Approximate necessary conditions for locally weak Pareto optimality (Q1335116)

Necessary conditions for a given point \(x^0\) to be a locally weak solution to the Pareto minimization problem: \[ \min (f_1(x), f_2(x),\dots, f_m(x)):= F(x),\;x\in X\subseteq \mathbb{R}^n, \] are presented under the condition that \(F\) is locally Fréchet differentiable. The conditions are in terms of the contingent cone. The case \(m= 2\) differs substantially from the case \(m> 2\). In the latter case the conditions are in terms of local \(\varepsilon\)-Pareto minima. There are some annoying misprints: In Theorem 2.1 and Theorem 3.1 one probably should read: \(\lambda^j\in -\mathbb{R}^2_-\) and \(\lambda^j\in - \mathbb{R}^m_-\) respectively. From this paper it is not clear how helpful these results are in solving Pareto minimization problems.