# University of Twente Student Theses

## Relations between semidefinite, copositive, semi-infinite and integer programming

Ahmed, F.
(2010)
*Relations between semidefinite, copositive, semi-infinite and integer programming.*

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Abstract: | Mathematical programming is a vast area of research in mathematics. On the basis of special structure this field can be further classified into many other, not necessarily completely distinct, classes. In this thesis we will focus on two classes, namely Cone Programming and Semi-infinite Programming. Semi-infinite programming represents optimization problems with infinite many constraints and finitely many variables. This field emerged in 1924, but the name semi-infinite programming was coined in 1965. Cone programming is the class of problems in which the variable should belong to a certain cone. The most interesting application of cone programming is cone programming relaxation which has numerous example in combinatorial optimization and other branches of science and mathematics. The most popular and well known cone programs are semidefinite programs. These programs got popularity due to there huge application in combinatorial optimization. Another class of cone programing is copositive programing. Copositive programming has recently gained attention of researchers for their application to solve hard combinatorial optimization problems. Our main focus in this thesis will be on copositive programming. Another problem of interest is to analyze the way how we can represent these different classes in terms of each other. We will consider the restrictions and benefits we will obtain for these kind of representations. Normally these kind of representations helps to use algorithms available for one class, for the solution/approximation or finding good bounds for other classes of problems. Eigenvalue optimization can be seen as the building block for the development of semidefinite programming. In this thesis we will investigate this relationship to answer the question whether one can solve semidefinite program by formulating it as an equivalent eigenvalue optimization with the aid of semi-infinite programming |

Item Type: | Essay (Master) |

Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |

Subject: | 54 computer science |

Programme: | Applied Mathematics MSc (60348) |

Link to this item: | https://purl.utwente.nl/essays/59751 |

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