caa a22 4500 475750586 CHVBK 20180406123522.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1023/A:1026558500809 doi (NATIONALLICENCE)springer-10.1023/A:1026558500809 On Two Applications of H-Differentiability to Optimization and Complementarity Problems [Elektronische Daten] [M.A. Tawhid, M. Gowda] In a recent paper, Gowda and Ravindran (Algebraic univalence theorems for nonsmooth functions, Research Report, Department of Mathematics and Statistics, University of Maryland, Baltimore, MD 21250, March 15, 1998) introduced the concepts of H-differentiability and H-differential for a function f : R n → R n and showed that the Fréchet derivative of a Fréchet differentiable function, the Clarke generalized Jacobian of a locally Lipschitzian function, the Bouligand subdifferential of a semismooth function, and the C-differential of a C-differentiable function are particular instances of H-differentials. In this paper, we consider two applications of H-differentiability. In the first application, we derive a necessary optimality condition for a local minimum of an H-differentiable function. In the second application, we consider a nonlinear complementarity problem corresponding to an H-differentiable function f and show how, under appropriate conditions on an H-differential of f, minimizing a merit function corresponding to f leads to a solution of the nonlinear complementarity problem. These two applications were motivated by numerous studies carried out for C 1, convex, locally Lipschitzian, and semismooth function by various researchers. Kluwer Academic Publishers, 2000 H -differentiability nationallicence nonlinear complementarity problem nationallicence NCP function nationallicence merit function nationallicence locally Lipschitzian function nationallicence generalized Jacobian nationallicence Tawhid M.A. Department of Mathematics and Statistics, University of Maryland, 21250, Baltimore County, Baltimore, MD, USA aut Gowda M. Department of Mathematics and Statistics, University of Maryland, 21250, Baltimore County, Baltimore, MD, USA aut Computational Optimization and Applications Kluwer Academic Publishers 17/2-3(2000-12-01), 279-299 0926-6003 17:2-3<279 2000 17 10589 https://doi.org/10.1023/A:1026558500809 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1026558500809 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Tawhid M.A. Department of Mathematics and Statistics, University of Maryland, 21250, Baltimore County, Baltimore, MD, USA aut NATIONALLICENCE 700 1- Gowda M. Department of Mathematics and Statistics, University of Maryland, 21250, Baltimore County, Baltimore, MD, USA aut NATIONALLICENCE 773 0- Computational Optimization and Applications Kluwer Academic Publishers 17/2-3(2000-12-01), 279-299 0926-6003 17:2-3<279 2000 17 10589 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer