Robust Unconstrained Minimization

Examples of this chapter can be found in the Vol3 Chapter5 directory in the WileyVolS. zip file available atwww.chem.pohmi.it/homes/gbuzzi. 

The optimization methods covered in the previous chapters encounter certain difficulties when 

If we encounter even one of these conditions, the problem becomes dramatically more complex and the computational time required to achieve the solution also increases. 

It is worth stressing that with multimodal functions, no one can guarantee that the global minimum will be found. 

Some of the methods introduced in the previous chapters may also fail when 

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The built-in function minsearch is based on a rather unsophisticated algorithm. There are more robust unconstrained minimization functions available in some of the MATLAB Toolboxes, but unfortunately, these are not standard. For simple problems, minsearch often works well enough. It is used here to minimize the sum of squares between fictitious data (program generated data) and a function in which the regression coefficients appear nonlinearly. 

The BzzMinimizationSimplex class is designed to solve unconstrained multidimensional minimization problems by means of the Nelder-Mead version of the Simplex method, whereas the BzzMinimizationRobust class uses the Optnov method combined with a robust version of the Simplex method. 

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