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Cooperative behavior of functions, relations and sets

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  • Jean-Paul Penot

Abstract

One of the main difficulties in nonsmooth analysis is to devise calculus rules. It is our purpose here to show that a certain cooperative behavior between functions (resp. sets, resp. multifunctions) yields calculus rules for subdifferentials (resp. normal cones, resp. coderivatives). In previous contributions, the qualification conditions ensuring calculus rules were given in a non symmetric way. The new conditions can be combined easily and encompass various criteria. We also address the important question of the extension of calculus rules from the Lipschitz case to the general case. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • Jean-Paul Penot, 1998. "Cooperative behavior of functions, relations and sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 229-246, November.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:2:p:229-246
    DOI: 10.1007/s001860050025
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    Cited by:

    1. Teodor Chelmuş & Marius Durea & Elena-Andreea Florea, 2019. "Directional Pareto Efficiency: Concepts and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 336-365, July.
    2. Elena-Andreea Florea, 2018. "Vector Optimization Problems with Generalized Functional Constraints in Variable Ordering Structure Setting," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 94-118, July.
    3. Marius Durea & Radu Strugariu & Christiane Tammer, 2017. "On Some Methods to Derive Necessary and Sufficient Optimality Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 738-763, December.
    4. Marius Durea & Radu Strugariu & Christiane Tammer, 2015. "On set-valued optimization problems with variable ordering structure," Journal of Global Optimization, Springer, vol. 61(4), pages 745-767, April.

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