On the local uniqueness of solutions of variational inequalities under H-differentiability
Journal of Optimization Theory and Applications
Necessary Optimality Conditions for Bilevel Optimization Problems Using Convexificators
Journal of Global Optimization
Computational Optimization and Applications
Second order optimality conditions for bilevel set optimization problems
Journal of Global Optimization
Generalized Hessians of $C^{1,1}$-Functions and Second-Order Viscosity Subjets
SIAM Journal on Optimization
Convexificators and strong Kuhn-Tucker conditions
Computers & Mathematics with Applications
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The notion of approximate Jacobian matrices is introduced for a continuous vector-valued map. It is shown, for instance, that the Clarke generalized Jacobian is an approximate Jacobian for a locally Lipschitz map. The approach is based on the idea of convexificators of real-valued functions. Mean value conditions for continuous vector-valued maps and Taylor's expansions for continuously Gâteaux differentiable functions (i.e., C1-functions) are presented in terms of approximate Jacobians and approximate Hessians, respectively. Second-order necessary and sufficient conditions for optimality and convexity of C1-functions are also given.