an:05382807
Zbl 1166.90014
Engau, Alexander
Variable preference modeling with ideal-symmetric convex cones
EN
J. Glob. Optim. 42, No. 2, 295-311 (2008).
00232168
2008
j
90C29 90B50
Multiobjective programming; multicriteria optimization; ordering cones; preference models
The paper addresses the problem of modeling preferences in multiple criteria decision making and multiobjective programming. Variable domination structures, where the dominated set of any point \(y\) is modeled by an ideal-symmetric convex cone \(D(y)\) that contains the nonnegative orthant, are used for this purpose. Well known results for multicriteria optimization with constant domination structures are generalized to this case. The results include results on weighted sum scalarization, necessary and sufficient conditions for nondominated points and further results for problems where the nondominated set \(N(Y,\mathbb{R}_\geq^m)\) is \(\mathbb{R}_\geq^m\)-convex or \(N(Y,\mathbb{R}_\geq^m)\) is \(\mathbb{R}_\geq^m\)-concave and \(\mathbb{R}_\geq^m\)-compact. The paper also contains some examples.
Matthias Ehrgott (Auckland)