D-Optimal designs for weighted polynomial regression—A functional approach

This paper is concerned with the problem of computing approximateD-optimal design for polynomial regression with analytic weight function on a interval [m ₀-a,m ₀+a]. It is shown that the structure of the optimal design depends ona and weight function. Moreover, the optimal support points and weights are analytic functions ofa ata=0. We make use of a Taylor expansion to provide a recursive procedure for calculating theD-optimal designs.     

On Approximate Solutions in Vector Optimization Problems Via Scalarization

This work deals with approximate solutions in vector optimization problems. These solutions frequently appear when an iterative algorithm is used to solve a vector optimization problem. We consider a concept of approximate efficiency introduced by Kutateladze and widely used in the literature to study this kind of solutions. Necessary and sufficient conditions for Kutateladze’s approximate solutions are given through scalarization, in such a way that these points are approximate solutions for a scalar optimization problem. Necessary conditions are obtained by using gauge functionals while monotone functionals are considered to attain sufficient conditions. Two properties are then introduced to describe the idea of parametric representation of the approximate efficient set. Finally, through scalarization, characterizations and parametric representations for the set of approximate solutions in convex and nonconvex vector optimization problems are proved and the obtained results are applied to Pareto problems. AMS Classification:90C29, 49M37 This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194.     

Epsilon efficiency

This paper considers the extension of -optimality for scalar problems to vector maximization problems, or efficiency problems, which havem objective functions defined on a set .It is shown that the natural extension of the scalar -optimality concepts [viz, given >0, given a solution setS, ifxS there exists an efficient solutiony with f(x)–f(y), and given an efficient solutiony, there exists anxS with f(x)–f(y)] do not hold for some methods used. Six concepts of -efficient sets are introduced and examined, to a very limited extent, in the context of five methods used for generating efficient points or near efficient points.In doing so, a distinction is drawn between methods in which the surrogate optimizations are carried out exactly, and those where terminal -optimal solutions are obtained.The author would like to thank the referees whose thoroughness was extremely helpful for the revised paper.     

Identifying the efficiency status in network DEA

Data envelopment analysis (DEA) is commonly employed to evaluate the efficiency performance of a decision making unit (DMU) that transforms exogenous inputs into final outputs. In such a black-box DEA approach, details of an internal production process of the DMU are typically ignored and hence the locations of inefficiency are not adequately provided. In view of this, DEA researchers have recently developed various network approaches by looking into the black box, where the inputs that enter the box and the outputs that come out of it are only considered. However, most of these network approaches evaluate divisional efficiency by using an optimal solution of their respective optimization problem. If such an optimal solution is used in the case when there are multiple optima, then managerial guidance based on this solution alone may be inappropriate because more appropriate targets from the viewpoint of management may be ignored. Taking this fact into account, therefore, we propose a network approach for identifying the efficiency status of each DMU and its divisions. This approach provides a practical computational procedure.     

The a-value of polymineral fine grain samples measured with the post-IR IRSL protocol

Recent post-IR IRSL (pIRIR) dating studies using polymineral fine grains assumed that the a-values obtained for the IRSL signal at 50 °C and the pIRIR signal at higher temperatures (e.g. 225 °C) are identical. However, the a-value of a sample depends on the stimulation method, and the assumption mentioned above remains to be tested. Using five polymineral fine grain samples, this study investigates whether a common a-value can be used for both the IR and the pIRIR signals. Applying the pIRIR protocol, the a-values were measured with three different methods of signal resetting (optical bleaching, end of SAR cycle, heating). In addition, uncorrected α- and β-irradiation induced growth curves were determined for three samples and fitted with single saturating exponential functions. For the investigated samples we found significant mean differences, 0.023 ± 0.012 and higher, in the a-values determined for the IR₅₀ and pIRIR₂₂₅ signals. Synthetic a-values deduced from uncorrected multiple-aliquot dose response curves seem to confirm this observation. Although, in summary, our results indicate that the practice of using a common a-value should be carefully re-considered, the physical reasons remain to be determined.     

On Approximate Efficiency in Multiobjective Programming

This paper is focused on approximate ( -efficient) solutions of multiobjective mathematical programs. We introduce a new -efficiency concept which extends and unifies different notions of approximate solution defined in the literature. We characterize these -efficient solutions in convex multiobjective programs through approximate solutions of linear scalarizations, which allow us to obtain parametric representations of different -efficiency sets. Several classical -efficiency notions are considered in order to show the concepts introduced and the results obtained.This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194.