Unconstrained robust

GRG Probably most robust of all three methods Versatile—especially good for unconstrained or linearly constrained problems but also works well for nonlinear constraints Once it reaches a feasible solution it remains feasible and then can be stopped at any stage with an improved solution Needs to satisfy equalities at each step of the algorithm... 

Risk assessment evaluates risk in terms of hazard and exposure, but reference to risk levels must account for different perceptions of risk as well as scientific uncertainties in risk assessment. In short, this research project considers the importance of social and institutional processes in influencing risk perceptions and risk acceptability. This book therefore takes a constrained relativist approach by incorporating risk perceptions in the research framework. An unconstrained relativist perspective would imply that no scientific study is reliable or robust. By contrast, a constrained relativist approach can provide a useful basis for examining the different social and cultural factors involved in regulatory risk management. 

Zafiriou (1991) used a number of examples to demonstrate that the presence of constraints can have a dramatic and often counterintuitive effect on MFC stability properties and can render tuning rules developed for stability or robustness of unconstrained MFC incorrect. The following examples show how the addition of constraints to a robustly stable unconstrained MFC system can lead to instabilities. 

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 use of quantum-chemistry computer codes for the determination of the equilibrium geometries of molecules is now almost routine owing to the availability of analytical gradients at SCF, MC-SCF and CP levels of theory and to the robust methods available from the held of numerical analysis for the unconstrained optimization of multi-variable functions (see, for example. Ref. 21). In general, one assumes a quadratic Taylor series expansion of the energy about the current position... 

These goals may conflict. For example, a rapidly convergent method for a large unconstrained nonlinear problem may require too much computer memory. On the other hand, a robust method may also be the slowest. Tradeoffs between convergence rate and storage requirements, and between robustness and speed, and so on, are central issues in numerical optimization. 

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. 

---