Three-Step Fixed Point Iteration for Generalized Multivalued Mapping in Banach Spaces

The convergence of three-step fixed point iterative processes for generalized multivalued nonexpansive mapping was considered in this paper. Under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the generalized multivalued nonexpansive mapping. Our results extend and improve some recent results

Consistent anticipatory route guidance

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2000.Includes bibliographical references (p. 241-251).Anticipatory route guidance consists of messages, based on traffic network forecasts, that assist drivers' path choice decisions. Guidance is consistent when the forecasts on which it is based are verified after drivers react to it. This thesis addresses the formulation and development of solution algorithms for the consistent anticipatory route guidance generation (RGG) problem. The thesis proposes a framework for the problem, involving a set of time-dependent variables and their relationships. Variables are network conditions, path splits and guidance messages. Relationships are the network loading map, transforming path splits into network conditions; the guidance map, transforming network conditions into guidance messages; and the routing map, transforming guidance messages into path splits. The basic relationships can be combined into three alternative composite maps that model a guidance problem. Consistent guidance corresponds to a fixed point of a composite map. With stochastic maps, RGG model outputs are stochastic process realizations. In this case, the consistency fixed point corresponds to stationarity of the RGG solution process. Numerical methods for fixed point computation were examined, focusing on approaches that are rigorous and applicable to large-scale problems. Methods included Gibbs sampling for highly stochastic maps; generalizations of functional iteration for deterministic maps; and the MSA and Polyak iterate averaging method for "noisy" (deterministic plus disturbance) maps. A guidance-oriented dynamic traffic simulator was developed to experiment with RGG solution methods. Computational tests using the simulator investigated the use of Gibbs sampling to compute general stochastic process outputs; and examined the performance of the averaging methods under different model formulations, problem settings and degrees of stochasticity. Gibbs sampling successfully generated realizations from the stationary solution process of a fully stochastic model, but entails considerable computational effort. For noisy problems, the MSA found fixed points in all cases considered. Polyak averaging converged between two and four times faster than the MSA in low or moderate stochasticity problems, and performed comparably to the MSA in other problems. Formulations involving path-level variables converged more quickly than those involving link-level variables.by Jon Alan Bottom.Ph.D

Frameworks for evaluating macroeconomic policies

This thesis brings together the three chapters that together form my PhD thesis. As indicated by the title, Frameworks for Evaluating Macroeconomic Policies, the common theme linking the three is a focus on the development of modeling frameworks that can be used for the evaluation of Macroeconomic policies. Ways in which these models can be compared with each other and with the data are recurrent themes. The first chapter How to Model Money? Racing Monetary Frameworks against the Quantity Theory of Money is about finding frameworks for evaluating monetary policies. Currently three main approaches exist: CashinAdvance, New Keynesian, and SearchMoney. Using empirical facts on the Quantity Theory of Money as a yardstick we compare these three frameworks. It results that all three frameworks are display the Quantity Theory of Money over the longrun, as in the data. But all three frameworks display way too much of the Quantity Theory of Money over the shortrun. The race thus ends in a draw, but one illustrative of the strengths and weaknesses of all three frameworks. The results suggest that better modeling of other causes of inflation, and of heterogeneity, are important to improving monetary models. The second chapter Evaluating a FlatTax Reform is a quantitative modelling of a flattax reform for the US. The modeling focuses on replicating the details of current US taxation and inequality. This later is important as the effects on inequality of such a tax reform are one of the main arguments given against it. The third chapter Estimation of BewleyHuggettAiyagari Models: Theory and Implementation present inprogress work developing theory relevant to simulated moment and simulated likelihood estimation of a class of heterogeneous agent models. Theory focuses on developing the required assumptions directly from model fundamentals, and from accounting for the dependence of the estimation on numerical solution and simulation of the models. Attention is also given to implementation of the estimators, in particular which algorithms work computationally. The three chapters are presented here in the form of three separate articles. However the common thread of developing frameworks for the evaluation of macroeconomic policies is clearly evident throughout. I hope they may be of interest to the readerHow to model money? : racing monetary frameworks against the quantity theory of money. Evaluating a flat-tax reform. Estimation of Bewley-Huggett-Aiyagari models : theory and implementationPresidente: Manuel Santos; Vocal: David Domeij; Secretario: Matthias Kredle