<Para ID="Par1">In this paper, we consider an inverse problem of identifying one or more unknown cavities in a heat conductor. We propose an algorithm for reconstructing the position and shape of the unknown cavities using the measured surface temperature of the heat conductor. The heat conductor is discretized...</para>

We consider a priori error analysis for a discretization of a linear quadratic parabolic optimal control problem with box constraints on the time-dependent control variable. For such problems one can show that a time-discrete solution with second order convergence can be obtained by a first...

This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation methods. We first recall two SDP relaxation methods for solving polynomial optimization problems with finitely many constraints. Then we propose an exchange algorithm with SDP...