Generalised convexity and duality in multiple objective programming
نویسندگان
چکیده
منابع مشابه
Integer Programming Duality in Multiple Objective Programming
The weighted sums approach for linear and convex multiple criteria optimization is well studied. The weights determine a linear function of the criteria approximating a decision makers overall utility. Any efficient solution may be found in this way. This is not the case for multiple criteria integer programming. However, in this case one may apply the more general e-constraint approach, result...
متن کاملOn duality in multiple objective linear programming
We discuss two approaches to duality for multiple objective linear problems. The first approach is based on a duality relation between a set and its complement in the outcome space. It allows us to obtain a number of known duality constructions. The second approach utilizes polarity between a polyhedral set and the epigraph of its support function. It leads to a parametric dual problem which is...
متن کاملGeometric Duality in Multiple Objective Linear Programming
We develop in this article a geometric approach to duality in Multiple Objective Linear Programming. This approach is based on a very old idea, the duality of polytopes, which can be traced back to the old Greeks. We show that there is an inclusion reversing one-to-one map between the minimal faces of the image of the primal objective and the maximal faces of the image of the dual objective map.
متن کاملDuality of Multi-objective Programming
The convexity theory plays an important role in many aspects of mathematical programming. In recent years, in order to relax convexity assumption, various generalized convexity notions have been obtained. One of them is the concept of ) , ( r p B− invexity defined by T.Antczak [1], which extended the class of B − invex functions with respect toη and b and the classes of ) , ( r p invex function...
متن کاملSecond Order Duality in Multiobjective Programming With Generalized Convexity
The purpose of this paper is concerned with a class of multi objective programming problems in which the objective functions and constrained functions are twice differentiable and containing the support functions of a compact convex set. For such mathematic programming, to deal with its dual problem, first, the concept of second order ( , ) B p r invexity is introduced. Further, the Mangasa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1989
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s000497270000277x