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Two approaches toward constrained vector optimization and identity of the solutions. (English) Zbl 1127.90404

Summary: In this paper we deal with a Fritz John type constrained vector optimization problem \[ \min_C f(x),\quad g(x) \in -K, \] where \(f \colon \mathbb{R}^n \rightarrow \mathbb{R}^m\), \(g \colon \mathbb{R}^n \rightarrow \mathbb{R}^p\). Here \(n,m\) and \(p\) are positive integers, \(K \subseteq \mathbb{R}^p\) is a closed convex cone and we assume that a partial ordering on \(\mathbb{R}^ m\) is induced by a cone \(C \subseteq \mathbb{R}^n\) which is closed and convex.

MSC:

90C29 Multi-objective and goal programming
26B25 Convexity of real functions of several variables, generalizations
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