Symbolic Global Optimization

The new functions Maximize and Minimize find the exact global maximum or minimum for a function over a region. They work with a wide range of inputs including transcendental functions, inequalities, fields, and all polynomials.

Example: Basic Uses

Here Maximize shows that the rectangle with the maximal area for a given circumference is a square.

This finds the minimum subject to the constraint x ≥ 3.

Maximize and Minimize can also solve polynomial programming problems in which the objective function and the constraints involve arbitrary polynomial functions of the variables. Many important geometric and other problems can be formulated in this way.

This finds the maximal volume of a cuboid that fits inside the unit sphere.

Maximize and Minimize normally assume that all variables you give are real. However, by giving a constraint such as , you can specify that a variable must in fact be an integer. This does minimization only over integer values of x and y.

		Documentation from The Mathematica Book Advaced Topic: Optimization
		Documentation from the Reference Guide Maximize Minimize