Optimality conditions and duality for arcwise connected interval optimization problems

OPSEARCH ◽  
2015 ◽  
Vol 52 (4) ◽  
pp. 870-883 ◽  
Author(s):  
Haijun Wang ◽  
Ruifang Zhang
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Interval Optimization ◽  
Arcwise Connected

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

2021 ◽  
Vol 78 (1) ◽  
pp. 139-156
Author(s):  
Antonio Boccuto
Keyword(s):  
Optimality Conditions ◽  
Vector Lattice ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Continuous Vector ◽  
Fixed Group ◽  
Composite Functions ◽  
Order Continuous

Abstract We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group G of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.

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