The Stability Of Second-order Global Minimum

In this paper, the definitions of stable second-order global minimum and tilt-stable global minimum are introduced. Using techniques of variational analysis, under the assumption that f is a proper and lower-semicontinuous function, certain implications among stable second-order global minimum, tilt stability of the glob-al minimum, local C1,1—smooth of the conjugate function f*, global strong metric regularity of the subdifferential (?)f, global metric regularity of the subdifferential, global strong pseudo-metric regularity of the subdifferential, global pseudo-metric regularity of the subdifferential, locally Lipschitz continuity of the inverse subdif-ferential and the global positive-defniteness of the second-order subdifferential are proven.