bv_cvxbook_extra_exercises

Nonnegativity of the weights implies l 0 denote the

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Unformatted text preview: s a special case in which the edges contain no more than two nodes. We consider a hypergraph with m nodes and assume coordinate vectors xj ∈ Rp , j = 1, . . . , m, are associated with the nodes. Some nodes are fixed and their coordinate vectors xj are given. The other nodes are free, and their coordinate vectors will be the optimization variables in the problem. The objective is to place the free nodes in such a way that some measure of the physical size of the nets is small. As an example application, we can think of the nodes as modules in an integrated circuit, placed at positions xj ∈ R2 . Every edge is an interconnect network that carries a signal from one module to one or more other modules. To define a measure of the size of a net, we store the vectors xj as columns of a matrix X ∈ Rp×m . For each edge S in the hypergraph, we use XS to denote the p × |S | submatrix of X with the columns associated with the nodes of S . We define fS (X ) = inf XS − y 1T . (41) y as the size...
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