Vector optimization problems with nonconvex preferences
- Authors: Huang, N. J. , Rubinov, Alex , Yang, Xiao
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 40, no. 4 (2008), p. 765-777
- Full Text: false
- Reviewed:
- Description: In this paper, some vector optimization problems are considered where pseudo-ordering relations are determined by nonconvex cones in Banach spaces. We give some characterizations of solution sets for vector complementarity problems and vector variational inequalities. When the nonconvex cone is the union of some convex cones, it is shown that the solution set of these problems is either an intersection or an union of the solution sets of all subproblems corresponding to each of these convex cones depending on whether these problems are defined by the nonconvex cone itself or its complement. Moreover, some relations of vector complementarity problems, vector variational inequalities, and minimal element problems are also given. © 2007 Springer Science+Business Media, Inc.
- Description: C1
Stability of semi-infinite inequality systems involving min-type functions
- Authors: López, Marco , Rubinov, Alex , Vera De Serio, Virginia
- Date: 2005
- Type: Text , Journal article
- Relation: Numerical Functional Analysis and Optimization Vol. 26, no. 1 (2005), p. 81-112
- Full Text: false
- Reviewed:
- Description: We study the stability of semi-infinite inequality systems that arise in monotonic analysis. These systems are defined by certain classes of abstract linear functions. We consider the cone R
- Description: C1
- Description: 2003001420
Stability of the lower level sets of ICAR functions
- Authors: López, Marco , Rubinov, Alex , Vera De Serio, Virginia
- Date: 2005
- Type: Text , Journal article
- Relation: Numerical Functional Analysis and Optimization Vol. 26, no. 1 (2005), p. 113-127
- Full Text: false
- Reviewed:
- Description: In this paper, we study the stability of the lower level set {x E R++n | f (x) ≤ 0} of a finite valued increasing convex-along-rays (ICAR) function f defined on R++n. In monotonic analysis, ICAR functions play the role of usual convex functions in classical convex analysis. We show that each ICAR function f is locally Lipschitz on int dom f and that the pointwise convergence of a sequence of ICAR functions implies its uniform convergence on each compact subset of R ++n. The latter allows us to establish stability results for ICAR functions in some sense similar to those for convex functions. Copyright © Taylor & Francis, Inc.
- Description: C1
- Description: 2003001419
Scalarization and nonlinear scalar duality for vector optimization with preferences that are not necessarily a pre-order relation
- Authors: Rubinov, Alex , Gasimov, Rafail
- Date: 2004
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 29, no. 4 (2004), p. 455-477
- Full Text: false
- Reviewed:
- Description: We consider problems of vector optimization with preferences that are not necessarily a pre-order relation. We introduce the class of functions which can serve for a scalarization of these problems and consider a scalar duality based on recently developed methods for non-linear penalization scalar problems with a single constraint.
- Description: C1
- Description: 2003000932