Multidimensional robust minimization

When conditions that require the BzzMinimizationTwoVeryRobust class are detected and the search domain has more than two dimensions, the methods described in Chapter 3 cannot be applied and greater robustness is called for. 

A new strategy proposed by Buzzi-Ferraris and Manenti (2010a) is described below. 

This strategy exploits the features of the Optnov method, originally developed to solve very narrow valley problems and already described in Section 3.2.4, but 

Let us suppose we know a direction that is oriented more or less along the bottom of the valley. The mistake made by many strategies is to adopt such a direction as the axis along which we should search for the one-dimensional minimum. Such a search will prove ineffective, usually because the direction is imprecise and the valley is nonlinear. 

To exploit the search direction that detects the bottom of the valley in a more or less accurate manner, it is necessary to shift our point of view. 

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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. 

The BzzMinimizationMultiVeryRobust class, implemented in the BzzMath library for robust multidimensional minimization, uses a number of points N > 4. If the number of processors np < 4, N = 4. If wp > 4 and the compiler exploits openMP directives, N = np so as to assign a dedicated processor to each object in the inner optimization. 

The class implemented in the BzzMath library for robust multidimensional minimization is BzzMinimizationMultiVeryRobust... 

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