Computable Error Bounds for Semidefinite Programming
Journal of Global Optimization
Optimal Hoffman-Type Estimates in Eigenvalue and Semidefinite Inequality Constraints
Journal of Global Optimization
On the Asymptotically Well Behaved Functions and Global Error Bound for Convex Polynomials
SIAM Journal on Optimization
Minimum recession-compatible subsets of closed convex sets
Journal of Global Optimization
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In 1952, A. J. Hoffman proved a fundamental result of an error bound on the distance from any point to the solution set of a linear system in $\hbox{{\bbb R}}^n$. In SIAM J. Control, 13 (1975), pp. 271--273, Robinson extended Hoffman's theorem to any system of convex inequalities in a normed linear space which satisfies the Slater constraint qualification and has a bounded solution set. This paper studies any system of convex inequalities in a reflexive Banach space which has an unbounded solution set. It is shown that Hoffman's error bound holds for such a system when a related convex system, which defines the recession cone of the solution set for the system, satisfies the Slater constraint qualification.