169 research outputs found
Aspects of a phase transition in high-dimensional random geometry
A phase transition in high-dimensional random geometry is analyzed as it
arises in a variety of problems. A prominent example is the feasibility of a
minimax problem that represents the extremal case of a class of financial risk
measures, among them the current regulatory market risk measure Expected
Shortfall. Others include portfolio optimization with a ban on short selling,
the storage capacity of the perceptron, the solvability of a set of linear
equations with random coefficients, and competition for resources in an
ecological system. These examples shed light on various aspects of the
underlying geometric phase transition, create links between problems belonging
to seemingly distant fields and offer the possibility for further
ramifications
A Cost Impact Assessment Tool for PFS Logistics Consulting
Response surface methodology (RSM) is used for optimality analysis of the cost parameters in mixed integer linear programming. This optimality analysis goes beyond traditional sensitivity and parametric analysis in allowing investigation of the optimal objective function value response over pre-specified ranges on multiple problem parameters. Design of experiments and least squares regression are used to indicate which cost parameters have the greatest impact on the optimal objective function value total cost-and to approximate the optimal total cost surface over the specified ranges on the parameters. The mixed integer linear programming problems of interest are the large-scale problems in supply chain optimization also known as facility location and allocation problems. Furthermore, this optimality analysis technique applies to optimality analysis of costs or right-hand-side elements in continuous linear programs and optimality analysis of costs in mixed of pure integer linear programs. A system which automates this process for supply chain optimization at PFS Logistics Consulting is also detailed, along with description of its application and impact in their daily operations
On Network Coding Capacity - Matroidal Networks and Network Capacity Regions
One fundamental problem in the field of network coding is to determine the
network coding capacity of networks under various network coding schemes. In
this thesis, we address the problem with two approaches: matroidal networks and
capacity regions.
In our matroidal approach, we prove the converse of the theorem which states
that, if a network is scalar-linearly solvable then it is a matroidal network
associated with a representable matroid over a finite field. As a consequence,
we obtain a correspondence between scalar-linearly solvable networks and
representable matroids over finite fields in the framework of matroidal
networks. We prove a theorem about the scalar-linear solvability of networks
and field characteristics. We provide a method for generating scalar-linearly
solvable networks that are potentially different from the networks that we
already know are scalar-linearly solvable.
In our capacity region approach, we define a multi-dimensional object, called
the network capacity region, associated with networks that is analogous to the
rate regions in information theory. For the network routing capacity region, we
show that the region is a computable rational polytope and provide exact
algorithms and approximation heuristics for computing the region. For the
network linear coding capacity region, we construct a computable rational
polytope, with respect to a given finite field, that inner bounds the linear
coding capacity region and provide exact algorithms and approximation
heuristics for computing the polytope. The exact algorithms and approximation
heuristics we present are not polynomial time schemes and may depend on the
output size.Comment: Master of Engineering Thesis, MIT, September 2010, 70 pages, 10
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Advances in Optimization and Nonlinear Analysis
The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics
Aspects of linear programming and accounting in a manufacturing company
Imperial Users onl
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