Nonlocal Stable Well-Posedness And Tilt-Stability

Noted that the main results on the stable well-posedness and tilt-stable minimum in the literature are of local existence,which is not convenient in applications.Recently,[Zheng-Zhu,J Global Optim.,2021]studied the global stable well-posedness and global tilt-stable minimum,which require the involved metric inequalities to hold over the entire space,and so is difficultly varified.In this thesis,adopting admissible functions φ,ψ and radii r,δ,r’,δ’,r,σ,δ,we consider the r-δ-φ-stable well-posedness and r’-δ’-ψ-1-tilt-stable minimum of a real valued function f,which are between the corresponding local and global notions.we establish the relationship appearing in the r-σ-δ-ψ-strongly metric regularity of subdifferential mapping ?f and the r-δ-φ-stable well-posedness of f,and we establish the exact quantitative relationship of the radii r,δ and r’,δ’ appearing in the r-δ-φ-stable well-posedness and r’-δ’-ψ-1-tilt-stable minimum of f.Our results further improve and extend the local results and global results in the literature.