Hybrid Runge-Kutta and quasi-Newton methods for unconstrained nonlinear optimization

摘要: Finding a local minimizer in unconstrained nonlinear optimization and fixed point of gradient system ordinary differential equations (ODEs) are two closely related problems. Quasi-Newton algorithms widely used while Runge-Kutta methods for the numerical integration ODEs. In this thesis, hybrid combining low-order implicit systems quasi-Newton type updates Jacobian matrix such as BFGS update considered. These numerically approximate flow, but exact is not to solve at each step. Instead, matrix-vector multiplications performed limited memory setting reduce storage, computations, need calculate information. For based on order least two, curve search implemented instead standard line algorithms. Stepsize control techniques also stepsize associated with underlying method. tested variety test problems their performance compared that algorithm.