Error bounds for nondifferentiable convex inequalities under a strong Slater constraint qualification |
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Authors: | O L Mangasarian |
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Institution: | (1) Computer Science Department, University of Wisconsin-Madison, 1210 West Dayton Street, 53706 Madison, WI, USA |
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Abstract: | A global error bound is given on the distance between an arbitrary point in then-dimensional real spaceR
n and its projection on a nonempty convex set determined bym 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.
This material is based on research supported by National Science Foundation Grant CCR-9322479 and Air Force Office of Scientific
Research grant F49620-97-1-0326. |
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Keywords: | Convex inequalities Error bounds Strong Slater constraint qualification |
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