EXTENSION OF HOFFMAN ERROR BOUND TO POLYNOMIAL SYSTEMS

Given any linear system (defined by linear inequalities/equalities) in R(n), Hoffman's error bound says that the distance from any point x i s an element of R(n) to the solution set of the linear system is bound ed by a constant (independent of x) times a certain residual function evaluated at x. This paper considers arbitrary (possibly nonconvex) po lynomial systems (defined by polynomial inequalities/equalities). It i s shown that the solution sets of such systems are, in general, Holder continuous as the right-hand side changes, in contrast to the Lipschi tzian continuity for the linear case. Also, for any convex quadratic i nequality system possessing an interior solution, the authors show tha t its solution set behaves in a Lipschitzian manner as the right-hand side varies. This result sharpens the earlier error bound results by M angasarian and Robinson for general convex differentiable inequality s ystems, which, in addition to the interiority assumption, require eith er an asymptotic constraint qualification condition or that the soluti on set be bounded.