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Demyanov Difference of Two Sets and Optimality Conditions of Lagrange Multiplier Type for Constrained Quasidifferentiable Optimization

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  • Y. Gao

    (China University of Mining and Technology)

Abstract

In the first part of this paper, the Demyanov difference of two sets is considered. An expression for the Demyanov difference of two sets, which are the convex hulls of a finite number of points, is presented. In the second part, first-order necessary optimality conditions of the Lagrange multiplier type, for quasidifferentiable optimization with equality and inequality constraints, are given by means of the Demyanov difference of subdifferential and negative superdifferential.

Suggested Citation

  • Y. Gao, 2000. "Demyanov Difference of Two Sets and Optimality Conditions of Lagrange Multiplier Type for Constrained Quasidifferentiable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 377-394, February.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:2:d:10.1023_a:1004613814084
    DOI: 10.1023/A:1004613814084
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    Cited by:

    1. Beissner, Patrick & Werner, Jan, 2023. "Optimal allocations with α-MaxMin utilities, Choquet expected utilities, and Prospect Theory," Theoretical Economics, Econometric Society, vol. 18(3), July.
    2. T. Antczak, 2016. "Optimality Conditions in Quasidifferentiable Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 708-725, November.
    3. Stephan Dempe & Maria Pilecka, 2016. "Optimality Conditions for Set-Valued Optimisation Problems Using a Modified Demyanov Difference," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 402-421, November.
    4. Joydeep Dutta, 2005. "Generalized derivatives and nonsmooth optimization, a finite dimensional tour," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 185-279, December.
    5. Y. Gao, 2004. "Representation of the Clarke Generalized Jacobian via the Quasidifferential," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 519-532, December.
    6. Y. Gao, 2006. "Differences of Polyhedra in Matrix Space and Their Applications to Nonsmooth Analysis," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 431-442, September.

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