Julia package for parsing QPS files.

QPS is a file format, which is proposed by Maros and Mészáros, used to encode convex quadratic programming problems in plain text files. It is an extension to the well-known MPS format. The authors also provide a set of large and/or ill-conditioned QP test problems on their website to be used to assess the performance of different solvers.

`QPSParser`

is a Julia package that aims at helping users parse problems written
in the QPS file format.

After installing the package via `Pkg.add("QPSParser")`

, we import the useful
parts of the package to our workspace by `using QPSParser`

.

To parse a QPS file, we use `parseqps("filename.qps")`

. The output will be an
object of type `MPSDescription`

, which is the description of the following
optimization problem as defined in `filename.qps`

:

```
minimize 0.5*x'*Q*x + q₁'*x + q₂
subject to A*x = b
c₁ ≤ C*x ≤ c₂
lb ≤ x ≤ ub
```

To illustrate, let's assume that the `QP Example`

given in Maros and Mészáros

```
NAME QP example
ROWS
N obj
G r1
L r2
COLUMNS
c1 r1 2.0 r2 -1.0
c1 obj 1.5
c2 r1 1.0 r2 2.0
c2 obj -2.0
RHS
rhs1 obj -4.0
rhs1 r1 2.0 r2 6.0
RANGES
BOUNDS
UP bnd1 c1 20.0
QUADOBJ
c1 c1 8.0
c1 c2 2.0
c2 c2 10.0
ENDATA
```

is saved as `filename.qps`

. Then,

```
julia> mps = parseqps("test/QPExample.qps")
QP instance: QP example.
---
minimize 0.5*x'*Q*x + q₁'*x + q₂
subject to A*x = b
c₁ ≤ C*x ≤ c₂
lb ≤ x ≤ ub
---
```

For more information on the function, type `?parseqps`

in Julia.

There are convenient getter functions defined for the `MPSDescription`

objects.

For instance, to get the `name`

and `variables`

of the given problem, we can
write

```
julia> name(mps)
"QP example"
julia> variables(mps)
2-element Array{Symbol,1}:
:c1
:c2
```

Then, we can get the `objective`

part of the example problem description above
by typing

```
julia> Q, q₁, q₂ = objective(mps);
julia> Q
2×2 Array{Float64,2}:
8.0 2.0
2.0 10.0
julia> q₁
2-element Array{Float64,1}:
1.5
-2.0
julia> q₂
4.0
```

Similarly, to get the `equalities`

and `inequalities`

defined on the `variables`

of the problem, we can write

```
julia> A, b = equalities(mps);
julia> A # no equalities given in the example
0×2 Array{Float64,2}
julia> b # no equalities given in the example
0-element Array{Float64,1}
julia> C, c₁, c₂ = inequalities(mps);
julia> C
2×2 Array{Float64,2}:
2.0 1.0
-1.0 2.0
julia> c₁
2-element Array{Float64,1}:
2.0
-Inf
julia> c₂
2-element Array{Float64,1}:
Inf
6.0
```

Finally, the lower and upper `bounds`

defined on the `variables`

of the problem
can be obtained by

```
julia> lb, ub = bounds(mps);
julia> lb
2-element Array{Float64,1}:
0.0
0.0
julia> ub
2-element Array{Float64,1}:
20.0
Inf
```

Please note that, in `MPSDescription`

objects, `c₁`

, `c₂`

, `lb`

and `ub`

can all
contain infinite values.

Sometimes, it might be useful to obtain the following canonical representation of the same optimization problem defined above:

```
minimize 0.5*x'*Q*x + q₁'*x + q₂
subject to A*x = b
C̃*x ≤ c̃
lb ≤ x ≤ ub
```

To achieve this, we can write `canon = canonical(mps)`

, which returns a
`CanonicalDescription`

object:

```
julia> canon = canonical(mps)
QP instance: QP example.
---
minimize 0.5*x'*Q*x + q₁'*x + q₂
subject to A*x = b
C̃*x ≤ c̃
lb ≤ x ≤ ub
---
julia> name(canon); # same as `name(mps)`
julia> variables(canon); # same as `variables(mps)`
julia> Q, q₁, q₂ = objective(canon); # same as `objective(mps)`
julia> A, b = equalities(canon); # same as `equalities(mps)`
julia> lb, ub = bounds(canon); # same as `bounds(mps)`
julia> C̃, c̃ = inequalities(canon);
julia> C̃
2×2 Array{Float64,2}:
-2.0 -1.0
-1.0 2.0
julia> c̃
2-element Array{Float64,1}:
-2.0
6.0
```

`QPSParser`

,

- does
**not**guarantee that`Q`

in the problem descriptions is positive semi-definite. Any user of the package*has to*check the definiteness of`Q`

in their applications, - gives both
`MPSDescription`

and`CanonicalDescription`

in**dense**format. In other words, all the matrices and vectors involved in the descriptions are dense matrices and vectors. This might be a limitation when dealing with large problems or using the package in low-memory platforms.

10/10/2017

almost 2 years ago

20 commits