Searching minimum
MathMate provides a procedure for extremum search (optimization).
This search is performed within a given interval. The extremum found is always a
local extremum, so if a function has several local extrema,
there is no guarantee that the least one will be found. However one
can reduce the interval and look for a better extremal value if desired.
Optimization can be performed in the Calculator mode or in the Optimization
mode. One possible way is described below.
To search for a minimum of an expression:
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Switch the Optimization mode on.
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Enter an expression, e.g. x^2
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Enter the interval ends
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If the expression contains several identifiers point out which one is to
be taken as the optimization variable and input the values of the other
parameters
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Click Start or press Enter
If MathMate detects only one parameter in the expression
which has not been assigned a value and no parameter is marked variable,
this parameter is taken as optimization variable. If all of the variables
are assigned some values, the expression is considered constant and the
result will be one of the ends of the interval. You may search the minimum of the same
expression again after having modified the optimization variable name, the search interval
or the parameter values.
Minimum is sought with the accuracy determined by the precision. The program always find
some local extremum if the expression is a well defined continuous function on the
search interval. The result of the search is a point at which the extremum is attained (up
to the given accuracy). The function value at the found point is also displayed. Note again
that this value provides a local minimum, not the global one. To look for a better minimum,
change the interval.
See also: