by numerical-methods.com

Optimization methods are required to find the value of x that minimises (or maximises) the function


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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