The sum of the squared entries in a vector or matrix.
sum_squares(expr)An Expression, vector, or matrix.
An Expression representing the sum of squares of the input.
set.seed(212)
m <- 30
n <- 20
A <- matrix(stats::rnorm(m*n), nrow = m, ncol = n)
b <- matrix(stats::rnorm(m), nrow = m, ncol = 1)
x <- Variable(n)
obj <- Minimize(sum_squares(A %*% x - b))
constr <- list(0 <= x, x <= 1)
prob <- Problem(obj, constr)
result <- solve(prob)
result$value
#> [1] 25.64897
result$getValue(x)
#> [,1]
#> [1,] 1.019360e-01
#> [2,] 1.414355e-01
#> [3,] -2.012287e-19
#> [4,] -4.393679e-19
#> [5,] 1.506072e-20
#> [6,] 5.633428e-20
#> [7,] -4.252601e-19
#> [8,] 2.212576e-01
#> [9,] 4.730655e-02
#> [10,] 4.641619e-02
#> [11,] 3.571723e-02
#> [12,] 2.292115e-01
#> [13,] -4.452617e-19
#> [14,] 8.158129e-21
#> [15,] 1.813679e-19
#> [16,] 2.612040e-01
#> [17,] -1.293152e-19
#> [18,] -3.681589e-19
#> [19,] 6.762751e-21
#> [20,] -2.353406e-19
result$getDualValue(constr[[1]])
#> [,1]
#> [1,] 0.0000000
#> [2,] 0.0000000
#> [3,] 12.8031354
#> [4,] 13.0734124
#> [5,] 9.6996644
#> [6,] 3.7263413
#> [7,] 11.2616650
#> [8,] 0.0000000
#> [9,] 0.0000000
#> [10,] 0.0000000
#> [11,] 0.0000000
#> [12,] 0.0000000
#> [13,] 6.0682997
#> [14,] 3.0700359
#> [15,] 0.6838339
#> [16,] 0.0000000
#> [17,] 5.7228351
#> [18,] 0.2429908
#> [19,] 6.9429350
#> [20,] 4.6553261