Nondegenerate Solutions and Related Concepts in Affine Variational Inequalities
Michael C. Ferris, Jong‐Shi Pang · SIAM Journal on Control and Optimization · 1996
The notion of a strictly complementary solution for complementarity problems is extended to that of a nondegenerate solution of variational inequalities. Several equivalent formulations of nondegeneracy are given. In the affIne case, an existence theorem for a nondegenerate solution is given in terms of several related concepts which are shown to be equivalent in this context. These include a weak sharp minimum, the minimum principle sufficiency, and error bounds. The gap function associated with the variational inequality plays a central role in this existence theorem.