Because of its extensive applications in disciplines such as
mathematical economics, game theory, and the geometry of normed spaces,
efficient points are well-known in vector optimization.
We present a unified approach to the "weak"
efficient points, based on the numerous types of efficient points introduced
and explored over time by several writers (see [1-7], [8]). (efficient points
defined by respect to cones that have some interiority properties).
We'll call these generalised weak efficient points -efficient
points, and we'll discuss their existence, dominance qualities, and comparison
results. We'll look at a generalised vector optimization problem using
-efficient points as an example. Because the conventional notion of solution
would have confined the study of the generalised problem to a classical
problem, the MIN problem, the definition of the notion of solution created some
challenges. Finally, the solution to this problem will be a net of approximate
efficient points, which is similar to the concept of asymptotically weakly
Pareto optimising sequence utilised in [9].
We develop the INFSUP problem, a generalisation of the
MINMAX problem, to obtain requirements on the existence and attributes of these
solutions. Following the research for the MINMAX problem (see, for example,
[10-14], [15,16], [17-19], a generalisation of the MINMAX problem is derived,
which includes saddle point theorems and duality results utilising an
appropriate lagrangian suited for the INFSUP problem.
We'll also show how our difficulties are related
to two specific problems: scalar and linear approximate problems.
Author(S) Details
Cristina Stamate
'Octav Mayer' Institute of Mathematics Romanian Academy-Ia»si branch 8,
Carol I street, Ia»si, Romania.
View Book:- https://stm.bookpi.org/RAMRCS-V6/article/view/5311
