Optimality conditions for nonsmooth multiobjective optimization using Hadamard directional derivatives (Q946309)

This paper considers a nonsmooth vector optimization problem. The authors use the Hadamard directional derivative for the vector function and a scalarization technique via signed distances to establish necessary and sufficient optimality conditions for weak efficiency as well as firm efficiency. For presenting the necessary first-order conditions, no continuity assumptions are imposed. To derive the second-order sufficient conditions, only the calmness property of the first-order derivatives is assumed. By some examples it is demonstrated that the new conditions are more advantageous than previous results from the literature (see e.g. papers by \textit{A. Guerraggio} and \textit{D. T. Luc}, J. Optim. Theory Appl. 109, 615--629 (2001; Zbl 1038.49027), ibid. 116, 117--129 (2003; Zbl 1030.90115) or \textit{I. Ginchev, A. Guerraggio, M. Rocca}, in: Giannessi, Franco (ed.) et al., Variational analysis and applications. Erice, Italy 2003, New York, NY: Springer. Nonconvex Optimization and its Applications 79, 427--450 (2005; Zbl 1148.90011), Math. Program. 104, No. 2--3 (B), 389--405 (2005; Zbl 1102.90058), Appl. Math., Praha 51, No. 1, 5-36 (2006; Zbl 1164.90399).