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Problem Scaling



It may happen that a user's problem uses variables or general constraints  whose normal numerical values are wildly different in magnitude. This poor scaling can cause difficulties for LANCELOT. As a precaution, the user may ask that the problem be (implicitly) rescaled before the optimization commences. The scaling algorithm used is not foolproof and should only really be used if the user encounters difficulties when solving the problem unscaled. It is frequently far better for the user to rescale his or her problem him or herself, so that all the variables have roughly the same value at a ``typical point''; the same advice hold for constraint functions. 

LANCELOT's scaling algorithm is invoked by the GET-SCALING-FACTORS keyword. This produces appropriate scale factors. These values may be printed by specifying the PRINT-SCALING-FACTORS keyword and are applied to the problem during the optimization when USE-SCALING-FACTORS is specified. The scale factors are applied to the general constraints  and variables separately when the USE-CONSTRAINT-SCALING-FACTORS and USE-VARIABLE-SCALING-FACTORS keywords are, respectively, included. The default is that no scaling is performed.