Generalized semi-infinite programming: Numerical aspects

Generalized semi-infinite optimization problems (GSIP) are considered. It is investigated how the numerical methods for standard semi-infinite programming (SIP) can be extended to GSIP. Newton methods can be extended immediately. For discretization methods the situation is more complicated. These difficulties are discussed and convergence results for a discretization and an exchange method are derived under fairly general assumptions. The question under which conditions GSIP represents a convex problem is answered

Transport Impacts on Land Use: Towards A Practical Understanding for Urban Policy Making – Introduction and Research Plan.

INTRODUCTION This working paper forms a general introduction to an EPSRC CASE research project, presenting the objectives of the research, the rationale behind the study, a summary of some of the results obtained so far, and a plan for the remainder of the research work. The project is due for completion in November 1996. In other words, the project is examining: 1. The current understanding of the nature of the influence that transport has upon activity patterns and land use. Specifically, this is making use of empirical studies of transport impacts on land use, plus behavioural studies of the factors in location choice. 2. Whether this relationship can be adequately represented in a predictive context. This consists of two elements. How the relationship of transport on land use can be studied and 'formalised', and secondly, the ability to use this relationship for estimation of land use response to transport impacts. Use will be made of published modelling studies, plus some original modelling work, using a model constructed for this research. 3. The benefits of predicting transport impacts upon land use to planners involved in strategic land use and transport planning. This is the main objective of the research, and addresses why transport impacts on land use appear to have a minor role in structure planning, why model representations are seldom used, and given a model's predictions, what use will be made of the model results. Initial results from the first round of interviews are given in this paper. There are several themes that underpin this research: The nature of the 'transport on land use' relationship. How far it can he formalised, what we know about it, and how it is best to study it. Strategic planning processes in the UK, how the planning system handles the transport on land use relationship, under what circumstances the relationship is important, and the role of model predictions in the planning process. Whether the remit of 'planning' should examine transport impacts on land use, plus anticipation of the impacts of local government reorganisation. The issue of whether predictive modellmg in this context is an appropriate tool beyond the scope of academic research

Historic Cities Project Task 4 – The Business Surveys: Questionnaire Design, Implementation and Initial Analysis.

The Historic Cities project examined the potential impacts of transport demand management strategies on three case study ‘historic’ cities in England. These cities are York, Cambridge and Norwich, all of which have the following characteristics: - they are cities which pre-date motorised transport, and thus tend to have city centres dominated by narrow streets; - they are all members of the Historic Towns Forum; - they have a high architectural and historic heritage, and attract many tourists each year; - they have severe congestion, and congestion related problems; - the city authorities are faced with the problems of maintaining the environmental quality of the city, while allowing the most efficient use of the transport infrastructure. The focus of the project was how transport demand management policies, particularly parking, pricing and road-space re-allocation, can contribute to the last bullet above. Task 4 in the Historic Cities project examined the predicted effects on the urban economy from a work place parking levy and road user charging. It is thought that a major barrier to the implementation of these instruments is the perception that they will have detrimental impacts on the local economy. This task examines whether this hypothesis is correct by examining the impacts on, and attitudes of, businesses in the case study cities. This working paper describes the survey work that was undertaken and presents the initial analysis of the results. It has the following sections: Section 1: introduces the research; Section 2: describes the policies to be studied; Section 3: describes the development and rationale for the questionnaire; Section 4: describes the sampling process; Section 5: presents the initial analysis of the results; Section 6: gives a summary and conclusions. This is the second Working paper that summaries the Task 4 study. The first working paper (537) outlined the business sector profile for each city. A third working paper (552) will present multi-variate analysis of the dataset

Linear bilevel problems: Genericity results and an efficient method for computing local minima

The paper is concerned with linear bilevel problems. These nonconvex problems are known to be NP-complete. So, no efficient method for solving the global bilevel problem can be expected. In this paper we give a genericity analysis of linear bilevel problems and present a new algorithm for computing efficiently local minimizers. The method is based on the given structural analysis and combines ideas of the Simplex method with projected gradient steps

On generalized semi-infinite optimization and bilevel optimization

The paper studies the connections and differences between bilevel problems (BL) and generalized semi-infinite problems (GSIP). Under natural assumptions (GSIP) can be seen as a special case of a (BL). We consider the so-called reduction approach for (BL) and (GSIP) leading to optimality conditions and Newton-type methods for solving the problems. We show by a structural analysis that for (GSIP)-problems the regularity assumptions for the reduction approach can be expected to hold generically at a solution but for general (BL)-problems not. The genericity behavior of (BL) and (GSIP) is in particular studied for linear problems

Structure or Noise?

