Approximate Fenchel-Lagrangian Duality for Constrained Set-Valued Optimization Problems
نویسندگان
چکیده
In this article, we construct a Fenchel-Lagrangian ε-dual problem for set-valued optimization problems by using the perturbation methods. Some relationships between the solutions of the primal and the dual problems are discussed. Moreover, an ε-saddle point theorem is proved.
منابع مشابه
Lagrangian duality and perturbational duality I ∗
Our approach to the Karush-Kuhn-Tucker theorem in [OSC] was entirely based on subdifferential calculus (essentially, it was an outgrowth of the two subdifferential calculus rules contained in the Fenchel-Moreau and Dubovitskii-Milyutin theorems, i.e., Theorems 2.9 and 2.17 of [OSC]). On the other hand, Proposition B.4(v) in [OSC] gives an intimate connection between the subdifferential of a fun...
متن کاملDuality and the “ convex ” Karush - Kuhn - Tucker theorem ∗ Erik
Our approach to the Karush-Kuhn-Tucker theorem in [OSC] was entirely based on subdifferential calculus (essentially, it was an outgrowth of the two subdifferential calculus rules contained in the Fenchel-Moreau and Dubovitskii-Milyutin theorems, i.e., Theorems 2.9 and 2.17 of [OSC]). On the other hand, Proposition B.4(v) in [OSC] gives an intimate connection between the subdifferential of a fun...
متن کاملA New Approach to Duality in Vector Optimization
In this article we develop a new approach to duality theory for convex vector optimization problems. We modify a given (set-valued) vector optimization problem such that the image space becomes a complete lattice (a sublattice of the power set of the original image space), where the corresponding infimum and supremum are sets that are related to the set of (minimal and maximal) weakly efficient...
متن کاملVariational Principles for Vector Equilibrium Problems Related to Conjugate Duality
This paper deals with the characterization of solutions for vector equilibrium problems by means of conjugate duality. By using the Fenchel duality we establish variational principles, that is, optimization problems with set-valued objective functions, the solution sets of which contain the ones of the vector equilibrium problems. The set-valued objective mappings depend on the data, but not on...
متن کاملϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces
We study Ε-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization of Ε-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between the Ε-Henig saddle point of the Lagrangian set-value...
متن کامل