Optimality conditions for fuzzy optimization problems under granular convexity concept

2022 ◽  
Author(s):  
Jianke Zhang ◽  
Xiaoyi Chen ◽  
Lifeng Li ◽  
Xiaojue Ma
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Fuzzy Optimization

The Karush–Kuhn–Tucker optimality conditions for fuzzy optimization problems

2015 ◽  
Vol 15 (1) ◽  
pp. 57-73 ◽  
Author(s):  
Y. Chalco-Cano ◽  
W. A. Lodwick ◽  
R. Osuna-Gómez ◽  
A. Rufián-Lizana
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Fuzzy Optimization

scholarly journals The Karush-Kuhn-Tucker Optimality Conditions for the Fuzzy Optimization Problems in the Quotient Space of Fuzzy Numbers

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Nanxiang Yu ◽  
Dong Qiu
Keyword(s):  
Optimality Conditions ◽  
Fuzzy Numbers ◽  
Quotient Space ◽  
Optimization Problems ◽  
Lagrange Function ◽  
Fuzzy Optimization ◽  
Solution Concepts ◽  
Kkt Optimality Conditions

We propose the solution concepts for the fuzzy optimization problems in the quotient space of fuzzy numbers. The Karush-Kuhn-Tucker (KKT) optimality conditions are elicited naturally by introducing the Lagrange function multipliers. The effectiveness is illustrated by examples.

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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