where f may be a function of any number of variables. (Note that the minimisation of f(x) is equivalent to the maximisation of -f(x)).

Clearly f(x) may have several local minima, it is often satisfactory to search for a local minimum; the problem of finding global optima is more difficult.

Unconstrained and Constrained Optimization

For the purposes of describing unconstrained and
constrained optimization let us ussume that
we wish to minimise f(x,y), a function of two variables.
If the solution is sought only in a region of the
x-y plane then the problem is termed
one of constrained optimization. If there
is no restriction on the solution (x,y)
then the problem is said to be one of
unconstrained optimization.

Linear and Non-linear programming

If f(x,y) = ax+by (or similar for equations of
more variables) then the f is said to be linear.
If the constraints are also linear (straight
lines in 2-variable problems) then
the problem is one of linear programming.

Non-linear programming is another name for constrained optimisation where f and/or the variables are non-linear.

Books on the methods described above are listed in www.science-books.net . Click on the topic of interest below.

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