Variants on Dantzig-Wolfe Decomposition with Applications to Multistage Problems

The initial representation of an LP problem to which the Dantzig-Wolfe decomposition procedure is applied, is of the essence. We study this here, and, in particular, we consider two transformations of the problem, by introducing suitable linking rows and variables. We study the application of the Dantzig-Wolfe procedure to these new representations of the original problem and the relationship to previously proposed algorithms. Advantages and disadvantages from a computational viewpoint are discussed. Finally we develop a decomposition algorithm based upon these ideas for solving multistage staircase-structured LP problems

Parallel Decomposition of Multistage Stochastic Programming Problems

A new decomposition method for multistage stochastic linear programming problems is proposed by the author. The method combines the ideas of the regularized decomposition method for two-stage programs and dynamic programming. With each node of the decision tree of the multistage stochastic problem a certain regularized subproblem is associated which generates decisions for its successors and some backward information for its predecessor. The subproblems are solved in parallel and exchange information in an asynchronous way through special buffers. After a finite time the method either finds an optimal solution to the problem or discovers its inconsistency. This method is especially convenient for implementation on a parallel computer

Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)

SP models combine the paradigm of dynamic linear programming with modelling of random parameters, providing optimal decisions which hedge against future uncertainties. Advances in hardware as well as software techniques and solution methods have made SP a viable optimisation tool. We identify a growing need for modelling systems which support the creation and investigation of SP problems. Our SPInE system integrates a number of components which include a flexible modelling tool (based on stochastic extensions of the algebraic modelling languages AMPL and MPL), stochastic solvers, as well as special purpose scenario generators and database tools. We introduce an asset/liability management model and illustrate how SPInE can be used to create and process this model as a multistage SP application

Decomposition techniques for large scale stochastic linear programs

Stochastic linear programming is an effective and often used technique for incorporating uncertainties about future events into decision making processes. Stochastic linear programs tend to be significantly larger than other types of linear programs and generally require sophisticated decomposition solution procedures. Detailed algorithms based uponDantzig-Wolfe and L-Shaped decomposition are developed and implemented. These algorithms allow for solutions to within an arbitrary tolerance on the gap between the lower and upper bounds on a problem\u27s objective function value. Special procedures and implementation strategies are presented that enable many multi-period stochastic linear programs to be solved with two-stage, instead of nested, decomposition techniques. Consequently, abroad class of large scale problems, with tens of millions of constraints and variables, can be solved on a personal computer. Myopic decomposition algorithms based upon a shortsighted view of the future are also developed. Although unable to guarantee an arbitrary solution tolerance, myopic decomposition algorithms may yield very good solutions in a fraction of the time required by Dantzig-Wolfe/L-Shaped decomposition based algorithms.In addition, derivations are given for statistics, based upon Mahalanobis squared distances,that can be used to provide measures for a random sample\u27s effectiveness in approximating a parent distribution. Results and analyses are provided for the applications of the decomposition procedures and sample effectiveness measures to a multi-period market investment model

Implementation Aids for Optimization Algorithms that Solve Sequences of Linear Programs by the Revised Simplex Method

We describe a collection of subroutines designed a) to facilitate the implementation of algorithms that are based upon linear programming, b) to serve as a tutorial on the development of such implementations. We make this collection the basis for a discussion of some of the broader issues of software development

Multivariate McCormick relaxations

McCormick (Math Prog 10(1):147–175, 1976) provides the framework for convex/concave relaxations of factorable functions, via rules for the product of functions and compositions of the form F ∘ f, where F is a univariate function. Herein, the composition theorem is generalized to allow multivariate outer functions F, and theory for the propagation of subgradients is presented. The generalization interprets the McCormick relaxation approach as a decomposition method for the auxiliary variable method. In addition to extending the framework, the new result provides a tool for the proof of relaxations of specific functions. Moreover, a direct consequence is an improved relaxation for the product of two functions, at least as tight as McCormick’s result, and often tighter. The result also allows the direct relaxation of multilinear products of functions. Furthermore, the composition result is applied to obtain improved convex underestimators for the minimum/maximum and the division of two functions for which current relaxations are often weak. These cases can be extended to allow composition of a variety of functions for which relaxations have been proposed

Health Literacy: Determinant of Health or Status Indicator?

