InhaltsverzeichnisSeite 1 Optimization of Nonlinear Problems Problem 1: Characterization of Optima Problem 2: Characterization in the presence of constraints Problem 3: Globality of Optima Seite 6 Smooth problems: Characterization of Optima Basic Algorithm for Smooth Unconstrained Problems Step 1: Choose search direction Step 1: Choose search direction Step 1: Choose search direction Step 1: Choose search direction Step 1: Choose search direction Step 2: Determination of Step Length Convergence: Gradient method Convergence: Newton's method Example 1: Gradient method Example 1: Gradient method Example 1: Newton's method Example 1: Newton's method Example 1: Comparison between methods Example 2: Gradient method Example 2: Gradient method Example 2: Newton's method Example 2: Newton's method Example 2: Comparison between methods What if the Hessian is not positive definite What if the Hessian is not positive definite What if the Hessian is not positive definite What if the Hessian is not positive definite What if the Hessian is not positive definite What if the Hessian is not positive definite What if the Hessian is not positive definite Quasi-Newton methods Practical line search strategies Practical line search strategies Practical line search strategies Practical line search strategies Practical line search strategies Practical line search strategies - Alternatives Seite 41 Least-Squares Problems: Background Least-Squares Problems: Background Least-Squares: Gauss-Newton Algorithm Least-Squares: Gauss-Newton Algorithm Seite 46 The Quadratic Penalty Method The Quadratic Penalty Method The Quadratic Penalty Method The Quadratic Penalty Method The Logarithmic Barrier Method The Logarithmic Barrier Method The Exact Penalty Method The Exact Penalty Method Necessary Conditions for Constrained Optima Newton's method for constrained problems Sequential Quadratic Programming (SQP) How does SQP work -- linear equality constraints How does SQP work -- nonlinear equality constraints How does SQP work -- nonlinear equality constraints Sequential Quadratic Programming (SQP) Summary Seite 63 |
Autor: Wolfgang Bangerth E-Mail: wolfgang.bangerth@iwr.uni-heidelberg.de Weitere Informationen: The other talks can be viewed at this page. |