1,720,989 research outputs found
Cones with bounded and unbounded bases and reflexivity
No full textIn this paper we prove two characterizations of reflexivity for a Banach space X. The first one is based on the existence in X of a closed convex cone with nonempty interior such that all the bases generated by a strictly positive functional are bounded, while the second one is stated in terms of non existence of a cone such that has bounded and unbounded bases (both generated by strictly positive functionals) simultaneously. We call such a cone mixed based cone. We study the features of this class of cones. In particular, we show that every cone conically isomorphic to the nonnegative orthant l^1 of l^1 is a mixed based cone and that every mixed based cone contains a conically isomorphic copy of l^1_+. Moreover we give a detailed description of the structure of a mixed based cone. This approach allows us to prove some results concerning the embeddings of l^1 and c_0 in a Banach space
Well-posedness and convexity in vector optimization
No full textWe study a notion of well-posedness in vector optimization
through the behaviour of minimizing sequences of sets, defined in terms of Hausdorff set-convergence. We show that the notion of strict efficiency is related to the notion of well-posedness. Using the obtained results we identify a class of well-posed vector optimization problems: the convex problems with compact efficient frontiers
Multiobjective problems with set constraints
No full textThe aim of this paper is to study necessary optimality conditions for vector valued problems having inequality constraints, equality ones and a set constraint. The study is based on the so called image space approach, which allows to state a necessary optimality condition in the image space and, as consequences, some necessary optimality conditions in the decision space more general than the ones known in the literature. The differentiable case and the convex case are also deepened on
An interior point method for linearly constrained multiobjective optimization based on suitable descent directions
No full textOn proper minimality in set optimization
No full textThe aim of this paper is to extend some notions of proper minimality from vector optimization to set optimization. In particular, we focus our
attention on the concepts of Henig and Geoffrion proper minimality, which are well-known in vector optimization. We introduce a
generalization of both of them in set optimizatio nwith finite dimensional spaces, by considering also a special class of polyhedral ordering
cones. In this framework, we prove that these two notions are equivalent, as it happens in the vector optimization context, where this property
is well-known. Then, we study a characterization of these proper minimal points through nonlinear scalarization, without considering
convexity hypotheses
Stability for convex vector optimization problems
No full textThis article deals with the convergence (in the sense of Kuratowski–Painlevé) of the set of the minimal points of A_n to the set of minimal points of A, whenever {A_n } is a sequence of closed convex subsets of an Euclidean space, converging in the same sense to the set A. Next, we consider the convex vector optimization problem under the assumption that the objective function f is such that all its sublevel sets, restricted to the feasible region, are bounded. For this problem we investigate the convergence of the solution sets of perturbed (with respect to the feasible region and the objective function) problems both in the image space and in the decision space. We consider also the same topics for a linear problem. Finally, we apply our results to the study of stability for a vector programming problem with convex inequality and linear equality constraints
Stability of a convex feasibility problem
Full text linkThe 2-sets convex feasibility problem aims at finding a point in the intersection of two closed convex sets A and B in a normed space X. More generally, we can consider the problem of finding (if possible) two points in A and B, respectively, which minimize the distance between the sets. In the present paper, we study some stability properties for the convex feasibility problem: we consider two sequences of sets, each of them converging, with respect to a suitable notion of set convergence, respectively, to A and B. Under appropriate assumptions on the original problem, we ensure that the solutions of the perturbed problems converge to a solution of the original problem. We consider both the finite-dimensional and the infinite-dimensional case. Moreover, we provide several examples that point out the role of our assumptions in the obtained results
Weak fixed point property and the space of affine functions
Full text linkFirst we prove that if a separable Banach space X contains an isometric
copy of an infinite-dimensional space A(S) of affine continuous functions
on a Choquet simplex S, then its dual X∗ lacks the weak∗ fixed point property
for nonexpansive mappings. Then, we show that the dual of a separable
L1-predual X fails the weak∗ fixed point property for nonexpansive mappings
if and only if X has a quotient isometric to some infinite-dimensional space
A(S). Moreover, we provide an example showing that “quotient” cannot be
replaced by “subspace”. Finally, it is worth mentioning that in our characterization
the space A(S) cannot be substituted by any space C(K) of continuous
functions on a compact Hausdorff K
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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