Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems
SIAM Journal on Control and Optimization
Conditioning and upper-Lipschitz inverse subdifferentials in nonsmooth optimization problems
Journal of Optimization Theory and Applications
Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis
SIAM Journal on Control and Optimization
On the Sensitivity Analysis of Hoffman Constants for Systems of Linear Inequalities
SIAM Journal on Optimization
Hoffman"s Least Error Bounds for Systems of Linear Inequalities
Journal of Global Optimization
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If K(t) are sets of admissible solutions in parametric programs then it is natural to ask about the Lipschitz-like property and the lower semi-continuity of the multifunction. Answers to this question are related to the problem of the continuity or Lipschitz continuity of the value function, namely having the lower semi-continuity of K(·) we get the upper semi-continuity of the function easily and the Lipschitz-like property of K(·) leads to the Lipschitz-continuity of it. Herein sufficient conditions to get these properties of the polyhedral multifunction of admissible solutions are given in terms of the lower limit of the Hoffman constant. It is shown that the multifunction is Lipschitz-like at these parameters at which the lower limit of the Hoffman constant are positive.