@MISC{Glineur98patternseparation, author = {Fr. Glineur}, title = {Pattern Separation Via Ellipsoids and Conic Programming}, year = {1998} }

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Abstract

this document. The first chapter is about mathematical programming. We will start by describing how and why researchers were led to study special types of mathematical programs, namely convex programs and conic programs. We will also provide a detailed discussion about conic duality and give a classification of conic programs. We will then describe what are self-scaled cones and why they are so useful in conic programming. Finally, we will give an overview of what can be modelled using a SQL conic program, keeping in mind our pattern separation problem. Since most of the material in the chapter is standard, many of the proofs are omitted. The second chapter will concentrate on pattern separation. After a short description of the problem, we will successively describe four different separation methods using SQL conic programming. For each method, various properties are investigated. Each algorithm has in fact been successively designed with the objective of eliminating the drawbacks of the previous one, CONTENTS 3 while keeping its good properties. We conclude this chapter with a small section describing the state of the art in pattern separation with ellipsoids. The third chapter reports some computational experiments with our four methods, and provides a comparison with other separation procedures. Finally, we conclude this work by providing a short summary, highlighting the author's personal contribution and giving some interesting perspectives for further research. Chapter 1 Conic programming 1.1 Introduction