In optimization theory, we usually assume that the image space is partially ordered by a nontrivial convex cone. In 1974, Yu [4] introduced more general concepts of ordering structures in
terms of domination structures. Recently, vector optimization problems with variable ordering
structures are investigated intensively, see e.g. [1, 2, 3].
In this talk, some optimality concept for vector optimization problems with a variable ordering
structure are considered. we present a generalization of Pascoletti-Serafini scalarization problem
and give some necessary and sufficient conditions that a vector optimization problem has a (weak)
nondominated element with respect to a variable ordering structure.
References
1. T.Q. Bao and B.S. Mordukhovich, Necessary nondomination conditions in set and vector
optimization with variable ordering structures, J. Optim. Theory Appl. 162 (2014), 350–370.
2. G. Eichfelder, Variable Ordering Structures in Vector Optimization, Springer, Berlin, (2014).
3. B. Soleimani and C. Tammer, Concepts for approximate solutions of vector optimization prob-
lems with variable order structures, Vietnam J. Math. 42 (2014), 543–566.
4. P.L. Yu, Cone convexity, cone extreme points, and nondominated solutions in decision problems
with multiobjectives, J. Optim. Theory Appl. 14 (1974), 319–377.