没有合适的资源?快使用搜索试试~ 我知道了~
Lecture_slides for Convex Optimization_Stephen Boyd
需积分: 10 2 下载量 85 浏览量
2017-10-30
15:11:58
上传
评论
收藏 1.66MB PDF 举报
温馨提示
试读
298页
Lecture_slides for Convex Optimization_Stephen Boyd
资源推荐
资源详情
资源评论
Convex Optimization — Boyd & Vandenberghe
1. Introduction
• mathematical optimization
• least-squares and linear programming
• convex optimization
• example
• course goals and topics
• nonlinear optimization
• brief history of convex optimization
1–1
Mathematical optimization
(mathematical) optimization problem
minimize f
0
(x)
subject to f
i
(x) ≤ b
i
, i = 1, . . . , m
• x = (x
1
, . . . , x
n
): optimization variables
• f
0
: R
n
→ R: objective function
• f
i
: R
n
→ R, i = 1, . . . , m: constraint functions
optimal solution x
?
has smallest value of f
0
among all vectors that
satisfy the constraints
Introduction 1–2
Examples
portfolio optimization
• variables: amounts invested in different assets
• constraints: budget, max./min. investment per asset, minimum return
• objective: overall risk or return variance
device sizing in electronic circuits
• variables: device widths and lengths
• constraints: manufacturing limits, timing requirements, maximum area
• objective: power consumption
data fitting
• variables: model parameters
• constraints: prior information, parameter limits
• objective: measure of misfit or prediction error
Introduction 1–3
Solving optimization problems
general optimization problem
• very difficult to solve
• methods involve some compromise, e.g., very long computation time, or
not always finding the solution
exceptions: certain problem classes can be solved efficiently and reliably
• least-squares problems
• linear programming problems
• convex optimization problems
Introduction 1–4
Least-squares
minimize kAx − bk
2
2
solving least-squares problems
• analytical solution: x
?
= (A
T
A)
−1
A
T
b
• reliable and efficient algorithms and software
• computation time proportional to n
2
k (A ∈ R
k×n
); less if structured
• a mature technology
using least-squares
• least-squares problems are easy to recognize
• a few standard techniques increase flexibility (e.g., including weights,
adding regularization terms)
Introduction 1–5
剩余297页未读,继续阅读
资源评论
山而王王
- 粉丝: 10
- 资源: 6
上传资源 快速赚钱
- 我的内容管理 展开
- 我的资源 快来上传第一个资源
- 我的收益 登录查看自己的收益
- 我的积分 登录查看自己的积分
- 我的C币 登录后查看C币余额
- 我的收藏
- 我的下载
- 下载帮助
安全验证
文档复制为VIP权益,开通VIP直接复制
信息提交成功