CVXR 使用 Mosek 解决二次最小化问题
CVXR using Mosek for a quadratic minimization problem
我正在尝试使用 R 包 CVXR 解决具有线性约束的二次优化问题。尽管默认求解器能够求解优化，但 Mosek 求解器不能。我希望使用 Mosek 的原因是因为我需要解决一个具有超过 250 个约束的更大问题，而默认求解器给出了一个不准确的解决方案，因此我希望使用 Mosek 解决更大的问题。这是一个简单的例子，Mosek 没有工作：
suppressMessages(suppressWarnings(library(CVXR)))
问题数据
set.seed(10)
n <- 10
SAMPLES <- 100
mu <- matrix(abs(rnorm(n)), nrow = n)
Sigma <- matrix(rnorm(n^2), nrow = n, ncol = n)
Sigma <- t(Sigma) %*% Sigma
表格问题
w <- Variable(n)
ret <- t(mu) %*% w
risk <- quad_form(w, Sigma)
constraints <- list(w >= 0, sum(w) == 1,ret==mean(mu))
风险规避参数
prob <- Problem(Minimize(risk), constraints)
result <- solve(prob,solver='MOSEK')
它给出了以下错误。
Error in py_call_impl(callable, dots$args, dots$keywords) :
TypeError: 'int' object is not iterable
10.stop(structure(list(message = "TypeError: 'int' object is not iterable",
call = py_call_impl(callable, dots$args, dots$keywords),
cppstack = structure(list(file = "", line = -1L, stack = c("1 reticulate.so 0x000000010d278f9b _ZN4Rcpp9exceptionC2EPKcb + 219",
"2 reticulate.so 0x000000010d27fa35 _ZN4Rcpp4stopERKNSt3__112basic_stringIcNS0_11char_traitsIcEENS0_9allocatorIcEEEE + 53", ...
9.mosek_intf at mosekglue.py#51
8.get_mosekglue()$mosek_intf(reticulate::r_to_py(A), b, reticulate::r_to_py(G),
h, c, dims, offset, reticulate::dict(solver_opts), verbose)
7.Solver.solve(solver, objective, constraints, object@.cached_data,
warm_start, verbose, ...)
6.Solver.solve(solver, objective, constraints, object@.cached_data,
warm_start, verbose, ...)
5.CVXR::psolve(a, b, ...)
4.CVXR::psolve(a, b, ...)
3.solve.Problem(prob, solver = "MOSEK")
2.solve(prob, solver = "MOSEK")
1.solve(prob, solver = "MOSEK")
有人知道怎么解决，可能是重新表达问题？
我的会话信息如下：
R version 3.5.2 (2018-12-20)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Mojave 10.14.1
Matrix products: default
BLAS: /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] reticulate_1.10 Matrix_1.2-15 CVXR_0.99-2 e1071_1.7-0.1 rstudioapi_0.9.0
[6] openxlsx_4.1.0
loaded via a namespace (and not attached):
[1] Rcpp_1.0.0 lattice_0.20-38 class_7.3-14 gmp_0.5-13.2 R.methodsS3_1.7.1
[6] grid_3.5.2 R6_2.3.0 jsonlite_1.6 zip_1.0.0 Rmpfr_0.7-2
[11] R.oo_1.22.0 R.utils_2.7.0 tools_3.5.2 bit64_0.9-7 bit_1.1-14
[16] compiler_3.5.2 scs_1.1-1 ECOSolveR_0.4
谢谢
Python错误
TypeError: 'int' object is not iterable'
表示在mosekglue.py expected a list to iterate over (somewhere unspecified), but received a scalar. This might be caused by the fact that -- since everything is a list in R -- reticulate handles single-element and multi-element lists different (see its type conversions中调用了mosek_intf）。
只阅读了源代码，我最好的猜测是 mosekglue.py (line 102) 失败了，因为你的问题只有一个二阶锥（具体来说，我相信网状发送 dims=dict(q: n) 而不是dims=dict(q: [n]))。
您的选择是在 GitHub 上向 CVXR 项目提交错误报告并等待，and/or 确认我的怀疑（甚至可能提出修复并将其贡献给项目）， and/or 用虚拟 material 修改你的问题，直到它通过界面。
这确实是 mosekglue.py 中的一个问题，已在 CVXR-0.99-3 及更高版本中解决；见 changelog
这是你的例子：
> suppressMessages(suppressWarnings(library(CVXR)))
> set.seed(10)
> n <- 10
> SAMPLES <- 100
> mu <- matrix(abs(rnorm(n)), nrow = n)
> Sigma <- matrix(rnorm(n^2), nrow = n, ncol = n)
> Sigma <- t(Sigma) %*% Sigma
> w <- Variable(n)
> ret <- t(mu) %*% w
> risk <- quad_form(w, Sigma)
> constraints <- list(w >= 0, sum(w) == 1,ret==mean(mu))
> prob <- Problem(Minimize(risk), constraints)
> result <- solve(prob,solver='MOSEK', verbose=TRUE)
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 24
