Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems

We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm (AAR). In the case of convex feasibility, firm nonexpansiveness of projection mappings is a global property that yields global convergence of MAP and for consistent problems AAR. Based on (\epsilon, \delta)-regularity of sets developed by Bauschke, Luke, Phan and Wang in 2012, a relaxed local version of firm nonexpansiveness with respect to the intersection is introduced for consistent feasibility problems. Together with a coercivity condition that relates to the regularity of the intersection, this yields local linear convergence of MAP for a wide class of nonconvex problems,Comment: 22 pages, no figures, 30 reference

Testing CPT and Lorentz Symmetry with Electrons and Positrons in Penning Traps

We present a theoretical analysis of signals for CPT and Lorentz violation in g-2 and charge-to-mass-ratio experiments on electrons and positrons in Penning traps. Experiments measuring anomaly frequencies are found to be the most sensitive to CPT violation. We find that the conventional figure of merit for CPT breaking, involving the difference of the electron and positron g factors, is inappropriate in this context, and an alternative is introduced. Bounds of approximately one part in 10^{20} are attainable.Comment: 5 pages, talk presented by R.B. at the 1998 Conference on Trapped Charged Particles and Fundamental Physics, Pacific Grove, California, August-September 199

Hydrogen and Antihydrogen Spectroscopy for Studies of CPT and Lorentz Symmetry

A theoretical study of possible signals for CPT and Lorentz violation arising in hydrogen and antihydrogen spectroscopy is described. The analysis uses a CPT- and Lorentz-violating extension of quantum electrodynamics, obtained from a general Lorentz-violating extension of the minimal standard model with both CPT-even and CPT-odd terms. Certain 1S-2S transitions and hyperfine Zeeman lines exhibit effects at leading order in small CPT-violating couplings.Comment: 9 pages, talk presented by A.K. at the 1998 Conference on Trapped Charged Particles and Fundamental Physics, Pacific Grove, California, August-September 199

Testing CPT and Lorentz Symmetry with Protons and Antiprotons in Penning Traps

A theoretical analysis is performed of Penning-trap experiments comparing protons and antiprotons to test CPT and Lorentz symmetry through measurements of anomalous magnetic moments and charge-to-mass ratios. Possible CPT and Lorentz violations arising at a fundamental level are treated in the context of a general extension of the standard model of particle physics and its restriction to quantum electrodynamics. In a suggested experiment measuring anomaly frequencies a bound on CPT violation of 10^{-23} for a relevant figure of merit is attainable. Experiments comparing cyclotron frequencies are sensitive within this theoretical framework to different kinds of Lorentz violation that preserve CPT. Constraints could be obtained on one figure of merit at 10^{-24} and on another in a related experiment with H- ions and antiprotons at the level of 10^{-25}.Comment: 5 pages, presented by N.R. at the 1998 Conference on Trapped Charged Particles and Fundamental Physics, Pacific Grove, California, August-September 199

On modeling pollution-generating technologies

We distinguish between intended production and residual generation and introduce the concept of by-production. We show that by-production provides the fundamental explanation for the positive correlation that is observed between intended production and residual generation. Most of the existing literature attributes the observed positive correlation to abatement options available to firms. We show that abatement options of firms add to the phenomenon of by-production in strengthening the observed positive correlation. The existing literature usually does not explicitly model abatement options of firms, but considers a reduced form of he technology, which satisfies standard disposability assumptions with respect to all inputs and intended outputs. We show that more than one implicit production relation is needed to capture all the technological trade-offs that are implied by by-production. From our model, we are able to derive a reduced form of the technology that is in the spirit of the one that is usually studied in the literature. However, we nd that our reduced form technology violates standard disposability with respect to inputs and intended outputs that cause pollution. We derive implications from the phenomenon of by-production for the econometric and Data Envelopment Analysis (DEA) speci cations of pollution-generating technologies. We derive a DEA specification of technologies that satisfy by-production. Such a specification can be used to study issues relating to measurement of efficiency, marginal abatement costs, productivity, etc., of firms with technologies that generate pollution. JEL Codes: D20 ; D24 ; D62 ; Q50pollution-generating technologies ; free disposability ; weak disposability ; data envelope analysis ; technical efficiency measurement

Axiomatic Foundations of Efficiency Measurement on Data-Generated Technologies

Dmitruk and Koshevoy [1991 JET] provided a complete characterization of the class of technologies for which there exists an efficiency index satisfying the Fare-Lovell [1978 JET] axioms. The technologies implicit in the standard mathematical-programming methods of measuring efficiency, data envelopment analysis (DEA) and free-disposal-hull (FDH) analysis, belong to this class. We assess the ability of three well-known indexes, the Debreu-Farrell index, the Fare-Lovell index, and the Zieschang index, to satisfy not only the Fare-Lovell axioms but also continuity axioms (for technologies as well as input quantities), on this restricted class of technologies. Our principal conclusions are that (a) restriction to these data-based technologies adds continuity in input quantities to the properties satisfied by the Fare-Lovell and the Zieschang indexes (thus eliminating a salient advantage of the Debreu-Farrell index), but (b) none of the indexes satisfies all Fare-Lovell axioms (nor all continuity axioms) on either DEA or FDH technologies, and hence (c) trade-offs among the indexes remain. These findings provide motivation for the search for an index that does satisfy these axioms on DEA and FDH technologies.Technical efficiency indexes; technical efficiency axioms