Optimization multidimensional

Having evaluated the system performance for each setting of the six variables, the variables are optimized simultaneously in a multidimensional optimization, using for example SQP, to maximize or minimize an objective function evaluated at each setting of the variables. However, in practice, many models tend to be nonlinear and hence a stochastic method can be more effective. 

Ishikawa, N. (2003) Simultaneous determination of ligand-field parameters of isostructural lanthanide complexes by multidimensional optimization. /. Phys. Chem. A, 107 (30), 5831-5835. 

Structure-Based In Silico Driven Multidimensional Optimization Paradigm 459... 

Fig. 14.9 Individual components of multidimensional optimization. This approach requires experimental compound profiling against key properties, which should be done on a designed compound subset to maximize information with a minimum number of molecules. These data are used to derive models for key properties, which are applied during the next design cycle. The results then led to augmented models. The process is characterized by a tight integration of in vitro and in silico tools for profiling compound series to guide chemical optimization.

Fig. 14.10 Example for multidimensional optimization on relevant properties during the lead optimization phase from leads to a development candidate. After some iteration, compound properties are either improved or show no further optimization potential.

Literature and Aventis Examples on Aspects of Multidimensional Optimization... 

This simple search method allows multidimensional optimization to be carried out experimentally the functional dependence of the target function on the individual parameters need not be known. The value of the target function (e.g., the yield of a... 

General programs for one-dimensional optimization are rarely included in the most recent implementations of multidimensional optimization programs. Certain... 

Below, we describe the main iterative methods used to solve multidimensional optimization problems. By the term iteration we mean that, given a point, x , where i is the progressive iteration number, the next point, xj+i, results in... 

Multidimensional optimization problems usually have more local minima. 

It is worth stressing that there are significant differences between the solution of nonlinear systems and multidimensional optimization. 

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