Optim Lett DOI 10.1007/s11590-015-0850-2 ORIGINAL PAPER Vector critical points and efficiency in vector optimization with Lipschitz functions C. Gutiérrez · B. Jiménez · V. Novo · G. Ruiz-Garzón Received: 11 March 2014 / Accepted: 7 January 2015 © Springer-Verlag Berlin Heidelberg 2015 Abstract In this work, we establish some relations between several notions of vector critical points and efficient, weak efficient and ideal efficient solutions of a vector optimization problem with a locally Lipschitz objective function. These relations are stated under pseudoinvexity hypotheses and via the generalized Jacobian. We provide a characterization of pseudoinvexity (resp. strong pseudoinvexity) through the property that every vector critical point is a weak efficient (resp. efficient) solution. We also obtain some properties of invex functions in connection with linear scalarizations. Several examples illustrating our results are also provided. Keywords Vector optimization · Weak efficiency · Efficiency · Vector critical point · Pseudoinvex function · Invex function · Generalized Jacobian · Linear scalarization C. Gutiérrez E.T.S. de Ingenieros de Telecomunicación, Universidad de Valladolid, Paseo de Belén 15, Campus Miguel Delibes, 47011 Valladolid, Spain e-mail: cesargv@mat.uva.es B. Jiménez · V. Novo (B) Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia (UNED), C/ Juan del Rosal 12, 28040 Madrid, Spain e-mail: vnovo@ind.uned.es B. Jiménez e-mail: bjimenez@ind.uned.es G. Ruiz-Garzón Departamento de Estadística e I.O, Universidad de Cádiz, Campus de Jerez de la Frontera, Avda. de la Universidad s/n, 11405 Jerez de la Frontera, Cádiz, Spain e-mail: gabriel.ruiz@uca.es 123