Exploiting Sparsity for Semi-Algebraic Set Volume Computation

We provide a systematic deterministic numerical scheme to approximate the volume (i.e., Lebesgue measure) of basic semi-algebraic set whose description follows correlative sparsity pattern. As in previous works (without sparsity), underlying strategy is consider an infinite-dimensional linear program on measures optimal value set. This particular instance generalized moment problem which turn can be approximated as closely desired by solving hierarchy semidefinite relaxations increasing size. The novelty with respect work that exploiting pattern we sparse formulation for associated are much smaller In addition, decompose into completely decoupled subproblems size, and some cases computations done parallel. To best our knowledge, it first contribution exploits computation sets possibly high-dimensional and/or non-convex non-connected.