Concept

# Optimization problem

Summary
In mathematics, 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:
• An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.
• A problem with continuous variables is known as a continuous optimization, in which an optimal value from a continuous function must be found. They can include constrained problems and multimodal problems.
Continuous optimization problem The standard form of a continuous optimization problem is \begin{align} &\underset{x}{\operatorname{minimize}}& & f(x) \ &\operatorname{subject;to} & &g_i(x) \leq 0, \quad i = 1,\dots,m \ &&&h_j(x) = 0, \quad j = 1, \dots,p \end{align} where
• f : ℝn → ℝ is the ob
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