Minimize

Minimize[f, x, y, ... ] minimizes f with respect to x, y, ... .

Minimize[f, cons, x, y, ... ] minimizes f subject to the constraints cons.

Minimize returns a list of the form , x -> , y -> , ... .

cons can contain equations, inequalities or logical combinations of these.

If f and cons are linear or polynomial, Minimize will always find a global minimum.

Minimize will return exact results if given exact input.

If the minimum is achieved only infinitesimally outside the region defined by the constraints, or only asymptotically, Minimize will return the infimum and the closest specifiable point.

By default, all variables are assumed to be real.

x Integers can be used to specify that a variable can take on only integer values.

If the constraints cannot be satisfied, Minimize returns +Infinity, x -> Indeterminate, ... .

Even if the same minimum is achieved at several points, only one is returned.

See Section 1.5.8 and Section 3.4.12.

Implementation Notes: see Section A.9.5.

See also: Maximize, NMinimize, FindMinimum, Min, D, FindInstance, LinearProgramming.

New in Version 5.0.

Further Examples