Stability Of Global Minimum Under Tilt Perturbatio

The stability of the global minimum and the global metric regularity of the subdifferential of the objective function under tilt perturbations are studied in this paper.We extend a set of local definitions to the global case.Using the relevant theories and techniques in variational analysis,we generalize and improve some existing conclusions in the literature.The full text consists of five chapters.In the first chapter,we introduce the research background and main work of this paper.In Chapter 2,we introduce the symbols used in this paper and some basic conclusions in the variational analysis.In Chapter 3,we introduce the definition of global ψ-openness for multifunctions.When ψ is a strictly increasing admissible function,we prove that the global ψ-openness and global ψ-metric regularity of multifunctions are equivalent.In Chapter 4,we extend the definition ofφ-regular functions to the global case and introduce the notion of continuously globally φ-regular functions.Furthermore,we provide two examples of continuously globallyφ-regular functions.Under the assumption that the objective function f is continuously globally φ-regular,we establish the relationships between stable global ψ-well-posedness of f and the global strong ψ-metric regularity of its subdifferential mapping (?)cf,whereφ(t):=∫0tψ(x)dx for all t ∈ R+.In Chapter 5,we introduce the concept of global uniform φ-growth condition and compare it with stable global φ-well-posedness.We investigate the connection between the global uniform φ-growth condition and the global strong ψ-pseudo-metric regularity of the subdifferential of the objective function.And we compare the results in the global case with those in the local case.For the tilt-stable global minimum,we show that the equivalence results for convex case still exist if the perturbed function is invex.