Optimization: NURBS and the quasi-Newton method

Optimization is important in both engineering and mathematics. The Quasi-Newton Method is widely used for optimization due to its speed and efficiency. NonUniform Rational B-Splines (NURBS) are piecewise parametric approximations to curves and surfaces. NURBS have great curve-fitting properties that can be applied to improve optimization performance. This dissertation investigated the use of NURBS in optimization, focusing primarily on the coupling of NURBS with the Quasi-Newton Method. A hybrid optimization procedure dubbed the NURBS-Quasi-Newton (NQN) Method was developed and utilized that can virtually assure that the global minimum will be found. A Method was also developed to implement Pure NURBS Optimization (PNO), which can be used to optimize non-continuous and singular functions as well as functions of point cloud data. It was concluded that NURBS offer significant benefits for optimization, both individually and coupled with Quasi-Newton Methods.