Absolute value of matrix

Specific Domains Optimization (Mathematical)
1

How to define the absolute value of all elements in the matrix?

using JuMP,Gurobi




 model = Model(Gurobi.Optimizer);
model=Model(Gurobi.Optimizer)
T=24
 @variable(model, 2 <= a[1:T,1:3]<= 2.5, Int)
@variable(model,-1<=PMT[1:T,1:3]<=20)
@variable(model,0<=WES_BT[1:T,1:3]<=20)



for i = 1:3
        for t = 2:T
            @constraint(model, WES_BT[t,i] == WES_BT[t-1,i]/0.98 )
            
        end
    end
     

@NLobjective(model,Min,sum(abs(0.3PMT+0.3a)))
@constraint(model,0 .<=PMT .<= 60)
optimize!(model)




term_status = JuMP.termination_status(model)
   primal_status = JuMP.primal_status(model)
   is_optimal = term_status == MOI.OPTIMAL

I try to use@NLobjectiveļ¼Œ
@NLobjective(model,Min,sum(abs(0.3PMT[i,j]+0.3a[i,j] for i in 1:T j in 1:3)))
The following error still occurs, I donā€™t know how to change it

LoadError: sum() can appear in nonlinear expressions  only if the argument is a generator statement, for example, sum(x[i] for i in 1:N).
Stacktrace:
 [1] error(::String) at .\error.jl:33
 [2] top-level scope at C:\Users\61940\.juliapro\JuliaPro_v1.4.2-1\packages\JuMP\YXK4e\src\parse_nlp.jl:247
 [3] top-level scope at C:\Users\61940\.juliapro\JuliaPro_v1.4.2-1\packages\JuMP\YXK4e\src\macros.jl:1328
in expression starting at E:\Juliaē؋åŗ\lizi.jl:23
2

Have you tried sum(abs(0.3PMT[i,j]+0.3a[i,j]) for i in 1:T j in 1:3) ? I am not proficient in JuMP but the error suggests that sum should take generator instead of the abs.

3

Iā€™ve tried, but it doesnā€™t seem right.

4

@odow
Iā€™m very sorry to ask you again!
In JuMP, how to add absolute value to the objective function, I only know that because of the absolute value, it becomes nonlinear and needs to be used @NLobjective
But how to realize the sum of matrix?

5

What you want is to broadcast the abs function to individual elements:

sum(abs.(0.3PMT+0.3a))
6

I changed it according to what you said, but the error is still the same```
@NLobjective(model,Min,sum(abs.(0.3PMT+0.3a)))

LoadError:sum() can appear in nonlinear expressions only if the argument is a generator statement, for example, sum(x[i] for i in 1:N).

7

No need for @NLobjective,you can formulate this as a linear program:

using JuMP
T = 24
model = Model()
@variables(model, begin
    2 <= a[1:T, 1:3]<= 2.5, Int
    0 <= PMT[1:T, 1:3] <= 60
    0 <= WES_BT[1:T, 1:3] <= 20
    abs_pmt[1:T, 1:3] >= 0
end)
@constraints(model, begin
    [i=1:3, t = 2:T], WES_BT[t, i] == WES_BT[t-1, i] / 0.98
    abs_pmt .>= 0.3 .* PMT + 0.3 .* a
    abs_pmt .>= -(0.3 .* PMT + 0.3 .* a)
end)
@objective(model, Min, sum(abs_pmt))
1 Like
8

This transformation is so ingeniousļ¼
But I still want to ask one more question: is it not easy to realize my previous idea of using for loops in objective ļ¼Ÿ

9

If it is a nonlinear objective function (for example, if there is a matrix summation of the square term in the objective function), then how to realize sum () I am more curious

10

As stated in the error message, you need to write @NLobjective(model, Min, sum(abs(PMT[t,i]) for t = 1:T, i=1:3)).

1 Like
11

The Mosek modeling cookbook has lots of interesting transformations: 2 Linear optimization ā€” MOSEK Modeling Cookbook 3.3.0

12

Your answer is always to the pointļ¼
I know that most solvers canā€™t solve the NLP problem. Thank you. Iā€™ll take a look at it.