A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
Nonlinear complementarity as unconstrained and constrained minimization
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
On the resolution of monotone complementarity problems
Computational Optimization and Applications
A semismooth equation approach to the solution of nonlinear complementarity problems
Mathematical Programming: Series A and B
Solution of monotone complementarity problems with locally Lipschitzian functions
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
A New Nonsmooth Equations Approach to Nonlinear Complementarity Problems
SIAM Journal on Control and Optimization
On unconstrained and constrained stationary points of the implicit Lagrangian
Journal of Optimization Theory and Applications
A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems
Computational Optimization and Applications
On Characterizations of P- and P0-Properties in Nonsmooth Functions
Mathematics of Operations Research
Regularization of P0-Functions in Box Variational Inequality Problems
SIAM Journal on Optimization
A New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm
SIAM Journal on Optimization
Regularity Properties of a Semismooth Reformulation of Variational Inequalities
SIAM Journal on Optimization
On the local uniqueness of solutions of variational inequalities under H-differentiability
Journal of Optimization Theory and Applications
Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems
Mathematics of Operations Research
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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 : Rn → Rn 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 C1, convex, locally Lipschitzian, and semismooth function by various researchers.