# Help on convex quadratic IP with cut generation

**URL:** https://discourse.julialang.org/t/help-on-convex-quadratic-ip-with-cut-generation/19650
**Category:** Optimization (Mathematical)
**Created:** [January 15, 2019, 8:16am UTC](https://discourse.julialang.org/t/help-on-convex-quadratic-ip-with-cut-generation/19650 "2019-01-15T08:16:29Z")
**Posts on this page:** 4
**Page:** 1

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### Author: ![WangQuanmeng](https://avatars.discourse-cdn.com/v4/letter/w/43a26b/32.png) [@WangQuanmeng](https://discourse.julialang.org/u/WangQuanmeng)
#### Post date: [January 15, 2019, 8:16am UTC](https://discourse.julialang.org/t/help-on-convex-quadratic-ip-with-cut-generation/19650/1 "2019-01-15T08:16:29Z")

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Hi,

I am solving a convex quadratic integer programming problem,

```julia
min f( x , y )
s.t. Ax + By <= b
      y being integral vector

```

where `f` is a convex quadratic function.

I have a set of valid inequalites for the feasible region `(x,y)` lives in, and I have defined a valid `CutGeneration` function for them.

The question is, when I use piecewise linear approximation of `f` some of my user cuts are used during solving.

```julia
m = Model( solver = gurobi() )

@variable x
@variable y , Bin
@variable c

@constraint of Ax + By <=b
@constraint c >= linear_approximation_f(x,y)

@objective Min c

function CutGeneration
if...
  println("User cut!")
  @usercut( ax + by <= d )
end

```

The output log is like

```julia
Cutting planes:
  User: 8
  Gomory: 11
  Cover: 7
  Implied bound: 278
  Clique: 1
  MIR: 85
  Flow cover: 156
  GUB cover: 9

```

When I move to exactly solve quadratic objective in epigraph form

```julia
# everything is the same, except exact form of f is used
m = Model( solver = gurobi() )

@variable x
@variable y , Bin
@variable c

@constraint of Ax + By <=b
@constraint c >= f(x,y)

@objective Min c

function CutGeneration
if...
  println("User cut!")
  @usercut( ax + by <= d)
end

```

During solving process, julia is really printing the sentences `user cut!` , which means the cut generation function correctly goes to the step of add user cut.

But the output log is like

```julia
Cutting planes:
  Gomory: 5
  Cover: 7
  Implied bound: 97
  MIR: 49
  Flow cover: 90
  GUB cover: 6
  Zero half: 3

```

Can someone help me on what happend ?

I put convex objective into epigraph form because later I have to implement another cutting plane on the epigraph of `f` in space `(x,y,c)`.

---

<div class="post-metadata">

### Author: ![leethargo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/leethargo/32/6004_2.png) [@leethargo](https://discourse.julialang.org/u/leethargo)
#### Post date: [January 15, 2019, 8:34am UTC](https://discourse.julialang.org/t/help-on-convex-quadratic-ip-with-cut-generation/19650/2 "2019-01-15T08:34:22Z")

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It’s difficult to comment on Gurobi internals, but maybe your user cuts are redundant in the second model, so they are not added to the model?

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### Author: ![WangQuanmeng](https://avatars.discourse-cdn.com/v4/letter/w/43a26b/32.png) [@WangQuanmeng](https://discourse.julialang.org/u/WangQuanmeng)
#### Post date: [January 15, 2019, 8:38am UTC](https://discourse.julialang.org/t/help-on-convex-quadratic-ip-with-cut-generation/19650/3 "2019-01-15T08:38:59Z")

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The feasible region of `(x,y)` are the same for both models. I am quite sure it is not redundant.

So is it better that I pose this problem to a website that is more related to gurobi ?

---

<div class="post-metadata">

### Author: ![leethargo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/leethargo/32/6004_2.png) [@leethargo](https://discourse.julialang.org/u/leethargo)
#### Post date: [January 15, 2019, 12:33pm UTC](https://discourse.julialang.org/t/help-on-convex-quadratic-ip-with-cut-generation/19650/4 "2019-01-15T12:33:10Z")

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> So is it better that I pose this problem to a website that is more related to gurobi ?

Maybe, but then be prepared to provide example code in Python or some other supported language.