凸优化工具箱cvx

神器CVX

一款免费的计算凸优化问题的工具箱，听说炒鸡好用，有木有？今天安装成功，按耐不住激动的心情，记录下一次成功安装步骤：

首先下载CVX：CVX网站首页可供软件下载

对照自己的机型，下载好放到MATLAB目录，注意不能放在原MATLAB->toolbox中。本人放在BIN文件夹下

解压缩

解压缩后，发现文件里有个read me 。英文不太好，没有完全看懂，但大概知道，如果想好好利用CVX工具箱还需要一把“钥匙”——license 文件。于是，并没有着急安装，网上搜了一堆CVX有关的资料，并没有发现有现成的license，然后乖乖按照read me中的网址找到了注册地址，软件是免费注册的，但是有区分学术型还是商业型，而且，只能用学校邮箱注册学术型（即后面是学校邮箱后缀的），注册后，邮箱自动接收一封邮件，附件即是license.dat。邮件内容如下：

Thank you for registering for a CVX license. Your license key is attached.

To install the license, follow these steps:

1) Make sure you have fully installed the latest version of CVX: http://cvxr.com/download

The attached license key works only with Build 883 or later of CVX 2.0.

If you receive strange errors during installation, this is a sign that

you need to update your CVX installation first.

2) Save the attached file ‘cvx_license.dat’ to a convenient location on

your hard drive.

3) At the MATLAB command line, run “cvx_setup” again, but add the full

path to your license file as an argument:

cvx_setup /path/to/license/file/cvx_license.dat

4) Once the license is installed, you are free to delete the file or move

it to a different location—CVX creates its own copy of the contents.

Full installation instructions can be found here:

http://cvxr.com/cvx/doc/install.html

If for some reason the license installation fails, please submit a bug

report at our help desk:

http://support.cvxr.com/

Please included the full output of the cvx_setup command in your report.

If, in the future, you need us to re-send your license key, or you need to

add a new host ID to your license, just visit the academic license page:

http://cvxr.com/cvx/academic

Thank you again for your interest in CVX!

Regards,

CVX Research, Inc.

http://cvxr.com

P.S. Please join The CVX Forum, our community Q&A site! If you are new to

CVX, you can search the question database, or add your own if it hasn’t yet

been asked. If you are a CVX expert, you can help your fellow users and earn

karma points in the process.

http://ask.cvxr.com

最后，把license.dat添加到解压缩的cvx文件夹下，开启MATLAB，运行cvx_setup。

CVX: Software for Disciplined Convex Programming (c)2014 CVX Research

Version 3.0beta, Build 1175 (1326ef2) Mon Nov 23 14:29:34 2015

Installation info:

Status: VERIFIED

Setting CVX paths…Warning: Duplicate directory name: G:\Program

Files\MATLAB\bin\work\cvx\builtins

In path (line 33)

In cvx_startup (line 128)

In cvx_setup (line 42)

Warning: Duplicate directory name: G:\Program

Files\MATLAB\bin\work\cvx\commands

In path (line 33)

In cvx_startup (line 128)

In cvx_setup (line 42)

Warning: Duplicate directory name: G:\Program

Files\MATLAB\bin\work\cvx\functions

In path (line 33)

In cvx_startup (line 128)

In cvx_setup (line 42)

Warning: Duplicate directory name: G:\Program

Files\MATLAB\bin\work\cvx\lib

In path (line 33)

In cvx_startup (line 128)

In cvx_setup (line 42)

Warning: Duplicate directory name: G:\Program

Files\MATLAB\bin\work\cvx\structures

In path (line 33)

In cvx_startup (line 128)

In cvx_setup (line 42)

Warning: Duplicate directory name: G:\Program

Files\MATLAB\bin\work\cvx\functions\vec_

In path (line 33)

In cvx_startup (line 128)

In cvx_setup (line 42)

Warning: Duplicate directory name: G:\Program

Files\MATLAB\bin\work\cvx

In path (line 33)

In cvx_startup (line 128)

In cvx_setup (line 42)

done.

Saving update path…done.

Searching for solvers…7 shims found.

3 solvers initialized (* = default):

Mosek 7.1.0.12 {cvx}\mosek\w64

* SDPT3 4.0 {cvx}\sdpt3

SeDuMi 1.34 {cvx}\sedumi

3 solvers not found:

ECOS https://github.com/ifa-ethz/ecos

GLPK http://glpkmex.sourceforge.net/

SCS https://github.com/cvxgrp/scs

1 solver skipped due to other errors:

Gurobi {cvx}\gurobi\w64

No valid Gurobi license was found. (Please note that this

license is not the same as the CVX license; it must be

obtained directly from Gurobi Optimization.) If you do have

a Gurobi license, the the Gurobi MEX file could not find it.

