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

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'

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

An easy way to obtain strong duality results in linear, linear semidefinite and linear semi-infinite programming

In linear programming it is known that an appropriate non-homogeneous Farkas Lemma leads to a short proof of the strong duality results for a pair of primal and dual programs. By using a corresponding generalized Farkas lemma we give a similar proof of the strong duality results for semidefinite programs under constraint qualifications. The proof includes optimality conditions. The same approach leads to corresponding results for linear semi-infinite programs. For completeness, the proofs for linear programs and the proofs of all auxiliary lemmata for the semidefinite case are included

Instruments of Transport Policy.

The material in this Working Paper was generated as input to DETR's Guidance on the Methodology for Multi Modal Studies (GOMMMS). DETR subsequently decided only to provide summary information on transport policy measures, and to leave the consultants involved in individual multi modal studies to make their own assessment of individual policy measures in the context of specific study areas. It has been decided to make this fuller document available as a reference source. The purpose of the review of policy measures was to provide summary information on the range of policy measures available, experience of their use and, based on past studies, their potential contribution to the range of policy objectives specified for GOMMMS. The review was based on an earlier one included in the Institution of Highways and Transportation's Guidelines on Developing Urban Transport Strategies (1996). This material was updated using references published since 1996 and expanded to cover policy measures relevant in inter-urban areas. It had been intended to circulate it for comment before publishing a revised version. However, DETR decided to use an abridged version before this consultation was complete. It should be borne in mind that this document has not, therefore, undergone the peer assessment which had been intended. To avoid unnecessary further work, the material is presented as it had been drafted for the GOMMMS Guidance document. The only modifications have been to change the chapter and paragraph numbers, and to remove the cross references to other parts of the Guidance document

Implementation of the Delta/Start Model.

This working paper outlines the steps undertaken to develop a dynamic land use transport model. The model is based around an existing transport modelling suite, called START, which has been applied to many urban areas in the UK and abroad. However, its integration with an explicit land use model (called DELTA) was new, and this paper describes the first implementation of the combined dynamic land use transport model for the study area of Fife and Lothian region. The model was used in a PhD thesis and an EPSRC ‘Sustainable Cities’ research project at the Institute for Transport Studies. The paper discusses the processes involved in the full implementation of this model, involving both software development, modification to existing software, and implementation. However, it focuses in particular upon the data requirements and calibration of the various submodels in DELTA. In general the model dataset has been generated using existing study area data from past START applications, plus data from the 1991 Census of population and employment. Not all the disaggregations of data required by the model were available from published, or on-line, sources, and so several disaggregations were undertaken. A feature of the model is that the calibration is undertaken for each submodel individually. In general, the model made use of past research into the relationships that it represents, combined with the judgement of the model developers where no other data was available. The implementation of the location model is discussed in detail, including the use of environmental variables in location choice. This fulfils the main aim of this paper; to provide the technical background for the research projects that make use of this model implementation

Interior points of the completely positive cone.

A matrix A is called completely positive if it can be decomposed as A = BB^T with an entrywise nonnegative matrix B. The set of all such matrices is a convex cone. We provide a characterization of the interior of this cone as well as of its dual