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题目:Nonlinear Minimization Techniques without Using Derivatives

报告人:Prof. Florian Jarre (Univ. Düsseldorf, Germany)


地点:西大楼 108

摘要: We discuss possible applications of minimization without (explicitly) using derivatives. While automatic differentiation offers an elegant and efficient alternative in many cases, due to its simplicity, the minimization without using derivative information is interesting in several respects: On the one side the applications mentioned above, on the other side a slight change in the use of the tools for minimization. There is a wealth of methods tuned to very expensive and/or noisy function evaluations, and there are methods in Matlab/Octave such as fmincon, fminunc, or minFunc that are tailored to situations where the derivative information is provided, and that use finite differences when derivatives are unavailable. We discuss modifications of the latter approach taking into account the fact that finite differences are numerically expensive compared to standard matrix operations. In particular, we consider a new line search based on least squares spline functions, a new finite difference setup, and the CDT-SQP method for equality- and inequality constrained minimization. Some numerical examples conclude the talk.