‎in this paper‎, ‎some kkt type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (minpp) are established‎. ‎we achieve‎ ‎this by employing a lagrange function for minpp‎. ‎in addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

Most panel method implementations use both low order basis function representations of the solution and flat panel representations of the body surface. Although several implementations of higher order panel methods exist, difficulties in robustly computing the self term integrals remain. In this paper, methods for integrating the single and double layer self term integrals are presented. The ap...