In this article an algorithm for computing upper and lower ? approximations of a (implicitly or explicitly) given convex function h defined on an interval of length T is developed. The approximations can be obtained under weak assumptions on h (in particular, no differentiability), and the error decreases quadratically with the number of iterations. To reach an absolute accuracy of ? the number of iterations is bounded by
A new approach is presented for analyzing multiple-attribute decision problems in which the set of actions is finite and the utility function is additive. The problem can be resolved if the decision makers (or group of decision makers) specifies a set of nonnegative weights for the various attributes or criteria, but we here assume that the decision maker(s) cannot provide a numerical value for each such weight. Ordinal information about these weights is therefore obtained from the decision maker(s), and this information is translated into a set of linear constraints which restrict the values of the weights. These constraints are then used to construct a polytope W of feasible weight vectors, and the subsets Hi (polytopes) of W over which each action ai has the greatest utility are determined. With the Comparative Hypervolume Criterion we calculate for each action the ratio of the hypervolume of Hi to the hypervolume of W and suggest the choice of an action with the largest such ratio. Justification of this choice criterion is given, and a computational method for accurately approximating the hypervolume ratios is described. A simple example is provided to evaluate the efficiency of a computer code developed to implement the method. 相似文献
Advances in the study of civil war have led to the proliferation of event count data, and to a corresponding increase in the use of (zero-inflated) count models for the quantitative analysis of civil conflict events. Our ability to effectively use these techniques is met with two current limitations. First, researchers do not yet have a definitive answer as to whether zero-inflated count models are a verifiably better approach to civil conflict modeling than are ‘less assuming’ approaches such as negative binomial count models. Second, the accurate analysis of conflict-event counts with count models – zero-inflated or otherwise – is severely limited by the absence of an effective framework for the evaluation of predictive accuracy, which is an empirical approach that is of increasing importance to conflict modelers. This article rectifies both of these deficiencies. Specifically, this study presents count forecasting techniques for the evaluation and comparison of count models' predictive accuracies. Using these techniques alongside out-of-sample forecasts, it then definitively verifies – for the first time – that zero-inflated count models are superior to comparable non-inflated models for the study of intrastate conflict events. 相似文献