minimize

Format: minimize( f(x), x, x1, x2, x3 )

Arguments: (real) f(x) Function or expression to be minimized

(node) x Name of the input variable in f(x)

(real) x1 Initial guess for the value of x or lower limit on x

(real) x2 Optional central guess for x

(real) x3 Optional upper limit on x

Returns: (real) The value of x where f(x) is minimized

Description: Minimize finds the value of x such that f(x) is locally minimized. You must supply minimize with either a single point guess for the value of x or a set of three points that define the specific minimum you seek to isolate. Minimize uses different methods to find the value of x depending on which of these starting methods you provide. If you provide values for x1, x2 and x3, these points must meet the following conditions: f(x1) > f(x2) and f(x3) > f(x2) and x1 < x2 < x3. If these conditions are met, minimize will always find a solution. If you provide a value for x1 only, minimize will search for a solution. If minimize fails to converge on a solution, try another value for x1.

To maximize a function, simply multiply it by -1 and use the minimize primitive. E.g., minimize(-f(x),x,x1).

Minimize is an approximated function and is subject to the tolerance set by precision. Minimize creates a temporary variable named x. If a node with this name already exists, it is replaced for all evaluations of f(x) and is then restored to its original state.

Note: If the expression f(x) is a tree node rather than a function based on x, the reset primitive must be used to cause the tree to recalculate on each iteration. Constants retain their value from the first evaluation and return this value on all subsequent evaluations. To cause the constant to be reevaluated, use an expression similar to

minimize({reset,f},x,x1,x2)

rather than

minimize(f,x,x1,x2))

Examples: minimize((x-5)^2,x,0) = 5

See Also: precision, simplex, solve