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Error Bounds for Degenerate Cone Inclusion Problems

Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610068, P. R. China, and Department of Decision Sciences, National University of Singapore, Singapore
Department of Decision Sciences and Singapore-MIT Alliance, National University of Singapore, Singapore
yiranhe{at}hotmail.com
jsun{at}nus.edu.sg

Error bounds for cone inclusion problems in Banach spaces are established under conditions weaker than Robinson’s constraint qualification. The results allow the cone to be more general than the origin and therefore also generalize a classical error bound result concerning equality-constrained sets in optimization. Applications in finite-dimensional differentiable inequalities and in tangent cones are discussed.

Key Words: cone inclusion problems; error bounds; Robinson’s constraint qualification; tangent cones
History: Received: June 27, 2003; revision received: April 5, 2004;revision received: December 20, 2004;