# 非线性规划

## 定义

nmp为正整数。令 XRn 的一个子集，令 fgihjX，对每个 i 属于 {1, …, m} 及每个 j 属于 {1, …, p}。

{\displaystyle {\begin{aligned}{\text{minimize }}&f(x)\\{\text{subject to }}&g_{i}(x)\leq 0{\text{ for each }}i\in \{1,\dotsc ,m\}\\&h_{j}(x)=0{\text{ for each }}j\in \{1,\dotsc ,p\}\\&x\in X.\end{aligned}}}

## 例子

x1 ≥ 0
x2 ≥ 0
x12 + x22 ≥ 1
x12 + x22 ≤ 2

f(x) = x1 + x2

### 3维实例

x12x22 + x32 ≤ 2
x12 + x22 + x32 ≤ 10

f(x) = x1x2 + x2x3

## 参考文献

1. ^ Bertsekas, Dimitri P. Nonlinear Programming Second. Cambridge, MA.: Athena Scientific. 1999. ISBN 1-886529-00-0.
2. ^ Ruszczyński, Andrzej. Nonlinear Optimization. Princeton, NJ: Princeton University Press. 2006: xii+454. ISBN 978-0691119151. MR 2199043.
3. ^ History matching production data and uncertainty assessment with an efficient TSVD parameterization algorithm, http://www.sciencedirect.com/science/article/pii/S0920410513003227
4. ^ Closed-loop field development under uncertainty using optimization with sample validation. http://dx.doi.org/10.2118/173219-PA