We have investigated two greedy strategies for finding an approximation to the minimum of a convex function E, defined on a Hilbert space H. We have proved convergence rates for a modification of the orthogonal matching pursuit and its weak version under suitable conditions on the objective function E. These conditions involve the behavior of the moduli of smoothness and the modulus of uniform convexity of E.

The present work deals with the calculation and the investigation of possible reductions of CO2 emissions in manufacturing a metal formed product. The industrial sector plays a significant role in the recent increase of the oncentration of Greenhouse Gases in the atmosphere, which is responsible for the advancing global warming. As an answer to fiscal and financial intervention of government policies aimed at counteracting this phenomenon, the environmental impact of products became a key aspect of a company’s strategy. However, literature still lacks effective methods and quantitative studies that look into the details of a single manufacturing process, discussing its environmental aspects and how they can be influenced by changes in the technological parameters. In an attempt to do that, an example of quantification and minimization of the carbon emissions occurring during the two manufacturing steps of the fabrication of an Al 6061 disc is provided. Electrical energy consumption occurring during the shearing and the upset forging of a billet was found by means of nonlinear finite element analysis and converted into CO2 emissions with a carbon emission signature value (CES). Environmental impact and frictional properties of both traditional lubrication and two non-conventional ecologically benign lubricants (palm oil ester and used cooking oil ester) were experimentally tested and are included in the study. A gradient-based optimization algorithm was implemented to determine the optimal geometry of the billet before the compression as well as the lubricant that minimize the total carbon emissions, within the proper technological limitations and constraints on the final product quality. A clear and effective method which would represent an auxiliary decision tool for a manufacturer in the metal forming sector is hereby presented. Results show that the selection of the manufacturing options can have an influence of more than 13% on the overall CO2 emission. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2009-12-19 16:39:12.071

As open pit mines get larger and their road networks more complex, haul road traffic is an area of increasing concern for mine operators. In particular, engineers from Barrick Gold Inc. have observed haul truck interactions in some of their larger open pit mines that are clearly disruptive to the haulage cycle. Such traffic effects cause uncertainty in haul times over identical routes and commercial dispatch systems do not explicitly account for this variability. This research, based on first-hand data collected from the Goldstrike Open Pit in Northern Nevada, focuses on assessing the level of variability in haul times, identifying the sources of said variability, and determining the effects on haulage optimization. Initial data analysis shows different levels of variability over the range of observed haul times, and further investigation identifies certain haulage parameters as significant sources of said variability, such as road topography and intersection effects. Focusing on these areas of interest, relevant data sets were manipulated to reduce levels of data dispersion and compared to observed results in order to quantify the effects in terms of changes to overall mean haul times along identical routes. It was observed that variability has a negative impact on travel times and moderate variability reduction was observed to increase productivity by 1–2 % when used as an input to a simple dispatch simulation program based on the Goldstrike Open Pit. / Thesis (Master, Mining Engineering) -- Queen's University, 2012-08-28 16:02:38.369

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Mixed integer programming (MIP) provides an important modeling and decision support tool for a wide variety of real-life problems. Unfortunately, practical MIPs are large-scale in size and pose serious difficulties to the available solution methodology and software. / This thesis presents a novel solution approach for large-scale mixed integer programming that integrates three bodies of research: interior point methods, decomposition techniques and branch-and-bound approaches. The combination of decomposition concepts and branch-and-bound is commonly known as branch-and-price, while the integration of decomposition concepts and interior point methods lead to the analytic centre cutting plane method (ACCPM). Unfortunately, the use of interior point methods within branch-and-bound methods could not compete with simplex based branch-and-bound due to the inability of "warm" starting. / The motivation for this study stems from the success of branch-and-price and ACCPM in solving integer and non-differentiable optimization problems respectively and the quest for a method that efficiently integrates interior-point methods and branch-and-bound. / The proposed approach is called an Interior Point Branch-and-Price method (IP-B&P) and works as follows. First, a problem's structure is exploited using Lagrangean relaxation. Second, the resulting master problem is solved using ACCPM. Finally, the overall approach is incorporated within a branch-and-bound scheme. The resulting method is more than the combination of three different techniques. It addresses and fixes complications that arise as a result of this integration. This includes the restarting of the interior-point methods, the branching rule and the exploitation of past information as a warm start. / In the first part of the thesis, we give the details of the interior-point branch-and-price method. We start by providing, discussing and implementing new ideas within ACCPM, then detail the IP-B&P method and its different components. To show the practical applicability of IP-B&P, we use the method as a basis for a new solution methodology for the production-distribution system design (PDSD) problem in supply chain management. In this second part of the thesis, we describe a two-level Lagrangean relaxation heuristic for the PDSD. The numerical results show the superiority of the method in providing the optimal solution for most of the problems attempted.

We propose an analytic center cutting plane algorithm for semidefinite programming (SDP). Reformulation of the dual problem of SDP into an eigenvalue optimization, when the trace of any feasible primal matrix is a positive constant, is well known. We transform the eigenvalue optimization problem into a convex feasibility problem. The problem of interest seeks a feasible point in a bounded convex set, which contains a full dimensional ball with &egr;(<1) radius and is contained in a compact convex set described by matrix inequalities, known as the set of localization. At each iteration, an approximate analytic center of the set of localization is computed. If this point is not in the solution set, an oracle is called to return a p-dimensional semidefinite cut. The set of localization then, is updated by adding the semidefinite cut through the center. We prove that the analytic center is recovered after adding a p-dimensional semidefinite cut in O(plog(p + 1)) damped Newton's iteration and that the ACCPM with semidefinite cuts is a fully polynomial approximation scheme. We report the numerical result of our algorithm when applied to the semidefinite relaxation of the Max-Cut problem.

An electric motor drive is a power-electronic based system that is used to precisely control the position, speed or torque developed by motor. With the growing complexity of drive systems and the expansion of the use of fast acting power-electronic controllers, computer simulation models are used instead of an explicit mathematical description of a complex system. The aim of this research is to study the use of the simulation based design method for advanced motor drives. The major problem for simulation of a drive system performance is the presence of both fast and slow dynamics in its response that result in relatively long time simulations with a small time step. Moreover, the simulation-based optimal design has a repetitive nature. Therefore, the simulation-based optimal design of a drive system is massively time consuming and requires extensive computing resources. In this research reduced intensity computer models are used to overcome this problem.