With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence, and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids, and flows.
The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Course requirements : Consisting of 10 courses and 2 rotation projects.
Projects are faculty-lead and aim to: provide practicum opportunities explore potential dissertation topics within the faculty advisor's area expose students to computational research problems in practical settings through interdisciplinary collaborations Qualifying Exams : This consists of an area exam that covers foundational materials within the student's area of research, and a thesis proposal in which the student describes a set of open research questions and the approaches that will be taken to answer them.
Teaching Requirements : Each student must attend a three-day summer workshop and a one semester department seminar on teaching, co-teach one course, and independently teach one introductory-level undergraduate course. Students must also attend a minimum of 6 hours of program-based ethics material CS , the programs teaching program and CS , Graduate Seminar.
Iterative Methods in Combinatorial Optimization (PhD Thesis)
CS should be completed in the fall of the second or third year of study. Students must fulfill the Graduate School residency requirements. Each student must present a deparment graduate seminar, complete an acceptable dissertation and deliver an oral defense. Outline: Motivated by computerized markets, you should consider direct exchange between matched agents, just two at a time. Yet, reasonable conditions ought suffice for convergence to market equilibrium. When well defined, the concept of gradient or margin is fundamental in optimization and economics.
To wit, for efficient allocation, margins ought coincide across alternative ends and users. Otherwise, scarce resources should be shifted from low valuation or from inferior yield to higher. Traditional use of this good maxim requires though, comparisons of differentials or gradients. For that reason, several questions come straight up: What happens if gradients aren't unique - or, no less important, if a best choice be at the boundary?
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- Available master theses in optimization.
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In such cases, which margins are essential? And how might these coincide? While addressing these questions, you should illustrate, maintain, refine and extend the said maxim, often referred to as Borch's theorem of insurance.
Outline: Many energy markets offer special procedures in order to begin or end ordinary trade more efficiently. Broadly, the early hour ought ease price discovery, whereas the last hour should facilitate execution of still standing orders. For either purpose, call auctions have been instrumental.
Their main feature is that all executable orders should be cleared by uniform linear pricing. Your project is to consider such an auction and elaborate on what an optimizing system operator tends to do.
Arguments should revolve around the market opening time - or the period just prior to that event. Outline: Consider two linear progams for which the right hand side vectors are in the same space. Merge these program into one. Why might this be advantageous? How should the gains be split?
Often, new master students have a suggestion for a master thesis. Their idea might for example be based on their interests, or they have heard of a problem with a background in an for example industrial application by someone they know. Students with such a suggestion are very welcome to present their idea to the appropriate group at the department.
Master students in optimization are offered very interesting theses within a broad range of applications and techniques.
Several theses have industrial applications in e. The projects typically involve modelling, analysis, development of new solution methods, implementation and experimentation.
For most theses, good programming skills are required. Students with a suggestion for a thesis meeting the above description, are very welcome to contact a member of the optimization group and present their idea. Ruckmann uib. Skip to main content. Ship routing and scheduling Maritime transportation is the obvious choice for heavy industrial activities where large volumes are transported over long distances. Advisor: Ahmad Hemmati. Pickup and delivery problem Among various problems considered in supply chain logistics, pickup and delivery problem with time windows is one of the most practical one that has received a lot of attentions in the operation research community.
Maritime inventory routing problem Maritime transportation is the obvious choice for heavy industrial activities where large volumes are transported over long distances. Covering location problem In a covering location problem, we seek location of a number of facilities on a network in such a way that the covered population is maximized.
Iterative Methods in Combinatorial Optimization (PhD Thesis) - PDF Free Download
Adaptive large neighbourhood search Adaptive large neighbourhood search is a popular and widely used algorithm in the literature in solving combinatorial problems and in particular routing problems. Location routing problem A location-routing problem may be defined as an extension to a multi depot vehicle routing problem in which there is a need to determine the optimal number and location of depots simultaneously with finding distribution routes.
Advisor: Trond Steihaug. What do we mean by an efficient algorithm? Application of Nonlinear Optimization Methods This topic covers the application of several solution methods for nonlinear optimization problems. Optimization Methods in Finance The use of mathematical optimization methods in finance is common-place and a continuously developing vivid area of research. Optimal portfolio selection with minimum buy-in constraints Investors in charge of selecting the assets to constitute a portfolio, will typically use the expected return as a measure of the expected value, and the variance as a measure of the risk.
Solution algorithms for the pooling problem In many industrial applications of network flow problems, such as oil refining and pipeline transportation of natural gas, the composition of the flow is of interest. Order Books, Markets, and Convex Analysis This project considers how an order market might evolve over a fairly short period - say, during a day. Bilateral exchange Outline: Motivated by computerized markets, you should consider direct exchange between matched agents, just two at a time.
Efficiency and equal margins When well defined, the concept of gradient or margin is fundamental in optimization and economics. Call auctions in energy markets Outline: Many energy markets offer special procedures in order to begin or end ordinary trade more efficiently. Cooperative linear programs Outline: Consider two linear progams for which the right hand side vectors are in the same space.