Qualitative analysis of basic notions in parametric convex programming. I. Parameters in the constraints

Abstract

The paper presents a qualitative analysis of basic notions in parametric convex programming for convex programs with parameters in the righthand sides of the constraints. These notions are the set of feasible parameters, the solvability set and the stability sets of the first and of the second kind. The functions encountered in the paper are assumed to possess first order partial continuous derivatives on $R^n$, the parameters assume arbitrary real values and therefore the results obtained in the paper can be used for a wide class of convex programs.