On Cone Characterizations of Strong and Lexicographic Optimality in Convex Multiobjective Optimization


DOI: 10.1007/s10957-009-9570-z

Cite this article as:
Mäkelä, M.M. & Nikulin, Y. J Optim Theory Appl (2009) 143: 519. doi:10.1007/s10957-009-9570-z


Various type of optimal solutions of multiobjective optimization problems can be characterized by means of different cones. Provided the partial objectives are convex, we derive necessary and sufficient geometrical optimality conditions for strongly efficient and lexicographically optimal solutions by using the contingent, feasible and normal cones. Combining new results with previously known ones, we derive two general schemes reflecting the structural properties and the interconnections of five optimality principles: weak and proper Pareto optimality, efficiency and strong efficiency as well as lexicographic optimality.


Multiple criteria Strong efficiency Lexicographic optimality Tangent cone Contingent cone Normal cone 

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland

Personalised recommendations