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
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