Lecture 6 Solving SDPs using Multiplicative Weights
نویسنده
چکیده
In this lecture, first we propose an algorithm to solve semidefinite programs and then we will apply it to MAXCUT problem as an example. As you will see, we need an oracle with specific properties for our method to work, so we will show how to build such an oracle for MAXCUT problem. Finally, we investigate the quality of the SDP relaxation for a more general cases of discrete quadratic programs. As we saw in lecture 04, the canonical form for a SDP is sup B • X s.t. Recall that we also added the assumption that A 1 = I and c 1 = R, implying that T race(X) ≤ R for any feasible X. The dual problem associated to this SDP is inf c T y s.t. m i=1 y i A i − B 0 y ≥ 0 Now suppose that we have the following oracle which is going to help up in our algorithm.
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