Second-Order Optimality Conditions for Vector Problems with Continuously Fréchet Differentiable Data and Second-Order Constraint Qualifications

被引：0
作者：
Vsevolod I. Ivanov
机构：
[1] Technical University of Varna,Department of Mathematics
来源：
Journal of Optimization Theory and Applications | 2015年 / 166卷
关键词：
Vector optimization; Second-order KKT optimality conditions; Second-order constraint qualifications; Nonsmooth optimization; C; problems with inequality constraints; 90C46; 90C29;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In the present paper, we consider the inequality constrained vector problem with continuously Fréchet differentiable objective functions and constraints. We obtain second-order necessary optimality conditions of Karush–Kuhn–Tucker type for weak efficiency. A new second-order constraint qualification of Zangwill type is introduced. It is applied in the optimality conditions. Some connections with other constraint qualifications are established.
引用
收藏
页码：777 / 790
页数：13
相关论文
共 28 条
[1]  
McCormick GP(1967)Second-order conditions for constrained minima SIAM J. Appl. Math. 15 641-652
[2]  
Ben-Tal A(1980)Second-order and related extremality conditions in nonlinear programming J. Optim. Theory Appl. 31 143-165
[3]  
Ben-Tal A(1982)A unified theory of first and second order conditions for extremum problems in topological vector spaces Math. Program. Study 19 39-76
[4]  
Zowe J(1988)Second-order necessary conditions of the Kuhn–Tucker type under new constraint qualification J. Optim. Theory Appl. 57 253-264
[5]  
Kawasaki H(1999)Second-order optimality conditions in multiobjective optimization problems J. Optim. Theory Appl. 102 37-50
[6]  
Aghezzaf B(2007)New results on second-order optimality conditions in vector optimization problems J. Optim. Theory Appl. 135 117-133
[7]  
Hachimi M(1998)Second-order conditions for optimization problems with constraints SIAM J. Control Optim. 37 303-318
[8]  
Hackimi M(2004)Optimality conditions in differentiable vector optimization via second-order tangent sets Appl. Math. Optim. 49 123-144
[9]  
Aghezzaf B(2011)On second-order optimality conditions for vector optimization J. Optim. Theory Appl. 149 332-351
[10]  
Penot J-P(1993)Second-order conditions in Numer. Funct. Anal. Optim. 14 621-632
123