Journal of Optimization Theory and Applications
On Two Applications of H-Differentiability to Optimization and Complementarity Problems
Computational Optimization and Applications
Quadratic one-step smoothing Newton method for P0-LCP without strict complementarity
Applied Mathematics and Computation
Computational Optimization and Applications
Smooth Convex Approximation to the Maximum Eigenvalue Function
Journal of Global Optimization
A New Path-Following Algorithm for Nonlinear P*Complementarity Problems
Computational Optimization and Applications
Computational Optimization and Applications
A nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems
Optimization Methods & Software
A non-interior-point smoothing method for variational inequality problem
Journal of Computational and Applied Mathematics
Calibrating Least Squares Semidefinite Programming with Equality and Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
Monotonicity of NFP mappings associated with variational
AMERICAN-MATH'12/CEA'12 Proceedings of the 6th WSEAS international conference on Computer Engineering and Applications, and Proceedings of the 2012 American conference on Applied Mathematics
Global bounds for the distance to solutions of co-coercive variational inequalities
Operations Research Letters
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Two recent papers [F. Facchinei, Math. Oper. Res., 23 (1998), pp. 735--745 and F. Facchinei and C. Kanzow, SIAM J. Control Optim., 37 (1999), pp. 1150--1161] have shown that for a continuously differentiable P0-function f, the nonlinear complementarity problem NCP$(f_\varepsilon)$ corresponding to the regularization $f_\varepsilon(x):=f(x)+\varepsilon x$ has a unique solution for every $\varepsilon0$, that dist ($x(\varepsilon), \,{\mathop{\rm SOL}}(f))\rightarrow 0$ as $\varepsilon \rightarrow 0$ when the solution set SOL(f) of NCP(f) is nonempty and bounded, and NCP(f) is stable if and only if the solution set is nonempty and bounded. These results are proved via the Fischer function and the mountain pass theorem. In this paper, we generalize these nonlinear complementarity results to a box variational inequality problem corresponding to a continuous P0-function where the regularization is described by an integral. We also describe an upper semicontinuity property of the inverse of a weakly univalent function and study its consequences.