Optimization algorithms, drawback

With the feasible path approach the optimization algorithm automatically performs case studies by variing input data. There are several drawbacks the process equations (32c) have to be solved every time the performance index is evaluated. Efficient gradient-based optimization techniques can only be used with great difficulties because derivatives can only be evaluated by perturbing the entire flowsheet with respect to the decision variables. This is very time consuming. Second, process units are often described by discrete and discontinuous relations or by functions that may be nondifferentiable at certain points. To overcome these problems quadratic module models can be... 

A great deal has been written about the optimality of the krlglng estimates and about the error characterization provided by Iso-varlance maps such as that of Figure 1. However, krlglng, and more generally data-free estimation algorithms, have several drawbacks. 

The traditional hierarchical and nonhierarchical (e.g., fc-means) clustering algorithms [69] have a number of drawbacks that require caution in their implementation for time series data. The hierarchical clustering algorithms assume an implicit parent-child relationship between the members of a cluster which may not be relevant for time series data. However, they can provide good initial estimates of patterns that may exist in the data set. The fc-means algorithm requires the estimate of the number of clusters (i.e., k) and its solution depends on the initial assignments as the optimization... 

In this appendix we describe a stencil algorithm which avoids many of the drawbacks of quadrature rules used in classical lattice models, while the extra computational cost is modest. The derivation consists of finding a unique and optimal set of stencil coefficients for a convolution with a Gaussian kernel, adapted to the special case of off-lattice density functional calculations. Stencil coefficients are the multipliers of the function values at corresponding grid points. 

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