A modified weighted Tchebycheff metric for multiple objective programming
Computers and Operations Research
A generalization of a theorem of Arrow, Barankin, and Blackwell
SIAM Journal on Control and Optimization
On the notion of proper efficiency in vector optimization
Journal of Optimization Theory and Applications
Stability and Duality of Nonconvex Problems via Augmented Lagrangian
Cybernetics and Systems Analysis
Introducing oblique norms into multiple criteria programming
Journal of Global Optimization
Augmented Lagrangian Duality and Nondifferentiable Optimization Methods in Nonconvex Programming
Journal of Global Optimization
Multicriteria Optimization
A multiobjective faculty-course-time slot assignment problem with preferences
Mathematical and Computer Modelling: An International Journal
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In this paper, a special separation property for two closed cones in Banach spaces is proposed, and a nonlinear separation theorem for the cones possessing this property is proved. By extending a usual definition of dual cones, an augmented dual of a cone is introduced. A special class of monotonically increasing sublinear functions is defined by using the elements of the augmented dual cone. Any closed cone possessing the separation property with its $\varepsilon$-conic neighborhood is shown to be approximated arbitrarily closely by a zero sublevel set of some function from this class. As an application, a simple and efficient scalarization technique for nonconvex vector optimization problems is suggested, and it is shown that any properly minimal point of a set in a Banach space can be calculated by minimizing a certain sublinear functional.