Paratingent derivative applied to the measure of the sensitivity in multiobjective differential programming

Abstract

We analyse the sensitivity of differential programs of the form Min f (x) subject to g(x) = b, x ∈ D where f and g are C1 maps whose respective images lie in ordered Banach spaces. Following previous works on multiobjective programming, the notion of T-optimal solution is used. The behaviour of some nonsingleton sets of T-optimal solutions according to changes of the parameter b in the problem is analysed. The main result of the work states that the sensitivity of the program is measured by a Lagrange multiplier plus a projection of its derivative. This sensitivity is measured by means of the paratingent derivative.