Second-order efficiency conditions and sensitivity of efficient points

被引：14

作者：

Bolintineanu, S ^{[1
]}

El Maghri, M ^{[1
]}

机构：

[1] Univ Perpignan, Lab Anal Nonlineaire & Optimisat, F-66025 Perpignan, France

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 1998年 / 98卷 / 03期

关键词：

vector optimization; multicriteria optimization; multiobjective programming; efficiency; weak efficiency; proper efficiency; post-Pareto analysis; efficiency conditions; sensitivity analysis;

D O I：

10.1023/A:1022619928631

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The paper deals with necessary and sufficient efficiency conditions of first and second order in vector differential optimization in Banach spaces. The conditions presented ensure the Frechet sensitivity of efficient (Pareto) points for a perturbed problem. In finite dimension, weaker conditions ensure the Lipschitz sensitivity and existence of directional derivatives of perturbed efficient points.

引用

页码：569 / 592

页数：24

共 50 条

[31] Second-order optimality conditions for scalar and vector optimization problems in Banach spaces
Gfrerer, Helmut
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2006, 45 (03) : 972 - 997
[32] On second-order optimality conditions for continuously Frechet differentiable vector optimization problems
Feng, Min
Li, Shengjie
OPTIMIZATION, 2018, 67 (12) : 2117 - 2137
[33] Optimality conditions in differentiable vector optimization via second-order tangent sets
Jiménez, B
Novo, V
APPLIED MATHEMATICS AND OPTIMIZATION, 2004, 49 (02): : 123 - 144
[34] New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization
C. Gutiérrez
B. Jiménez
V. Novo
Journal of Optimization Theory and Applications, 2009, 142 : 85 - 106
[35] Optimality conditions in differentiable vector optimization via second-order tangent sets
Bienvenido Jiménez
Vicente Novo
Applied Mathematics and Optimization, 2004, 49 (2): : 123 - 144
[36] First and second-order optimality conditions without differentiability in multivalued vector optimization
Khanh, Phan Quoc
Tung, Nguyen Minh
POSITIVITY, 2015, 19 (04) : 817 - 841
[37] New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization
Gutierrez, C.
Jimenez, B.
Novo, V.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2009, 142 (01) : 85 - 106
[38] Second-order sensitivity analysis for parametric equilibrium problems in set-valued optimization
Nguyen Le Hoang Anh
RAIRO-OPERATIONS RESEARCH, 2019, 53 (04) : 1245 - 1260
[39] Sensitivity and stability for the second-order contingent derivative of the proper perturbation map in vector optimization
Q. L. Wang
S. J. Li
Optimization Letters, 2012, 6 : 731 - 748
[40] Sensitivity and stability for the second-order contingent derivative of the proper perturbation map in vector optimization
Wang, Q. L.
Li, S. J.
OPTIMIZATION LETTERS, 2012, 6 (04) : 731 - 748

← 1 2 3 4 5 →