Cohort studies have consistently shown underground miners exposed to high levels of radon to be at excess risk of lung cancer, and extrapolations based on those results indicate that residential radon may be responsible for nearly 10-15% of all lung cancer deaths per year in the United States. However, case-control studies of residential radon and lung cancer have provided ambiguous evidence of radon lung cancer risks. Regardless, alpha-particle emissions from the short-lived radioactive radon decay products can damage cellular DNA. The possibility that a demonstrated lung carcinogen may be present in large numbers of homes raises a serious public health concern. Thus, a systematic analysis of pooled data from all North American residential radon studies was undertaken to provide a more direct characterization of the public health risk posed by prolonged radon exposure. To evaluate the risk associated with prolonged residential radon exposure, a combined analysis of the primary data from seven large scale case-control studies of residential radon and lung cancer risk was conducted. The combined data set included a total of 4081 cases and 5281 controls, representing the largest aggregation of data on residential radon and lung cancer conducted to date. Residential radon concentrations were determined primarily by a-track detectors placed in the living areas of homes of the study subjects in order to obtain an integrated 1-yr average radon concentration in indoor air. Conditional likelihood regression was used to estimate the excess risk of lung cancer due to residential radon exposure, with adjustment for attained age, sex, study, smoking factors, residential mobility, and completeness of radon measurements. Although the main analyses were based on the combined data set as a whole, we also considered subsets of the data considered to have more accurate radon dosimetry. This included a subset of the data involving 3662 cases and 4966 controls with a-track radon measurements within the exposure time window (ETW) 5-30 yr prior to the index date considered previously by Krewski et al. (2005). Additional restrictions focused on subjects for which a greater proportion of the ETW was covered by measured rather than imputed radon concentrations, and on subjects who occupied at most two residences. The estimated odds ratio (OR) of lung cancer generally increased with radon concentration. The OR trend was consistent with linearity (p = .10), and the excess OR (EOR) was 0.10 per Bq/m3 with 95% confidence limits (-0.01, 0.26). For the subset of the data considered previously by Krewski et al. (2005), the EOR was 0.11 (0.00, 0.28). Further limiting subjects based on our criteria (residential stability and completeness of radon monitoring) expected to improve radon dosimetry led to increased estimates of the EOR. For example, for subjects who had resided in only one or two houses in the 5-30 ETW and who had a-track radon measurements for at least 20 yr of this 25-yr period, the EOR was 0.18 (0.02, 0.43) per 100 Bq/m3. Both esti...

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These results provide direct evidence of an association between residential radon and lung cancer risk, a finding predicted using miner data and consistent with results from animal and in vitro studies.

We propose an augmented Lagrangian-type algorithm for the solution of generalized Nash equilibrium problems (GNEPs). Specifically, we discuss the convergence properties with regard to both feasibility and optimality of limit points. This is done by introducing a secondary GNEP as a new optimality concept. In this context, special consideration is given to the role of suitable constraint qualifications that take into account the particular structure of GNEPs. Furthermore, we consider the behaviour of the method for jointly-convex GNEPs and describe a modification which is tailored towards the computation of variational equilibria. Numerical results are included to illustrate the practical performance of the overall method.Note that we do not include equality constraints in our GNEP simply for the sake of notational convenience; our subsequent approach can easily be extended to equality and inequality constraints. Apart from this, the above setting is very general since, so far, we do not assume any convexity assumptions on the mappings θ ν and c ν as is done in many other GNEP papers where only the player-convex or jointly-convex case is considered, cf. [2,8,7,10,12,17,28] for more details. It follows that our framework can, in principle, be applied to very general classes of GNEPs.In the meantime, there exist a variety of methods for the solution of GNEPs, though most of them are designed for player-or jointly-convex GNEPs and therefore do not cover the GNEP in its full generality. We refer the interested reader once again to the two survey papers [12,17] and the references therein for a quite complete overview of the existing approaches. One of the main problems when solving a GNEP is an inherent singularity property that arises when some players share the same constraints, see [11] for more details. Hence, second-order methods with fast local convergence are difficult to design. This also motivates us to consider methods which may not be locally superlinearly or quadratically convergent, but have nice global convergence properties.Penalty-type schemes belong to this class of methods. The first penalty method for GNEPs that we are aware of is due to Fukushima [18]. A related penalty algorithm was also proposed in [13], and a modification of this algorithm is described in [14] where only some of the constraints are penalized. While all these approaches prove exactness results under suitable assumptions, they suffer from the drawback that the resulting penalized subproblems are nonsmooth Nash equilibrium problems and therefore difficult to solve numerically.Taking this into account, it is natural to apply an augmented Lagrangian-type approach in order to solve GNEPs because the resulting subproblems then have a higher degree of smoothness and should therefore be easier to solve. This idea is not completely new since Pang and Fukushima [22] applied this idea to quasi-variational inequalities (QVIs). An improved version of that method can be found in [20], also for QVIs. Since the GNEP is a special instance of a QVI...

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of inequality constraints with infinite-dimensional image space. Moreover, we discuss the convergence properties of our algorithm with regard to feasibility, global optimality, and KKT conditions. Some numerical results are given to illustrate the practical viability of the method.

Switching-constrained optimization problems form a difficult class of mathematical programs since their feasible set is almost disconnected while standard constraint qualifications are likely to fail at several feasible points. That is why the application of standard methods from nonlinear programming does not seem to be promising in order to solve such problems. In this paper, we adapt the relaxation method from Kanzow and Schwartz (SIAM J. Optim., 23(2):770-798, 2013) for the numerical treatment of mathematical programs with complementarity constraints to the setting of switching-constrained optimization. It is shown that the proposed method computes M-stationary points under mild assumptions. Furthermore, we comment on other possible relaxation approaches which can be used to tackle mathematical programs with switching constraints. As it turns out, adapted versions of Scholtes' global relaxation scheme as well as the relaxation scheme of Steffensen and Ulbrich only find W-stationary points of switching-constrained optimization problems in general. Some computational experiments visualize the performance of the proposed relaxation method.

The most direct way to derive risk estimates for residential radon progeny exposure is through epidemiologic studies that examine the association between residential radon exposure and lung cancer. However, the National Research Council concluded that the inconsistency among prior residential radon casecontrol studies was largely a consequence of errors in radon dosimetry. This paper examines the impact of applying various epidemiologic dosimetry models for radon exposure assessment using a common data set from the Iowa Radon Lung Cancer Study ( IRLCS ). The IRLCS uniquely combined enhanced dosimetric techniques, individual mobility assessment, and expert histologic review to examine the relationship between cumulative radon exposure, smoking, and lung cancer. The a priori defined IRLCS radon -exposure model produced higher odds ratios than those methodologies that did not link the subject's retrospective mobility with multiple, spatially diverse radon concentrations. In addition, the smallest measurement errors were noted for the IRLCS exposure model. Risk estimates based solely on basement radon measurements generally exhibited the lowest risk estimates and the greatest measurement error. The findings indicate that the power of an epidemiologic study to detect an excess risk from residential radon exposure is enhanced by linking spatially disparate radon concentrations with the subject's retrospective mobility.

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