STABILITY OF SEMI-INFINITE INEQUALITY SYSTEMS INVOLVING MIN-TYPE FUNCTIONS
Marco A. López, Alexander M. Rubinov, Virginia N. Vera deSerio · Numerical Functional Analysis and Optimization · 2005
We study the stability of semi-infinite inequality systems that arise in monotonic analysis. These systems are defined by certain classes of abstract linear functions. We consider the cone of vectors with positive coordinates as a base space and we consider two classes of abstract linear functions: (1) min-type functions of the form a(x): = ana, x = min i=1, …, n a i x i , x ∈ . The class of corresponding abstract convex functions consists of increasing convex-along-rays functions; in particular, convex increasing functions belong to this class. (2) Min-type functions of the form l(x): = min(ana, x, 1), x ∈ . The class of corresponding abstract convex functions consists of increasing co-radiant functions; in particular, concave nonnegative increasing functions belong to this class. We study stability of the feasible set mapping from different points of view (lower semicontinuity, continuity in the Bouligand sense, metric regularity, the existence of strong Slater points, adapted Robinson–Ursescu condition). We also study a stable abstract linear presentation of a lower level set of corresponding abstract convex functions. Some solvability results are also presented.