Semidefinite Programming in Combina - torial and Polynomial Optimization
نویسنده
چکیده
In recent years semidefinite programming has become awidely used tool for designing more efficient algorithms for approximating hard combinatorial optimization problems and, more generally, polynomial optimization problems, which deal with optimizing a polynomial objective function over a basic closed semi-algebraic set. The underlying paradigm is that while testing nonnegativity of a polynomial is a hard problem, one can test efficiently whether it can be written as a sum of squares of polynomials by using semidefinite programming. In this note we sketch some of the main mathematical tools that underlie this approach and illustrate its application to some graph problems dealing with maximum cuts, stable sets and graph colouring.
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تاریخ انتشار 2008