Martin Mevissen

Mean squared error minimization for inverse moment problems

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Martin Mevissen
    • Categories Convex Optimization, Semi-definite Programming

    We consider the problem of approximating the unknown density $u\in L^2(\Omega,\lambda)$ of a measure $\mu$ on $\Omega\subset\R^n$, absolutely continuous with respect to some given reference measure $\lambda$, from the only knowledge of finitely many moments of $\mu$. Given $d\in\N$ and moments of order $d$, we provide a polynomial $p_d$ which minimizes the mean square error … Read more

    Exploiting Sparsity in Linear and Nonlinear Matrix Inequalities via Positive Semidefinite Matrix Completion

  • Sunyoung Kim
  • Masakazu Kojima
  • Martin Mevissen
  • Makoto Yamashita
    • Categories Semi-definite Programming Tags , , ,

    A basic framework for exploiting sparsity via positive semidefinite matrix completion is presented for an optimization problem with linear and nonlinear matrix inequalities. The sparsity, characterized with a chordal graph structure, can be detected in the variable matrix or in a linear or nonlinear matrix-inequality constraint of the problem. We classify the sparsity in two … Read more