Approximate efficiency and scalar stationarity in unbounded nonsmooth convex vector optimization problems (Q1594871)

The author considers the class \({\mathcal F}\) of convex vector functions having the property that every scalarly stationary sequence is a weakly efficient sequence. He characterizes the class \({\mathcal F}\) showing the number of necessary, sufficient and equivalent conditions for a function \(F\) to be in the class \({\mathcal F}\) provided that \(F\) is in some general space \(\Gamma_0(X,Y,C)\) of all functions satisfying kinds of convexity and semicontinuity conditions. The paper is a generalization of the result of [\textit{A. Auslender} and \textit{J.-P. Crouzeix}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 6, Suppl., 101-121 (1989; Zbl 0675.90070)] and [\textit{A. Auslender}, \textit{R. Cominetti} and \textit{J.-P. Crouzeix}, SIAM J. Optim. 3, No. 4, 669-687 (1993; Zbl 0808.90102)] to a nonsmooth convex vector optimization problem in infinite-dimensional spaces.