On continuity properties of the solution map in linear complementarity problems.
For the standard linear complementarity problem \[ x \geq 0, Mx +q \geq 0, x^{T}(Mx +q) =0; \] its solution set can be viewed as the value of the mapping \(S_{M}\) at \(q\). The author shows that \(S_{M}\) is Lipschitz continuous on its effective domain if and only if it is lower semicontinuous on this set. Under the additional assumption that \(M\) belongs to the class \(Q\), the same result was established in the previous work of the author.
scientific article; zbMATH DE number 1885661