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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 | )abbrev category OPTCAT NumericalOptimizationCategory
++ Author: Brian Dupee
++ Date Created: January 1996
++ Date Last Updated: March 1996
++ Description:
++ \axiomType{NumericalOptimizationCategory} is the \axiom{category} for
++ describing the set of Numerical Optimization \axiom{domains} with
++ \axiomFun{measure} and \axiomFun{optimize}.
NumericalOptimizationCategory() : Category == SIG where
LDFH ==> List DoubleFloat
LEDFH ==> List Expression DoubleFloat
LSAH ==> Record(lfn:LEDFH, init:LDFH)
EDFH ==> Expression DoubleFloat
LOCDFH ==> List OrderedCompletion DoubleFloat
NOAH ==> Record(fn:EDFH, init:LDFH, lb:LOCDFH, cf:LEDFH, ub:LOCDFH)
SIG ==> SetCategory with
measure : (RoutinesTable,NOAH) -> Record(measure:Float,explanations:String)
++ measure(R,args) calculates an estimate of the ability of a particular
++ method to solve an optimization problem.
++
++ This method may be either a specific NAG routine or a strategy (such
++ as transforming the function from one which is difficult to one which
++ is easier to solve).
++
++ It will call whichever agents are needed to perform analysis on the
++ problem in order to calculate the measure. There is a parameter,
++ labelled \axiom{sofar}, which would contain the best compatibility
++ found so far.
measure : (RoutinesTable,LSAH) -> Record(measure:Float,explanations:String)
++ measure(R,args) calculates an estimate of the ability of a particular
++ method to solve an optimization problem.
++
++ This method may be either a specific NAG routine or a strategy (such
++ as transforming the function from one which is difficult to one which
++ is easier to solve).
++
++ It will call whichever agents are needed to perform analysis on the
++ problem in order to calculate the measure. There is a parameter,
++ labelled \axiom{sofar}, which would contain the best compatibility
++ found so far.
numericalOptimization : LSAH -> Result
++ numericalOptimization(args) performs the optimization of the
++ function given the strategy or method returned by \axiomFun{measure}.
numericalOptimization : NOAH -> Result
++ numericalOptimization(args) performs the optimization of the
++ function given the strategy or method returned by \axiomFun{measure}.
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