Averaging scheme has attracted extensive attention in deep learning as well traditional machine learning. It achieves theoretically optimal convergence and also improves the empirical model performance. However, there is still a lack of sufficient analysis for strongly convex optimization. Typically, about last iterate gradient descent methods, which referred to individual convergence, fails at...

Acknowledgments It is a great pleasure to thank all those who have contributed to this thesis. A great many thanks are due to H.-D. Doebner for innumerable, invaluable and elucidating conversations. I am indebted to D. Mayer for helpful suggestions in the early stages of the work reported here. I am greatly obliged to W. L ucke and P. Nattermann whose readiness to help in scientiic as well as o...

We consider a generalization of the capacitated vehicle routing problem known as the cumulative vehicle routing problem in the literature. Cumulative VRPs are known be a simple model for fuel consumption in VRPs. We examine four variants of the problem, and give constant factor approximation algorithms. Our results are based on a well-known heuristic of partitioning the traveling salesman tours...

This paper presents the fuzzy induced heavy ordered weighted averaging (FIHOWA) operator. It is an aggregation operator that uses the main characteristics of three well known aggregation operators: the heavy OWA, the induced OWA and the fuzzy OWA operator. Therefore, this operator provides a parameterized family of aggregation operators that includes the OWA operator and the total operator as s...

Ranking decision making units (DMUs) is one of the most important applications of data envelopment analysis (DEA). In this paper, we exploit the power of individual appreciativeness in developing a methodology that combines crossevaluation, preference voting and ordered weighted averaging (OWA). We show that each stage of the proposed methodology enhances discrimination among DMUs while offerin...

We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is v5νΩðt − t0Þ where t0 is the initial time, t is the tim...

In this paper, we discuss a framework for weighted combination of classifiers for word sense disambiguation (WSD). This framework is essentially based on DempsterShafer theory of evidence (Dempster, 1967; Shafer, 1976) and ordered weighted averaging (OWA) operators (Yager, 1988). We first determine various kinds of features which could provide complementarily linguistic information for the cont...

We study a stochastic model of influence where agents have “yes” or “no” inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ordered weighted averaging operators, which are anonymous: they only depend on how many agents sha...

Suppose A1, . . . , AN are rotation matrices on n-dimensional Euclidean space R, i.e., Aj ∈ SO(n). We want to consider some element of SO(n) that represents an “average” of these elements Aj . There are a number of possible ways to define the notion of an average in this context. One approach has been to write Aj = ej with Zj a real, skew-symmetric n × n matrix (i.e., Zj ∈ skew(n)), and define ...