A modified weighted Tchebycheff metric for multiple objective programming
Computers and Operations Research
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
On augmented Lagrangians for Optimization Problems with a Single Constraint
Journal of Global Optimization
Multicriteria Optimization
Handbook of Multicriteria Analysis
Handbook of Multicriteria Analysis
A Nonlinear Cone Separation Theorem and Scalarization in Nonconvex Vector Optimization
SIAM Journal on Optimization
A multiobjective faculty-course-time slot assignment problem with preferences
Mathematical and Computer Modelling: An International Journal
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This paper presents the conic scalarization method for scalarization of nonlinear multi-objective optimization problems. We introduce a special class of monotonically increasing sublinear scalarizing functions and show that the zero sublevel set of every function from this class is a convex closed and pointed cone which contains the negative ordering cone. We introduce the notion of a separable cone and show that two closed cones (one of them is separable) having only the vertex in common can be separated by a zero sublevel set of some function from this class. It is shown that the scalar optimization problem constructed by using these functions, enables to characterize the complete set of efficient and properly efficient solutions of multi-objective problems without convexity and boundedness conditions. By choosing a suitable scalarizing parameter set consisting of a weighting vector, an augmentation parameter, and a reference point, decision maker may guarantee a most preferred efficient or properly efficient solution.