Paratingent Derivative Applied to the Measure of the Sensitivity in Multiobjective Differential Programming

Abstract

We analyse the sensitivity of differential programs of the form $\text{Min}f(x)$ subject to $g(x)=b,x\in D$ where $f$ and $g$ are ${𝒞}^1$ 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.