We show how rate-distortion theory provides a mechanism for automated theory building by naturally distinguishing between regularity and randomness. We start from the simple principle that model variables should, as much as possible, render the future and past conditionally independent. From this, we construct an objective function for model making whose extrema embody the trade-off between a model's structural complexity and its predictive power. The solutions correspond to a hierarchy of models that, at each level of complexity, achieve optimal predictive power at minimal cost. In the limit of maximal prediction the resulting optimal model identifies a process's intrinsic organization by extracting the underlying causal states. In this limit, the model's complexity is given by the statistical complexity, which is known to be minimal for achieving maximum prediction. Examples show how theory building can profit from analyzing a process's causal compressibility, which is reflected in the optimal models' rate-distortion curve--the process's characteristic for optimally balancing structure and noise at different levels of representation.Comment: 6 pages, 2 figures; http://cse.ucdavis.edu/~cmg/compmech/pubs/son.htm

How to split the eigenvalues of a one-parameter family of matrices

We are concerned with families $F$ of $n \times n$-matrices $F(t)$ depending smoothly on the parameter $t \in \mathbb{R}$. We survey results on the behaviour of eigenvalues of $F(t)$ for certain classes of matrices. We are especially interested in the question whether multiple eigenvalues can be avoided generically. In the set of families of symmetric matrices $F(t)$, for example, generically all eigenvalues of $F(t)$ are simple for all $t \in \mathbb{R}$. We consider a class of natural perturbations $\widetilde{F}$ of a given matrix family $F$ such that $\widetilde{F}$ lies in the generic class, i.e.\ $\widetilde{F}$ avoids double eigenvalues `as far as possible'

A note on perfect partial elimination

In Gaussian elimination it is often desirable to preserve existing zeros (sparsity). This is closely related to perfect elimination schemes on graphs. Such schemes can be found in polynomial time. Gaussian elimination uses a pivot for each column, so opportunities for preserving sparsity can be missed. In this paper we consider a more flexible process that selects a pivot for each nonzero to be eliminated and show that recognizing matrices that allow such perfect partial elimination schemes is NP-hard

Business Sector Profiles for Cambridge, York and Norwich. Historic Cities Project Task 4

The Historic Cities project is examining the potential impacts of transport demand management strategies on several case study 'historic' cities in England. These cities are York, Cambridge and Norwich, all of which have the following characteristics; they are cities which pre-date motorised transport, and thus tend to have city centres dominated by narrow streets; - they are all members of the Historic Towns Forum; - they have a high architectural and historic heritage, and attract many tourists each year; - they have severe congestion and congestion related problems; - the city authorities are faced with the problems of maintaining the environmental quality of the city, while allowing the most efficient use of the transport infrastructure. The Historic Cities project is examining how transport restraint policies, particularly parking, pricing and road-space reallocation, can contribute to the last bullet above. It is examining this via a series of surveys and modelling of the city traffic patterns under different policies. The main 'tasks' (work packages) are as follows; 1 Travel choices; using a stated preference experiment on mode choices from various traffic demand policies; 2 Traffic effects; Modelling of policies in the various cities using network traffic models; 3 Environmental effects; using the outputs from (2) 4 Urban economy effects; using a survey of businesses 5 Public attitudes; using a survey of resident's attitudes and anticipated responses; Task 4 in the Historic Cities project is examining the perceived and predicted effects on the urban economy from four transport instruments that attempt to restrain car use. It is thought that a major barrier to the implementation of these projects is their detrimental impacts on the local economy. This task examines whether this hypothesis is correct by examining the impacts on, and attitudes of, businesses in the case study cities. This paper presents background information on the cities, building up a business profile of each. The data sources are mostly published information, although city specific business databases were analysed to obtain a cross classification of the business profile. This is the first of a series of Working Papers on Task 4. The next Working Paper will outline the survey of firms that was undertaken, its initial results. It will use the business sector profile to determine how generally representative the samples are of the cities business sectors