Error bounds for nondifferentiable convex inequalities under a strong Slater constraint qualification

Error bounds for nondifferentiable convex inequalities under a strong Slater constraint qualification

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Article ID: iaor20001075
Country: Netherlands
Volume: 83
Issue: 2
Start Page Number: 187
End Page Number: 194
Publication Date: Oct 1998
Journal: Mathematical Programming
Authors:
Abstract:

A global error bound is given on the distance between an arbitrary point in the n-dimensional real space Rn and its projection on a nonempty convex set determined by m convex, possibly nondifferentiable, inequalities. The bound is in terms of a natural residual that measures the violations of the inequalities multiplied by a new simple condition constant that embodies a single strong Slater constraint qualification (CQ) which implies the ordinary Slater CQ. A very simple bound on the distance to the projection relative to the distance to a point satisfying the ordinary Slater CQ is given first and then used to derive the principal global error bound.

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