Abstract
The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. First of all, we deal with systems described via one convex inequality and extend the achieved results, by making use of a celebrated scalarization function, to convex inequality systems expressed by means of a general vector function. We also propose a second approach for guaranteeing the existence of global error bounds of the latter, which meanwhile sharpens the classical result of Robinson.
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Dedicated to Professor Marco A. López on the occasion of his 60th birthday.
Research of R.I. Boţ was partially supported by DFG (German Research Foundation), project WA 922/1-3.
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Boţ, R.I., Csetnek, E.R. Error bound results for convex inequality systems via conjugate duality. TOP 20, 296–309 (2012). https://doi.org/10.1007/s11750-011-0187-7
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DOI: https://doi.org/10.1007/s11750-011-0187-7