In mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions.
Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: The standard form of a continuous optimization problem is[1]
By convention, the standard form defines a minimization problem.
A maximization problem can be treated by negating the objective function.
Formally, a combinatorial optimization problem A is a quadruple[citation needed] (I, f, m, g), where The goal is then to find for some instance x an optimal solution, that is, a feasible solution y with
For example, if there is a graph G which contains vertices u and v, an optimization problem might be "find a path from u to v that uses the fewest edges".
The usual decision version is then an inadequate definition of the problem since it only specifies acceptable solutions.