HOLDER STABLE MINIMIZERS, TILT STABILITY, AND HOLDER METRIC REGULARITY OF SUBDIFFERENTIALS

Using techniques of variational analysis and dual techniques for smooth conjugate functions, for a local minimizer of a proper lower semicontinuous function f on a Banach space, p is an element of (0, +infinity) and q = 1+p/p , we prove that the following two properties are always equivalent: (i) (x) over bar is a stable q-order minimizer of f and (ii) (x) over bar is a tilt-stable p-order minimizer of f. We also consider their relationships in conjunction with the p-order strong metric regularity of the subdifferential mapping partial derivative f.