Quantitative Relationship Of Moduli And Radii In The Holder Tilt Stable Minimizer And Metric Regularity

The Holder tilt stable local minimizer is an imporment concept in optimization and has been studied widely.As an extension of Holder tilt stable local minimizers,with a positive number p replacing 1,tilt stable p-order minimizers were introduced and studied in[1]and described by the p-order metric regularity of the subdifferential mapping(?)f of the concerned proper lower semicontinuous function f.In the paper,we establish the exact quantitative relationship of the moduli and radii appearing in the p-order metric regularity of the subdifferential mapping(?)f and the tilt stable p-order minimizer of f.