No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

In each iteration of the interior point method (IPM) at least one linear system has to be solved. The main computational effort of IPMs consists in the computation of these linear systems. Solving the corresponding linear systems with a direct method becomes very expensive for large scale problems. In this thesis, we have been concerned with using an iterative method for solving the reduced KKT systems arising in IPMs for linear programming. The augmented system form of this linear system has a number of advantages, notably a higher degree of sparsity than the normal equations form. We design a block triangular preconditioner for this system which is constructed by using a nonsingular basis matrix identified from an estimate of the optimal partition in the linear program. We use the preconditioned conjugate gradients (PCG) method to solve the augmented system. Although the augmented system is indefinite, short recurrence iterative methods such as PCG can be applied to indefinite system in certain situations. This approach has been implemented within the HOPDM interior point solver. The KKT system is solved approximately. Therefore, it becomes necessary to study the convergence of IPM for this inexact case. We present the convergence analysis of the inexact infeasible path-following algorithm, prove the global convergence of this method and provide complexity analysis.

Nitrate discharges from diffuse agricultural sources have long term effects on groundwater and surface water quality. Market-based instruments have been proposed as a means of balancing the demand for nitrate intensive farming and the capacity of the natural water bodies to dilute nitrates. Trading is complicated by the dispersed, delayed, and protracted effects of diffuse sources. Market mechanisms proposed to date have failed to incorporate these physical characteristics of nitrate pollution correctly. We propose a new market mechanism for allocating and pricing nitrate discharge permits, based on the design of modern electricity markets which use LP models to find optimal prices and dispatch schedules. The system operates as a centralized auction. The sources submit bids to the auction indicating the benefits gained from each unit of nitrate discharge. The auction operator runs an LP which maximises the benefits from trade, subject to a set of environmental and operational constraints. The LP solution produces the optimal prices and allocations relative to the economic values indicated in the bids. Our contributions include alternative LP models to suit different hydro-geological and socio-economic conditions. We present a generalized LP model which can include constraints that describe nitrate residence and transport in groundwater and surface water, the ability of water bodies to accept nitrates, and the operational limitations of the commercial sources. We show how to adapt available methods to incorporate the complex physical systems into an optimisation model. We present a double-sided market model which allows the polluters to buy permits, and environmental agents to lease out the ability of the natural water resources to accept nitrates. The model allows the providers of environmental services to participate in the market as sellers. We build up and prove the concepts by explaining the prices and allocations produced by the LP models. Based on the theory of nodal pricing applied in electricity markets, we discuss the price structures and relationships and show how the prices would reflect the spatial and temporal effects of diffuse nitrate discharges. We interpret the information generated from the outcomes of trading and discuss how the available tools and information can be used by the market participants to optimize their bids. We expand the proposed market model to include point sources, and identify the factors that determine the extent to which the point and nonpoint sources can trade with each other. In addition, we develop measures of the extent to which the diffuse sources themselves can trade with each other. We demonstrate the models and the resulting prices and allocations, using a catchment nitrate transport model.

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Results found in this thesis draw attention to limitations in the conventional approach to modelling forest management strategy, where models have insufficient spatial resolution and ignore industry. Addressing these limitations, a Model One linear programming framework was developed in which models built can model strategically relevant spatial resolution, and include industry representation. In a case-study on Nova Scotia's Crown Central Forest, models from this framework were compared with Woodstock\texttrademark, a commercial modelling framework. When strategically relevant spatial resolution was modelled, these models found solutions in substantially less time than Woodstock. Of further interest, the framework's industry representation allows novel analysis to be performed. A comparison between a model that includes industry and a conventional model demonstrates that the conventional model schedules unprofitable stands for harvest. Then, models with industry representation are used to demonstrate industry based analysis, such as assessing the cost of a clearcut restriction policy and investigating the benefit of industrial expansion. Taken together, the results herein contained make an argument for modelling forest management strategy at strategically relevant spatial resolution, and including industry representation in modelling.