1,721,018 research outputs found
On the study of multistage stochastic vector quasi-variational problems
Full text linkThis paper focuses on the study of multistage stochastic vector generalized quasi-variational inequalities with a variable ordering structure. The proposed multistage stochastic vector quasi-variational problems are defined in a suitable functional setting relative to a finite set of final possible states and certain information fields; these formulations are a multicriteria extension of the multistage stochastic variational inequalities. A relevant aspect of these problems is the presence of the nonanticipativity constraints on the variables of the problem; stage by stage, these constraints impose the measurability with respect to the information field at that stage. Without requiring any assumption of monotonicity, we prove some existence results by using a nonlinear scalarization technique. On this basis, we analyze multistage stochastic vector Nash equilibrium problems: as an example, we focus on a suitable multistage stochastic bicriteria Cournot oligopolistic model
ON THE NOTION OF PROPER EFFICIENCY IN VECTOR OPTIMIZATION
No full textWe consider the main definitions of proper efficiency for a vector optimization problem in topological linear spaces. The implications among these definitions generalize the inclusion structure holding in Euclidean spaces with componentwise ordering
Robust bi-objective mean-CVaR portfolio selection: Applications to energy sector
Full text linkA new approach to optimizing or hedging a portfolio of financial positions is presented and tested with applications to energy market. Motivated by uncertainty in the estimation of problem data we consider robust bi-objective optimization problems with mean and conditional value-at-risk objective functions where the underlying probability distribution of portfolio return is only known to belong to a certain set. To tackle the problem of uncertainty we consider two different approaches: in the first one, uncertainty is represented by an elliptic set centered at the sample estimators of mean and covariance matrix; in the second one, uncertainty takes into account experts beliefs. For both approaches, we derive analytical semi-closed-form solutions for the worst case mean-CVaR portfolio; in addition, we provide a characterization of the location of the robust Pareto frontier with respect to the corresponding original Pareto frontier
Well-posedness and stability for abstract spline problems
No full textIn this work well-posedness and stability properties of the abstract spline problem are studied in the
framework of reflexive spaces. Tykhonov well-posedness is proved without restrictive assumptions. In the
context of Hilbert spaces, also the stronger notion of Levitin–Polyak well-posedness is established. A sequence
of parametric problems converging to the given abstract spline problem is considered in order to
study stability. Under natural assumptions, convergence results for sequences of solutions of the perturbed
problems are obtained
Sectionwise connected sets in vector optimization
No full textWe introduce the notion of sectionwise connected set as a new tool to investigate nonconvex vector optimization. Indeed, the image of a K-convex set through a K-quasiconnected vector function is proved
to be sectionwise connected. Some properties of the minimal frontiers of sectionwise connected sets are studied
On 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
An interior point method for linearly constrained multiobjective optimization based on suitable descent directions
No full textQuasiconcavity of sets and connectedness of the efficient frontier in ordered vector spaces
No full textWe introduce new notions of quasiconcavity of sets in ordered vector spaces, extending the properties of sets which are images of convex sets by quasiconcave functions. This allows us to generalize known results and obtain new ones on the connectedness of the sets of various types of efficient solutions
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