Cones : 1
Scalar variables : 23
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator - tries : 0 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 24
Cones : 1
Scalar variables : 23
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 13
Optimizer - Cones : 1
Optimizer - Scalar variables : 22 conic : 12
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 89 after factor : 91
Factor - dense dim. : 0 flops : 2.54e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 6.9e+00 1.0e+00 0.00e+00 2.756709152e+01 2.756709152e+01 1.0e+00 0.00
1 2.7e-01 1.8e+00 2.2e-01 -6.02e-01 -9.936262607e+00 4.762263760e+00 2.7e-01 0.00
2 9.9e-02 6.8e-01 4.3e-01 1.23e+00 9.201188225e-01 -6.807855573e-01 9.9e-02 0.00
3 3.6e-02 2.5e-01 4.4e-01 1.97e+00 -1.264256365e-01 -5.225584219e-01 3.6e-02 0.00
4 9.2e-03 6.3e-02 1.8e-01 2.33e+00 2.868592743e-01 2.542157558e-01 9.2e-03 0.00
5 2.0e-03 1.4e-02 8.8e-02 1.17e+00 2.840102253e-01 2.769232377e-01 2.0e-03 0.00
6 3.7e-04 2.5e-03 3.9e-02 1.04e+00 2.879204145e-01 2.866174921e-01 3.7e-04 0.00
7 6.3e-05 4.3e-04 1.6e-02 1.02e+00 2.901039465e-01 2.898751147e-01 6.3e-05 0.00
8 1.3e-05 8.8e-05 7.4e-03 1.00e+00 2.902381000e-01 2.901914751e-01 1.3e-05 0.00
9 3.6e-06 2.5e-05 4.0e-03 1.00e+00 2.902501323e-01 2.902366424e-01 3.6e-06 0.00
10 1.1e-06 7.4e-06 2.2e-03 1.00e+00 2.902666158e-01 2.902625442e-01 1.1e-06 0.00
11 3.6e-07 2.5e-06 1.3e-03 1.00e+00 2.902689540e-01 2.902675850e-01 3.6e-07 0.00
12 5.7e-08 3.9e-07 5.1e-04 1.00e+00 2.902716546e-01 2.902714343e-01 5.7e-08 0.00
13 6.6e-09 4.6e-08 1.7e-04 1.00e+00 2.902720234e-01 2.902719974e-01 6.6e-09 0.00
Optimizer terminated. Time: 0.00
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 2.9027202344e-01 nrm: 1e+00 Viol. con: 6e-09 var: 0e+00 cones: 0e+00
Dual. obj: 2.9027199740e-01 nrm: 1e+01 Viol. con: 0e+00 var: 8e-08 cones: 0e+00
> result$value
[1] 0.290272
>
我正在尝试使用 R 包 CVXR 解决具有线性约束的二次优化问题。尽管默认求解器能够求解优化，但 Mosek 求解器不能。我希望使用 Mosek 的原因是因为我需要解决一个具有超过 250 个约束的更大问题，而默认求解器给出了一个不准确的解决方案，因此我希望使用 Mosek 解决更大的问题。这是一个简单的例子，Mosek 没有工作：
suppressMessages(suppressWarnings(library(CVXR)))
问题数据
set.seed(10)
n <- 10
SAMPLES <- 100
mu <- matrix(abs(rnorm(n)), nrow = n)
Sigma <- matrix(rnorm(n^2), nrow = n, ncol = n)
Sigma <- t(Sigma) %*% Sigma
表格问题
w <- Variable(n)
ret <- t(mu) %*% w
risk <- quad_form(w, Sigma)
constraints <- list(w >= 0, sum(w) == 1,ret==mean(mu))
风险规避参数
prob <- Problem(Minimize(risk), constraints)
result <- solve(prob,solver='MOSEK')
它给出了以下错误。
Error in py_call_impl(callable, dots$args, dots$keywords) :
TypeError: 'int' object is not iterable
10.stop(structure(list(message = "TypeError: 'int' object is not iterable",
call = py_call_impl(callable, dots$args, dots$keywords),
cppstack = structure(list(file = "", line = -1L, stack = c("1 reticulate.so 0x000000010d278f9b _ZN4Rcpp9exceptionC2EPKcb + 219",
"2 reticulate.so 0x000000010d27fa35 _ZN4Rcpp4stopERKNSt3__112basic_stringIcNS0_11char_traitsIcEENS0_9allocatorIcEEEE + 53", ...
9.mosek_intf at mosekglue.py#51
8.get_mosekglue()$mosek_intf(reticulate::r_to_py(A), b, reticulate::r_to_py(G),
h, c, dims, offset, reticulate::dict(solver_opts), verbose)
7.Solver.solve(solver, objective, constraints, object@.cached_data,
warm_start, verbose, ...)
6.Solver.solve(solver, objective, constraints, object@.cached_data,
warm_start, verbose, ...)
5.CVXR::psolve(a, b, ...)
4.CVXR::psolve(a, b, ...)
3.solve.Problem(prob, solver = "MOSEK")
2.solve(prob, solver = "MOSEK")
1.solve(prob, solver = "MOSEK")
有人知道怎么解决，可能是重新表达问题？
我的会话信息如下：
R version 3.5.2 (2018-12-20)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Mojave 10.14.1
Matrix products: default
BLAS: /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] reticulate_1.10 Matrix_1.2-15 CVXR_0.99-2 e1071_1.7-0.1 rstudioapi_0.9.0
[6] openxlsx_4.1.0
loaded via a namespace (and not attached):
[1] Rcpp_1.0.0 lattice_0.20-38 class_7.3-14 gmp_0.5-13.2 R.methodsS3_1.7.1
[6] grid_3.5.2 R6_2.3.0 jsonlite_1.6 zip_1.0.0 Rmpfr_0.7-2
[11] R.oo_1.22.0 R.utils_2.7.0 tools_3.5.2 bit64_0.9-7 bit_1.1-14
[16] compiler_3.5.2 scs_1.1-1 ECOSolveR_0.4
谢谢
Python错误
TypeError: 'int' object is not iterable'
表示在mosekglue.py expected a list to iterate over (somewhere unspecified), but received a scalar. This might be caused by the fact that -- since everything is a list in R -- reticulate handles single-element and multi-element lists different (see its type conversions中调用了mosek_intf）。
只阅读了源代码，我最好的猜测是 mosekglue.py (line 102) 失败了，因为你的问题只有一个二阶锥（具体来说，我相信网状发送 dims=dict(q: n) 而不是dims=dict(q: [n]))。
您的选择是在 GitHub 上向 CVXR 项目提交错误报告并等待，and/or 确认我的怀疑（甚至可能提出修复并将其贡献给项目）， and/or 用虚拟 material 修改你的问题，直到它通过界面。
这确实是 mosekglue.py 中的一个问题，已在 CVXR-0.99-3 及更高版本中解决；见 changelog
这是你的例子：
> suppressMessages(suppressWarnings(library(CVXR)))
> set.seed(10)
> n <- 10
> SAMPLES <- 100
> mu <- matrix(abs(rnorm(n)), nrow = n)
> Sigma <- matrix(rnorm(n^2), nrow = n, ncol = n)
> Sigma <- t(Sigma) %*% Sigma
> w <- Variable(n)
> ret <- t(mu) %*% w
> risk <- quad_form(w, Sigma)
> constraints <- list(w >= 0, sum(w) == 1,ret==mean(mu))
> prob <- Problem(Minimize(risk), constraints)
> result <- solve(prob,solver='MOSEK', verbose=TRUE)
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 24
Cones : 1
Scalar variables : 23
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator - tries : 0 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 24
Cones : 1
Scalar variables : 23
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 13
Optimizer - Cones : 1
Optimizer - Scalar variables : 22 conic : 12
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 89 after factor : 91
Factor - dense dim. : 0 flops : 2.54e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 6.9e+00 1.0e+00 0.00e+00 2.756709152e+01 2.756709152e+01 1.0e+00 0.00
1 2.7e-01 1.8e+00 2.2e-01 -6.02e-01 -9.936262607e+00 4.762263760e+00 2.7e-01 0.00
2 9.9e-02 6.8e-01 4.3e-01 1.23e+00 9.201188225e-01 -6.807855573e-01 9.9e-02 0.00
3 3.6e-02 2.5e-01 4.4e-01 1.97e+00 -1.264256365e-01 -5.225584219e-01 3.6e-02 0.00
4 9.2e-03 6.3e-02 1.8e-01 2.33e+00 2.868592743e-01 2.542157558e-01 9.2e-03 0.00
5 2.0e-03 1.4e-02 8.8e-02 1.17e+00 2.840102253e-01 2.769232377e-01 2.0e-03 0.00
6 3.7e-04 2.5e-03 3.9e-02 1.04e+00 2.879204145e-01 2.866174921e-01 3.7e-04 0.00
7 6.3e-05 4.3e-04 1.6e-02 1.02e+00 2.901039465e-01 2.898751147e-01 6.3e-05 0.00
8 1.3e-05 8.8e-05 7.4e-03 1.00e+00 2.902381000e-01 2.901914751e-01 1.3e-05 0.00
9 3.6e-06 2.5e-05 4.0e-03 1.00e+00 2.902501323e-01 2.902366424e-01 3.6e-06 0.00
10 1.1e-06 7.4e-06 2.2e-03 1.00e+00 2.902666158e-01 2.902625442e-01 1.1e-06 0.00
11 3.6e-07 2.5e-06 1.3e-03 1.00e+00 2.902689540e-01 2.902675850e-01 3.6e-07 0.00
12 5.7e-08 3.9e-07 5.1e-04 1.00e+00 2.902716546e-01 2.902714343e-01 5.7e-08 0.00
13 6.6e-09 4.6e-08 1.7e-04 1.00e+00 2.902720234e-01 2.902719974e-01 6.6e-09 0.00
Optimizer terminated. Time: 0.00
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 2.9027202344e-01 nrm: 1e+00 Viol. con: 6e-09 var: 0e+00 cones: 0e+00
Dual. obj: 2.9027199740e-01 nrm: 1e+01 Viol. con: 0e+00 var: 8e-08 cones: 0e+00
> result$value
[1] 0.290272
>