scholarly journals On ε-optimality conditions for multiobjective fractional optimization problems

2011 ◽  
Vol 2011 (1) ◽  
pp. 6 ◽  
Author(s):  
Moon Kim ◽  
Gwi Kim ◽  
Gue Lee
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Fractional Optimization

scholarly journals Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
W. A. Oliveira ◽  
A. Beato-Moreno ◽  
A. C. Moretti ◽  
L. L. Salles Neto
Keyword(s):  
Optimality Conditions ◽  
Pareto Optimality ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Sufficient Optimality Conditions ◽  
Objective Functions ◽  
Convex Constraints ◽  
Fractional Optimization ◽  
Convexity Assumptions

One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set. The present work is concerned with the constrained vector quadratic fractional optimization problem. It shows that sufficient Pareto optimality conditions and the main duality theorems can be established without the assumption of generalized convexity in the objective functions, by considering some assumptions on a linear combination of Hessian matrices instead. The main aspect of this contribution is the development of Pareto optimality conditions based on a similar second-order sufficient condition for problems with convex constraints, without convexity assumptions on the objective functions. These conditions might be useful to determine termination criteria in the development of algorithms.

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.

scholarly journals Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account

2017 ◽  
Vol 9 (4) ◽  
pp. 168
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Minimum Principle ◽  
Necessary Optimality Conditions ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Scalar Optimization ◽  
Scalar And Vector Optimization

We take into condideration necessary optimality conditions of minimum principle-type, that is for optimization problems having, besides the usual inequality and/or equality constraints, a set constraint. The first part pf the paper is concerned with scalar optimization problems; the second part of the paper deals with vector optimization problems.

scholarly journals Optimality conditions and duality for multiobjective semi-infinite programming with data uncertainty via Mordukhovich subdifferential

2021 ◽  
pp. 13-13
Author(s):  
Thanh-Hung Pham
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Data Uncertainty ◽  
Mordukhovich Subdifferential ◽  
New Concepts ◽  
Infinite Programming

Based on the notation of Mordukhovich subdifferential in [27], we propose some of new concepts of convexity to establish optimality conditions for quasi ?-solutions for nonlinear semi-infinite optimization problems with data uncertainty in constraints. Moreover, some examples are given to illustrate the obtained results.

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