Theory of Error Bounds with Applications

SB29.1 On the Extension of Frank-Wolfe Theorem to the Quadratically Constrained Quadratic Program Shuzhong Zhang, Zhi-Quan Luo --- Erasmus Univer. Rotterdam, Econometric Inst., PO Box 1738, Rotterdam, 3000 DR , The Netherlands (zhang@few.eur.nl)

We study the continuity of the feasible set defined by convex¨ quadratic inequalities and show that if a convex quadratic function¨ is bounded below over such set then its infimum is always attained.¨ We also present some results on the nonconvex case.

SB29.2 New Characterizations of the Existence of an Error Bound for a Convex Inequality System Sien Deng --- Northern IL Univ., Dept. of Math., DeKalb, IL 60625 , (deng@math.niu.edu)

We discuss various new characterizations of the existence of a¨ global/local error bound for a convex inequality system as well as¨ their applications.

SB29.3 Global Error Bounds & Metric Regularity in Optimization Wu Li --- Old Dominion Univ., Dept. of Math. & Stats., Norfolk, VA 23529 , (wuli@math.odu.edu)

Metric regularity can be considered as a special form of local error¨ bounds. However, under certain conditions metric regularity is¨ equivalent to global error bounds. We establish a relation between¨ weak Slater condition and an estimate of the distance from a point¨ to the intersection of finitely many convex sets.