Please consult the Gurobi documentation for assistance.

Saving updated preferences…done.

Testing with a simple model…Warning: Duplicate directory name: G:\Program

Files\MATLAB\bin\work\cvx\sdpt3

In path (line 33)

In cvx_setspath (line 41)

In cvx_solve (line 112)

In cvx_finish (line 57)

In cvx_end (line 11)

In cvx_setup (line 262)

Warning: Duplicate directory name: G:\Program

Files\MATLAB\bin\work\cvx\sdpt3\HSDSolver

In path (line 33)

In cvx_setspath (line 41)

In cvx_solve (line 112)

In cvx_finish (line 57)

In cvx_end (line 11)

In cvx_setup (line 262)

Warning: Duplicate directory name: G:\Program

Files\MATLAB\bin\work\cvx\sdpt3\Solver

In path (line 33)

In cvx_setspath (line 41)

In cvx_solve (line 112)

In cvx_finish (line 57)

In cvx_end (line 11)

In cvx_setup (line 262)

Warning: Duplicate directory name: G:\Program

Files\MATLAB\bin\work\cvx\sdpt3\Solver\Mexfun

In path (line 33)

In cvx_setspath (line 41)

In cvx_solve (line 112)

In cvx_finish (line 57)

In cvx_end (line 11)

In cvx_setup (line 262)

done!

To change the default solver, type “cvx_solver ”.

To save this change for future sessions, type “cvx_save_prefs”.

Please consult the users’ guide for more information.

WARNING: An existing copy of “square.m” was found in your MATLAB path:

G:\Program Files\MATLAB\toolbox\signal\signal\square.m

Models using SQUARE() in CVX expressions will not be affected; but outside

of CVX, this version will be used, and it likely has a different meaning.

To avoid any confusion, just use X.^2 instead of SQUARE(X) in CVX.

虽然这么多warning，但本着能用就行，不能用再说的心态，找了段代码测试：

m = 16;n = 8;

A = randn(m,n);

b = randn(m,1);

x_ls = A\b;

cvx_begin

variable x(n)

minimize(norm(A*x-b))

cvx_end

Calling SDPT3 4.0: 17 variables, 9 equality constraints

For improved efficiency, SDPT3 is solving the dual problem.

num. of constraints = 9

dim. of socp var = 17, num. of socp blk = 1

SDPT3: Infeasible path-following algorithms

version predcorr gam expon scale_data

NT 1 0.000 1 0

it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime

0|0.000|0.000|1.6e+00|1.5e+00|2.3e+01| 0.000000e+00 0.000000e+00| 0:0:00| chol 1 1

1|0.966|1.000|5.4e-02|2.3e-02|2.4e+00|-2.828286e+00 -4.600017e+00| 0:0:00| chol 1 1

2|1.000|0.984|5.7e-08|3.6e-03|4.6e-02|-2.847732e+00 -2.878229e+00| 0:0:00| chol 1 1

3|0.989|0.989|7.0e-09|2.7e-04|5.3e-04|-2.871110e+00 -2.870469e+00| 0:0:00| chol 1 1

4|0.989|0.989|2.2e-08|3.0e-06|5.8e-06|-2.871376e+00 -2.871369e+00| 0:0:00| chol 1 1

5|0.990|0.990|2.3e-10|3.2e-08|7.0e-08|-2.871379e+00 -2.871379e+00| 0:0:00| chol 1 1

6|0.990|0.990|2.5e-12|3.5e-10|8.5e-10|-2.871379e+00 -2.871379e+00| 0:0:00|

stop: max(relative gap, infeasibilities) < 1.49e-08

number of iterations = 6

primal objective value = -2.87137926e+00

dual objective value = -2.87137926e+00

gap := trace(XZ) = 8.45e-10

relative gap = 1.25e-10

actual relative gap = -1.02e-10

rel. primal infeas (scaled problem) = 2.49e-12

rel. dual ” ” ” = 3.51e-10

rel. primal infeas (unscaled problem) = 0.00e+00

rel. dual ” ” ” = 0.00e+00

norm(X), norm(y), norm(Z) = 1.4e+00, 2.9e+00, 4.1e+00

norm(A), norm(b), norm(C) = 1.2e+01, 2.0e+00, 4.3e+00

Total CPU time (secs) = 0.23

CPU time per iteration = 0.04

termination code = 0

DIMACS: 2.5e-12 0.0e+00 5.7e-10 0.0e+00 -1.0e-10 1.3e-10

Status: Solved

Optimal value (cvx_optval): +2.87138

虽然不太明白是什么鬼，但是至少直接计算出来的x_ls和凸优化方法计算的x的结果是一样的。

剩下的，以后再研究。

DONE!