Semideenite Programming in Combinatorial Optimization 1
نویسنده
چکیده
We discuss the use of semideenite programming for combinato-rial optimization problems. The main topics covered include (i) the Lovv asz theta function and its applications to stable sets, perfect graphs, and coding theory, (ii) the automatic generation of strong valid inequalities, (iii) the maximum cut problem and related problems, and (iv) the embedding of nite metric spaces and its relationship to the sparsest cut problem.
منابع مشابه
Semideenite Programs and Combinatorial Optimization
Outline 1. Introductory examples: Shannon capacity and maximum cuts. 2. Preliminaries: linear programming, semideenite matrices. 3. General properties of semideenite programs: equivalent forms, Farkas Lemma, Duality Theorem, Ellipsoid method, Interior point method. 4. Getting semideenite programs I: eigenvalues of graphs and the method of variables. 5. Getting semideenite programs II: geometric...
متن کامل658 Michel
We describe a few applications of semideenite programming in combinatorial optimization. Semideenite programming is a special case of convex programming where the feasible region is an aane subspace of the cone of positive semideenite matrices. There has been much interest in this area lately, partly because of applications in com-binatorial optimization and in control theory and also because o...
متن کاملSemideenite Programs and Combinatorial Optimization
Outline 1. Introductory examples: Shannon capacity and maximum cuts. 2. Preliminaries: linear programming, semideenite matrices. 3. General properties of semideenite programs: equivalent forms, Farkas Lemma, Duality Theorem, Ellipsoid method, Interior point method. 4. Getting semideenite programs I: eigenvalues of graphs and the method of variables. 5. Getting semideenite programs II: geometric...
متن کاملSemideenite Programming in Combinatorial Optimization
This chapter surveys the use of semideenite programming in combinatorial optimization. It was written as part of DONET, a European network supported by the European Community within the frame of the Training and Mobility of Researchers Programme (contract number ERB TMRX-CT98-0202). It will appear as Chapter 12 of the \Handbook of 1 From combinatorial optimization to SDP In this section we inve...
متن کاملSolving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization
We present a dual-scaling interior-point algorithm and show how it exploits the structure and sparsity of some large scale problems. We solve the positive semideenite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints. We report the rst computational results of interior-point algorithms for approximating the maximum cut semideenite programs with dimen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997