# JuMP Efficient Quadratic Objective Formulation

**URL:** <https://discourse.julialang.org/t/jump-efficient-quadratic-objective-formulation/6177>\
**Category:** Optimization (Mathematical)\
**Created:** [October 1, 2017, 12:30am UTC](https://discourse.julialang.org/t/jump-efficient-quadratic-objective-formulation/6177 "2017-10-01T00:30:45Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Kenney](https://avatars.discourse-cdn.com/v4/letter/k/df705f/32.png) [@Kenney](https://discourse.julialang.org/u/Kenney)\
**Post date:** [October 1, 2017, 12:30am UTC](https://discourse.julialang.org/t/jump-efficient-quadratic-objective-formulation/6177/1 "2017-10-01T00:30:45Z")

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Hi everyone,

I (eventually) want to run an MIQP where the objective is a simple sum of squares say sum((Y-XB)^2). Without even getting to the constraints or the integer part of the problem, I’m running into issues simply formulating the objective for large X and Y (say X~500x1000 and Y~500x1). Specifically, I get an “OutofMemoryError()”, note that I’m not solving anything yet just setting up the model. I have a simple function snippet below I’ve been using to see how big I can make X before things break. The use of “dot()” may be silly/naive to more experienced julia users, it was just working faster then writing out the whole thing as a sum. So far I’ve made it up to n=500 and p=900 before the error appears (applying @time to this shows the output: “64.652337 seconds (1.81 M allocations: 18.305 GB, 19.55% gc time)”)  
I’m working on a cluster and have to request memory for jobs, so theoretically I could request more though that puts me further down the queue. So if there are glaring inefficiencies here or nice tricks to use, any input would be great!

`function test(n,p)
X=randn(n,p)
Y=randn(n)
m=Model(solver=CplexSolver())
@variable(m, B[1:p])
W = Y-X*B
@objective(m,Min,dot(W,W))
end`

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**Author:** ![joaquimg](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/joaquimg/32/223_2.png) [@joaquimg](https://discourse.julialang.org/u/joaquimg)\
**Post date:** [October 1, 2017, 6:55pm UTC](https://discourse.julialang.org/t/jump-efficient-quadratic-objective-formulation/6177/2 "2017-10-01T18:55:51Z")

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Try re-writting this way:

```julia
function test2(n,p)
    X=randn(n,p)'
    Y=randn(n)
    m=Model(solver=CplexSolver())
    @variable(m, B[1:p])
    @variable(m, w[1:n])
    @constraint(m, ctr[i in 1:n], w[i]==Y[i]-sum(X[j,i]*B[j] for j in 1:p))
    @objective(m,Min,sum(w[i]*w[i] for i in 1:n))
    nothing    
end

```

p=n=1000 takes 1s on my notebook

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<div class="post-metadata">

**Author:** ![Kenney](https://avatars.discourse-cdn.com/v4/letter/k/df705f/32.png) [@Kenney](https://discourse.julialang.org/u/Kenney)\
**Post date:** [October 1, 2017, 7:27pm UTC](https://discourse.julialang.org/t/jump-efficient-quadratic-objective-formulation/6177/3 "2017-10-01T19:27:44Z")

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Thanks joaquimg! Works great, just curious but is there any particular reason to transpose X and go across rows in sum(X[j,i]\*B[j] rather then columns? Are longer matrices faster to process/store then wider ones?

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**Author:** ![joaquimg](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/joaquimg/32/223_2.png) [@joaquimg](https://discourse.julialang.org/u/joaquimg)\
**Post date:** [October 1, 2017, 7:31pm UTC](https://discourse.julialang.org/t/jump-efficient-quadratic-objective-formulation/6177/4 "2017-10-01T19:31:17Z")

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That was not the key feature in the rewrite, but inner loop should go column-wise in julia.  
Actually the I should have written: `X=randn(p,n)`.

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<div class="post-metadata">

**Author:** ![Kenney](https://avatars.discourse-cdn.com/v4/letter/k/df705f/32.png) [@Kenney](https://discourse.julialang.org/u/Kenney)\
**Post date:** [October 1, 2017, 7:44pm UTC](https://discourse.julialang.org/t/jump-efficient-quadratic-objective-formulation/6177/5 "2017-10-01T19:44:13Z")

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Got it, and, if I’m understanding correctly, it seems like the key features would be defining placeholder variables and working with looped operations rather then straight matrix/vector multiplication.