11/06/22 11:49:10.60
We introduce a new concept of algebraic type of closure
in real linear spaces
which is called VECTOR CLOSURE.
The properties of this are nearer to the topological closure
than the algebraic closure. Through this closure we introduce
new concepts of generalized convexlikeness,
with which it is possible to characterize the weakly efficient solutions
in vector optimization (with and without constraints) through scalarization,
multiplier rule and saddle-point theorems.
Author Keywords: Generalized convexlikeness; Vector-convexlikeness; Vector optimization; Weak efficiency
Article Outline
1. Introduction
2. Vector closure
3. Generalized convexlikeness
4. Optimality results
5. Concluding remarks