On Optimization over the Efficient Set in Linear Multicriteria Programming - 山本 芳嗣; Horst R.; Thoai N.V.; Yamamoto Yoshitsugu; Zenke D. (Journal of optimization theory and applications, 2007)
The efficient set of a linear multicriteria programming problem can be represented\nby a reverse convex constraint of the form g(z) ≤ 0, where g is a concave\nfunction. Consequently, the problem of optimizing some real function over the efficient\nset belongs to an important problem class of global optimization called reverse\nconvex programming. Since the concave function used in the literature is only defined\non some set containing the feasible set of the underlying multicriteria programming\nproblem, most global optimization techniques for handling this kind of reverse convex\nconstraint cannot be applied. The main purpose of our article is to present a\nmethod for overcoming this disadvantage. We construct a concave function which is\nfinitely defined on the whole space and can be considered as an extension of the existing\nfunction. Different forms of the linear multicriteria programming problem are\ndiscussed, including the minimum maximal flow problem as an example. application/pdf