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Using high impedance differential protection for internal short-circuits (see section 7.6.1.2.1). This type of protection is only used for motors above roughly 2 MW. Using biased differential protection. This type of protection is only used for motors above roughly 2 MW. By fuse for equipment with contactor + fuse. It must be remembered that fuses protect a motor against overcurrents above the starting current and do not therefore provide protection against overloads. The rating of fuses is determined in relation to the: nominal current I n ; starting current I st ; start-up time Tst ; maximum number of start-ups per hour; maximum number of successive start-ups.

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algorithm (Berndt et al 1974) is offered in some econometrics packages, although it is generally ignored by modern optimization researchers Another example, the downhill simplex method, invented by Nelder and Mead (1965), is most appropriate where derivatives are absent, but is sometimes seen in statistical routines being applied to differentiable functions, possibly because of its brevity and appearance in the popular Numerical Recipes library4 4432 Cautions: Scaling and Convergence One important source of dif culty in common optimization practice is scaling In unconstrained optimization, a problem is said to be poorly scaled if changes in one independent variable yield much larger variations in the function value than changes in another variable (Note that scaling resembles, but is not identical to, conditioning, which refers to the change in function value as all inputs change slightly See 2 for a discussion of conditioning.

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General considerations in adolescence include transition planning with options for continued residence with parents or a group home with other individuals who have PWS. Regardless of setting or age, individuals with PWS will need a structured environment with monitoring of eating behavior and weight balance to prevent morbid obesity. Because of the tendency for obsessive-compulsive behavior, it is suggested that schedules be very predictable and repetitive; change in the environment can precipitate behavioral problems (Medved & Percy, 2001). Coping skills and social skills present as problematic de cits for individuals with PWS, but no studies of interventions for these speci c skills with individuals with PWS were identi ed. There is some research to suggest that serotonin reuptake inhibitors or other medications, such as risperidone, may have indirect and positive effects on weight management by decreasing other problem behaviors (Medved & Percy, 2001).

) Scaling is often a result of differences in measurement scale across variables, although such differences are neither necessary nor suf cient for a problem to be poorly scaled A problem s scaling is affected by changing the measurement units of a variable Poor scaling results in two types of problems First, some algorithms, such as gradient-based descent methods, conjugate gradient methods, and trust region methods, are affected directly by scaling level Other algorithms, such as Newton and quasi-Newton algorithms (of which BFGS is a member) are not directly affected and are said to be scale-invariant, Second, even scale-invariant algorithms, however, are susceptible to rounding problems in their implementations, and the likelihood of rounding problems often becomes greater when problems are poorly scaled, since poor scaling can lead indirectly to the addition or subtraction of quantities of widely different magnitudes.

So, in practice, it is best to rescale poorly scaled problems even when using scale-invariant algorithms (Note that some software packages offer automatic rescaling as an optimization option Although potentially convenient, we suggest using the techniques described in 3 to gauge the reliability of the package when this option is enabled In the course of our testing of a variety of statistical packages, for example, we found cases, particularly in Microsoft Excel, in which the automatic scaling routines used in the program actually led to less accurate optimization results) Convergence criteria are another common source of dif culty in the use of optimization software We note some precautions here and discuss convergence criteria selection and convergence diagnostics in detail in 8 (See also 10 for examples of how a poor choice of stopping rule can cause false convergence, and thus incorrect estimates, in logistic regressions.

) Three precautions are warranted with respect to algorithm convergence First, software packages often offer convergence criteria that do not distinguish between lack of algorithmic progress (such as lack of change in the objective function) and true convergence (in which the gradients of the function are tested for.

13

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= 1+

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