Existence of weakly efficient solutions in nonsmooth vector optimization (Q932556)

The authors consider the following two vector optimization problems 1. An infinite-dimensional problem \[ \text{Minimize }f(x)\text{ subject to }x\in K \] where \(X\) and \(Y\) are two Banach spaces, \(f: X\to Y\) is a given function and \(K\) is a nonempty subset of \(X\). 2. A finite-dimensional problem \[ \text{Minimize }f(x):=(f_1(x),\dots,f_p(x))\text{ subject to }x\in X, \] where \(f_i: \mathbb{R}^n\to\mathbb{R}\) \((i= 1,\dots, p)\) are given functions and \(X\) is a nonempty subset of \(\mathbb{R}^n\). For these problems, the existence of weakly efficient solutions are studied. The results are stated under hypotheses of generalized convexity.