bv_cvxbook_extra_exercises

# n are given samples from the joint distribution of

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Unformatted text preview: x optimization. (b) Numerical example. Solve the problem instance given in max_alg_conn_data.m, which uses F = 1T and g = 1 (so the problem is to allocate a total weight of 1 to the edges of the graph). Compare the algebraic connectivity for the graph obtained with the optimal weights w⋆ to the one obtained with wunif = (1/m)1 (i.e., a uniform allocation of weight to the edges). Use the function plotgraph(A,xy,w) to visualize the weighted graphs, with weight vectors w⋆ and wunif . You will ﬁnd that the optimal weight vector v ⋆ has some zero entries (which due to the ﬁnite precision of the solver, will appear as small weight values); you may want to round small values (say, those under 10−4 ) of w⋆ to exactly zero. Use the gplot function to visualize the original (given) graph, and the subgraph associated with nonzero weights in w⋆ . Brieﬂy comment on the following (incorrect) intuition: “The more edges a graph has, the more connected it is, so the optimal weight assignment shoul...
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