最优化，是应用数学的一个分支，主要研究以下形式的问题：

主要研究以下形式的问题：

这类定式有时还称为“数学规划”（譬如，线性规划）。许多现实和理论问题都可以建模成这样的一般性框架。

典型的，一般为欧几里得空间中的子集，通常由一个必须满足的约束等式或者不等式来规定。 的元素被称为是可行解。函数被称为目标函数，或者代价函数。一个最小化（或者最大化）目标函数的可行解被称为最优解。

一般情况下，会存在若干个局部的极小值或者极大值。局部极小值定义为对于一些，以及所有的 满足

In mathematics, computer science and operations research, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.

In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains.