红色的符号是决策变量，蓝色的符号是常量.

Symbols in red are decision variables and symbols in blue are constants.

R代码:

> library(Rglpk)
> library(CVXR)
> 
> x <- c(1, 3, 6, 4, 7, 9, 6, 2, 3)
> n <- length(x)
> delta <- Variable(n, boolean=T)
> y <- Variable(2)
> order <- list()
> for (i in 2:n) {
+     order[[as.character(i)]] <- delta[i-1] <= delta[i]
+ }
> 
> 
> problem <- Problem(Minimize(abs(y[1]-y[2])),
+                    c(order,
+                      y[1] == t(1-delta) %*% x,
+                      y[2] == t(delta) %*%x))
> result <- solve(problem,solver = "GLPK", verbose=T)
GLPK Simplex Optimizer, v4.47
30 rows, 12 columns, 60 non-zeros
      0: obj =  0.000000000e+000  infeas = 4.100e+001 (2)
*     7: obj =  0.000000000e+000  infeas = 0.000e+000 (0)
*     8: obj =  0.000000000e+000  infeas = 0.000e+000 (0)
OPTIMAL SOLUTION FOUND
GLPK Integer Optimizer, v4.47
30 rows, 12 columns, 60 non-zeros
9 integer variables, none of which are binary
Integer optimization begins...
+     8: mip =     not found yet >=              -inf        (1; 0)
+     9: >>>>>  1.000000000e+000 >=  0.000000000e+000 100.0% (2; 0)
+     9: mip =  1.000000000e+000 >=     tree is empty   0.0% (0; 3)
INTEGER OPTIMAL SOLUTION FOUND
> result$getValue(delta)
      [,1]
 [1,]    0
 [2,]    0
 [3,]    0
 [4,]    0
 [5,]    0
 [6,]    1
 [7,]    1
 [8,]    1
 [9,]    1
> result$getValue(y)
     [,1]
[1,]   21
[2,]   20
> 

绝对值由CVXR自动线性化.

The absolute value is automatically linearized by CVXR.