An increasing burden of preventable diseases, persistent health inequalities, and new infectious diseases call for responsible citizens to take care of their health and health decisions. Therefore, health literacy appears to be a promising concept to foster better health behaviours. However, health literacy is a broad concept and interventions targeting health literacy show mixed results. Against this background, this thesis’ aim is twofold. First, it explores health literacy as determinant of health. Secondly, and entwined with the first, it aims to provide a better conceptual understanding of health literacy. For the empirical analyses, data from Swiss male young adults were used. Three studies were carried out, each with different statistical approaches, to obtain a better understanding of the pathways between health literacy, its contextual factors, and favourable health outcomes. The studies’ results do not support the notion that health literacy – as a distinct phenomenon – has a causal importance to health. Rather, the findings suggest that health literacy should be acknowledged as a multifactorial phenomenon with many different dimensions, dependencies, and conversion factors. The latter either amplify or impede health literacy’s positive effects on health. Finally, the results indicate that potential health literacy interventions are likely to only address a selection of these aspects and may have limited or no benefit on health depending on personal and contextual factors. This umbrella text also presents conceptual work that could not be presented in the three journal articles. The health literacy staircase model (HL-SM) introduced here, describes the embeddedness of health literacy in contextual factors and addresses the complex path from knowledge to decision-making and decision-implementation. Further, it discusses several shortcomings of previous health literacy definitions and conceptualizations that are presented in the introduction section. The HL-SM was developed after the second publication and inspired the third study that explores the role of decision-making ability as a mediator from health literacy to health. This thesis calls for more health literacy research focussing on informed health decision-making in every-day contexts. Further, health literacy research is urged to give more emphasis to the concept’s boundaries, dependencies, and conversion factors. Without paying attention to prevailing contextual factors, there is considerable danger towards an individualization of a primarily societal problem

Near-inertial internal wave field in the Canada Basin from ice-tethered profilers

Author Posting. © American Meteorological Society, 2014. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 44 (2014): 413–426, doi:10.1175/JPO-D-13-0117.1.Salinity and temperature profiles from drifting ice-tethered profilers in the Beaufort gyre region of the Canada Basin are used to characterize and quantify the regional near-inertial internal wave field over one year. Vertical displacements of potential density surfaces from the surface to 750-m depth are tracked from fall 2006 to fall 2007. Because of the time resolution and irregular sampling of the ice-tethered profilers, near-inertial frequency signals are marginally resolved. Complex demodulation is used to determine variations with a time scale of several days in the amplitude and phase of waves at a specified near-inertial frequency. Characteristics and variability of the wave field over the course of the year are investigated quantitatively and related to changes in surface wind forcing and sea ice cover.The ITP program and J. Toole’s contributions were supported by the National Science Foundation Office of Polar Programs Arctic Observing Network. We acknowledge the support of the Office of Naval Research (Grant N00014-11-1-0454) for this study. Support for H. Dosser was also provided by the Natural Sciences and Engineering Research Council of Canada.2014-08-0

Invasive Species Forecasting System: A Decision Support Tool for the U.S. Geological Survey: FY 2005 Benchmarking Report v.1.6

The National Institute of Invasive Species Science (NIISS), through collaboration with NASA's Goddard Space Flight Center (GSFC), recently began incorporating NASA observations and predictive modeling tools to fulfill its mission. These enhancements, labeled collectively as the Invasive Species Forecasting System (ISFS), are now in place in the NIISS in their initial state (V1.0). The ISFS is the primary decision support tool of the NIISS for the management and control of invasive species on Department of Interior and adjacent lands. The ISFS is the backbone for a unique information services line-of-business for the NIISS, and it provides the means for delivering advanced decision support capabilities to a wide range of management applications. This report describes the operational characteristics of the ISFS, a decision support tool of the United States Geological Survey (USGS). Recent enhancements to the performance of the ISFS, attained through the integration of observations, models, and systems engineering from the NASA are benchmarked; i.e., described quantitatively and evaluated in relation to the performance of the USGS system before incorporation of the NASA enhancements. This report benchmarks Version 1.0 of the ISFS