Using NLOPT/Gurobi for solving mixed constraint optimization - r

Question

I am currently working on a project, and I want to use R and NLOPT package (or Gurobi) to solve the following optimization problem:
Find min ||y-y_h||_L^2 such that x = Ay_h, y >= 0, where x, y are given vector of size 16*1, A = 16*24 matrix is also given.
My attempt:
R code
nrow=16;
ncol = 24;
lambda = matrix(sample.int(100, size = ncol*nrow, replace = T),nrow,ncol);
lambda = lambda - diag(lambda)*diag(x=1, nrow, ncol);
y = rpois(ncol,lambda) + rtruncnorm(ncol,0,1,mean = 0, sd = 1);
x = matrix (0, nrow, 1);
x_A1 = y[1]+y[2]+y[3];
x_A2 = y[4]+y[7]+y[3];
x_B1 = y[4]+y[5]+y[6];
x_B2 = y[11]+y[1];
x_C1 = y[7]+y[8]+y[9];
x_C2 = y[2]+y[5]+y[12];
x_D1 = y[10]+y[11]+y[12];
x_D2 = y[3]+y[6]+y[9];
x_E1 = y[13]+y[14]+y[15];
x_E2 = y[18]+y[19]+y[23];
x_F1 = y[20]+y[21]+y[19];
x_F2 = y[22]+y[16]+y[13];
x_G1 = y[23]+y[22]+y[24];
x_G2 = y[14]+y[17]+y[20];
x_H1 = y[16]+y[17]+y[18];
x_H2 = y[15]+y[21]+y[24];
d <- c(x_A1, x_A2,x_B1, x_B2,x_C1, x_C2,x_D1, x_D2,x_E1,
x_E2,x_F1, x_F2,x_G1, x_G2,x_H1, x_H2)
x <- matrix(d, nrow, byrow=TRUE)
A = matrix(c(1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_A^1
0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_A^2
0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_B^1
1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_B^2
0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_C^1
0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0, #x_C^2
0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0, #x_D^1
0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_D^2
0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0, #x_E^1
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0, #x_E^2
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0, #x_F^1
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0, #x_F^2
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0, #x_G^2
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1, #x_G^1
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0, #x_H^1
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1), #x_H^2
nrow, ncol, byrow= TRUE)
Tried two codes to solve the problem: min ||y - y_h||_L^2 where x= Ay_h, y>=0 where x,y,A are all given above.
# f(x) = ||yhat-y||_L2
eval_f <- function( yhat ) {
return( list( "objective" = norm((mean(yhat-y))^2, type = "2")))
}
# inequality constraint
eval_g_ineq <- function( yhat ) {
constr <- c(0 - yhat)
return( list( "constraints"=constr ))
}
# equalities constraint
eval_g_eq <- function( yhat ) {
constr <- c( x-A%*%yhat )
return( list( "constraints"=constr ))
}
x0 <- y
#lower bound of control variable
lb <- c(matrix (0, ncol, 1))
local_opts <- list( "algorithm" = "NLOPT_LD_MMA",
"xtol_rel" = 1.0e-7 )
opts <- list( "algorithm" = "NLOPT_LD_AUGLAG",
"xtol_rel" = 1.0e-7,
"maxeval" = 1000,
"local_opts" = local_opts )
res <- nloptr( x0=x0,
eval_f=eval_f,
eval_grad_f = NULL,
lb=lb,
eval_g_ineq = eval_g_ineq,
eval_g_eq=eval_g_eq,
opts=opts)
print(res)
Gurobi code:
**#model <- list()
#model$B <- A
#model$obj <- norm((y-yhat)^2, type = "2")
#model$modelsense <- "min"
#model$rhs <- c(x,0)
#model$sense <- c('=', '>=')
#model$vtype <- 'C'
#result <- gurobi(model, params)
#print('Solution:')
#print(result$objval)
#print(result$yhat)**
My question: First, when I ran the R code above, it kept giving me this message:
Error in is.nloptr(ret) :
wrong number of elements in gradient of objective
In addition: Warning message:
In is.na(f0$gradient) :
is.na() applied to non-(list or vector) of type 'NULL'
I tried to avoid computing gradient, as I do not have any information on the density function of y. Could anyone please help me fix the error above?
For the Gurobi code, I got this message: Error: is(model$A, "matrix") || is(model$A, "sparseMatrix") || is(model$A, .... is not TRUE
But my matrix A is correctly inputted, so what does this error mean?

Answer 1

I start to use nloptr only several days ago. This question is already an old one but I will still answer it. when you are using 'nloptr' with 'NLOPT_LD_AUGLAG' algorithm, the 'LD' stands for local and using gradient... So you need to choose something else with 'LN' in the middle. For ex., 'NLOPT_LN_COBYLA' should work fine without gradient.
Actually you can just look up the nloptr package manual.