Lagrange Multipliers for ε-Pareto Solutions in Vector Optimization with Nonsolid Cones in Banach Spaces

2009 ◽  
Vol 145 (1) ◽  
pp. 196-211 ◽  
Author(s):  
M. Durea ◽  
J. Dutta ◽  
C. Tammer
Keyword(s):  
Banach Spaces ◽  
Vector Optimization ◽  
Lagrange Multipliers ◽  
Pareto Solutions

scholarly journals Structure of Pareto Solutions of Generalized Polyhedral-Valued Vector Optimization Problems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Qinghai He ◽  
Weili Kong
Keyword(s):  
Banach Spaces ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Solution Set ◽  
Pareto Optimal ◽  
Pareto Solution ◽  
Value Set ◽  
Set Valued Mapping ◽  
Optimal Value

In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP) and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP). In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.

Duality in Vector Optimization Under Type 1 α-Invexity in Banach Spaces

2008 ◽  
Vol 29 (9-10) ◽  
pp. 1128-1139 ◽  
Author(s):  
S. K. Mishra ◽  
R. P. Pant ◽  
J. S. Rautela
Keyword(s):  
Banach Spaces ◽  
Vector Optimization

scholarly journals On the existence of Pareto solutions for polynomial vector optimization problems

2018 ◽  
Vol 177 (1-2) ◽  
pp. 321-341 ◽  
Author(s):  
Do Sang Kim ◽  
Tiến-Sơn Phạm ◽  
Nguyen Van Tuyen
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problems ◽  
Polynomial Vector ◽  
Pareto Solutions
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