Meshless methods have been extensively popularized in literature in recent years, due to their flexibility in solving boundary value problems. The meshless local Petrov-Galerkin(MLPG) method for solving the bending problem of the thin plate is presented and discussed in the present paper. The method uses the moving least-squares approximation to interpolate the solution variables, and employs a...

We present a faster interior-point method for optimizing sum-of-squares (SOS) polynomials, which are central tool in polynomial optimization and capture convex programming the Lasserre hierarchy. Let $$p = \sum _i q^2_i$$ be an n-variate SOS of degree 2d. Denoting by $$L:= \left( {\begin{array}{c}n+d\\ d\end{array}}\right) $$ $$U:= {\begin{array}{c}n+2d\\ 2d\end{array}}\right) dimensions vector...