Abstract
AbstractIn Haeser and Ramos (J Optim Theory Appl, 187:469–487, 2020), a generalization of the normal cone from single objective to multiobjective optimization is introduced, along with a weakest constraint qualification such that any local weak Pareto optimal point is a weak Kuhn–Tucker point. We extend this approach to other generalizations of the normal cone and corresponding weakest constraint qualifications, such that local Pareto optimal points are weak Kuhn–Tucker points, local proper Pareto optimal points are weak and proper Kuhn–Tucker points, respectively, and strict local Pareto optimal points of order one are weak, proper and strong Kuhn–Tucker points, respectively. The constructions are based on an appropriate generalization of polarity to pairs of matrices and vectors.
Funder
Karlsruher Institut für Technologie (KIT)
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Management Science and Operations Research,Control and Optimization
Reference40 articles.
1. Aghezzaf, B., Hachimi, M.: On a gap between multiobjective optimization and scalar optimization. J. Optim. Theory Appl. 109(2), 431–435 (2001)
2. Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming. Wiley, New York (2006)
3. Benson, H.P.: An improved definition of proper efficiency for vector maximization with respect to cones. J. Math. Anal. Appl. 71(1), 232–241 (1979)
4. Bigi, G.: Optimality and Lagrangian Regularity in Vector Optimization. Ph.D. Thesis, Universita di Pisa, Pisa (2003)
5. Borwein, J.M.: Proper efficient points for maximizations with respect to cones. SIAM J. Control Optim. 15(1), 57–63 (1977)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献