The Optimality Conditions and Numerical Simulation On The Three-Dimensional Layout Optimization Problem

We consider problems requiring to pack cylindrical objects into the cylindrical layout space by minimizing the static non-equilibrium quantity. So far there is few literature discussing the optimality conditions about layout problem. We present the main properties and the optimality conditions based on the three-dimensional layout optimization model with behavioral constraints. Moreover, we introduce a mass vector and a symmertrical matrix H(2¿¿^T /0 0/2¿¿^T) which is semi-positively definite, such that we can obtain the transformed layout optimal model and descent the computation amount. Finally, by the sequential quadratic programming method (SQP) and Quasi-Newton method , the numerical experiments and the computational results are presented.