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It is well known that every scalar convex function is locally Lipschitz on the interior of its domain in finite dimensional spaces. The aim of this paper is to extend this result for both vector functions and set-valued mappings acting between infinite dimensional spaces with an order generated by a proper convex cone C. Under the additional assumption that the ordering cone C is normal, we prove...
In this study, we present a bi-objective facility location model that considers both partial coverage and service to uncovered demands. Due to limited number of facilities to be opened, some of the demand nodes may not be within full or partial coverage distance of a facility. However, a demand node that is not within the coverage distance of a facility should get service from the nearest facility...
Pulido et al. (Annals Oper Res 158:133–141, 2008) present an extension of the classical bankruptcy problem (O’Neill in Math Social Sci 2:345–371, 1982) where the involved agents have, apart from the claims vector, an additional reference vector. To analyze this extended problem, they propose the extreme and the diagonal approaches, both of them restricted to the case in which the reference vector...
This paper is concerned with the stability for a generalized Ky Fan inequality when it is perturbed by vector-valued bifunction sequence and set sequence. By continuous convergence of the bifunction sequence and Painlevé–Kuratowski convergence of the set sequence, we establish the Painlevé–Kuratowski convergence of the approximate solution mappings of a family of perturbed problems to the corresponding...
The concept of critical angle between two linear subspaces has applications in statistics, numerical linear algebra and other areas. Such concept has been abundantly studied in the literature. Part I of this work is an attempt to build up a theory of critical angles for a pair of closed convex cones. The need of such theory is motivated, among other reasons, by some specific problems arising in regression...
By applying excess functions, we propose alternative formulations and related dynamic processes for the normalized Banzhaf index and the Shapley value, respectively.
This paper discusses games where cooperation is restricted by a hierarchical structure. The model assumes that there is a hierarchy between certain coalitions given by a partition. Face games (González-Díaz and Sánchez-Rodríguez in Games Econ Behav 62:100–105, 2008) play a central role in the definition of the proposed hierarchical game. It turns out that the Shapley value of the hierarchical game...
Fire is a natural component of many terrestrial ecosystems; however, uncontrolled intense wildfires can cause loss of human life and destruction of natural resources. Prescribed burning is a management activity undertaken for the purposes of both wildfire hazard reduction and the preservation of fire-adapted ecosystems. Achievement of prescribed burn targets is made difficult by operational constraints...
The coefficient of variation is a useful statistical measure, which has long been widely used in many areas. In real-world applications, there are situations where the observations are inexact and imprecise in nature and they have to be estimated. This paper investigates the sample coefficient of variation (CV) with uncertain observations, which are represented by interval values. Since the observations...
In the paper, we establish necessary and sufficient optimality conditions for quasi-relative efficient solutions of a constrained set-valued optimization problem using the Lagrange multipliers. Many examples are given to show that our results and their applications are more advantageous than some existing ones in the literature.
In this paper, we consider parametric primal and dual equilibrium problems in locally convex Hausdorff topological vector spaces. Sufficient conditions for the approximate solution maps to be Hausdorff continuous are established. We provide many examples to illustrate the essentialness of the imposed assumptions. As applications of these results, the Hausdorff continuity of the approximate solution...
In Fragnelli et al. (TOP 22:892–933, 2014), we considered a bankruptcy problem with the additional constraint that the estate has to be assigned in integer unities, allowing for non-integer claims. We dealt with the question of existence and uniqueness of a solution and proposed the “box method” that is strongly oriented towards the constrained equal losses solution; uniqueness may be guaranteed by...
This paper deals with an economic production quantity (EPQ) inventory model with reworkable defective items when a given multi-shipment policy is used. In this work, it is assumed that in each cycle, the rework process of all defective items starts when the regular production process finishes. After the rework process, a portion of reworked items fails. This portion becomes scrap and only the perfect...
The concept of critical (or principal) angle between two linear subspaces has applications in statistics, numerical linear algebra, and other areas. Such concept has been abundantly studied in the literature, both from a theoretical and computational point of view. Part I of this work is an attempt to build a general theory of critical angles for a pair of closed convex cones. The need of such theory...
In this paper, we consider general linear semi-infinite programming (LSIP) problems and study the existence and computation of optimal solutions at special generalized corner points called generalized ladder points (glp). We develop conditions, including an equivalent condition, under which glp optimal solutions exist. These results are fundamentally important to the ladder method for LSIP, which...
We propose an extension of the classical real-valued external penalty method to the multicriteria optimization setting. As its single objective counterpart, it also requires an external penalty function for the constraint set, as well as an exogenous divergent sequence of nonnegative real numbers, the so-called penalty parameters, but, differently from the scalar procedure, the vector-valued method...
We present a generalized formulation of the pooling problem. Our formulation is different from the standard formulations in explicitly modeling component flows. Modeling the physical components directly, allows easy inclusion of processing facilities that may alter the flow composition. It also allows adding composite quality constraints that cannot be added directly as quality parameters as they...
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