Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems
SIAM Journal on Control and Optimization
Sensitivity analysis in variational inequalities
Mathematics of Operations Research
Nonlinear functional analysis and its applications
Nonlinear functional analysis and its applications
An implicit-function theorem for a class of nonsmooth functions
Mathematics of Operations Research
Stability of Locally Optimal Solutions
SIAM Journal on Optimization
Coderivatives in parametric optimization
Mathematical Programming: Series A and B
Lower semicontinuity of the solution map to a parametric vector variational inequality
Journal of Global Optimization
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In the present paper, we will study the solution stability of parametric variational conditions $${{0 \in f(\mu, x)+ N_{K(\lambda)}(x)},}$$ where M and 驴 are topological spaces, $${f : M \times R^n \to R^n}$$ is a function, $${K : \Lambda\to 2^{R^n}}$$ is a multifunction and N K(驴)(x) is the value at x of the normal cone operator associated with the set K(驴). By using the degree theory and the natural map we show that under certain conditions, the solution map of the problem is lower semicontinuous with respect to parameters (μ,驴). Our results are different versions of Robinson's results [15] and proved directly without the homeomorphic result between the solution sets.