. I. Boţ & E. R. Csetnek & A. Moldovan, 2008. "Revisiting Some Duality Theorems via the Quasirelative Interior in Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 67-84, October.
    2. Daniele, Patrizia, 2010. "Evolutionary variational inequalities and applications to complex dynamic multi-level models," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(6), pages 855-880, November.
    3. M. G. Cojocaru & P. Daniele & A. Nagurney, 2005. "Projected Dynamical Systems and Evolutionary Variational Inequalities via Hilbert Spaces with Applications1," Journal of Optimization Theory and Applications, Springer, vol. 127(3), pages 549-563, December.
    4. A. Maugeri & F. Raciti, 2010. "Remarks on infinite dimensional duality," Journal of Global Optimization, Springer, vol. 46(4), pages 581-588, April.
    5. 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.
    6. Patrizia Daniele, 2006. "Dynamic Networks and Evolutionary Variational Inequalities," Books, Edward Elgar Publishing, number 3516.
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    Cited by:

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