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28 changes: 22 additions & 6 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -7,13 +7,11 @@ A solver for Mixed-Integer Convex Optimization that uses Frank-Wolfe methods for

## Overview

The Boscia.jl solver combines (a variant of) the Frank-Wolfe algorithm with a branch-and-bound like algorithm to solve mixed-integer convex optimization problems of the form
`min_{x ∈ C, x_I ∈ Z^n} f(x)`,
where `f` is a differentiable convex function, `C` is a convex and compact set, and `I` is a set of indices of integral variables.

They are especially useful when we have a method to optimize a linear function over `C` and the integrality constraints in a compuationally efficient way.
`C` is specified using the MathOptInterface API or any DSL like JuMP implementing it.
The Boscia.jl solver uses a combination of a variant of the Frank-Wolfe algorithm and a branch-and-bound-like algorithm to solve mixed-integer convex optimization problems. These problems are of the form:
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**min_{x ∈ C, x_I ∈ Z^n} f(x)**,
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where f is a differentiable convex function, C is a convex and compact set, and I is a set of indices for integer variables.

This approach is particularly effective when we can efficiently optimize a linear function over C and handle the integer constraints. The set C is specified using the MathOptInterface API or any domain-specific language (DSL) like Julia for Mathematical Programming (**JuMP**) that implements this API.
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A paper presenting the package with mathematical explanations and numerous examples can be found here:
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> Convex integer optimization with Frank-Wolfe methods: [2208.11010](https://arxiv.org/abs/2208.11010)
Expand All @@ -22,6 +20,14 @@ A paper presenting the package with mathematical explanations and numerous examp

## Installation

If you haven't downloaded JULIA yet go on this link and download it according to your system requirement . ['Julia'](https://julialang.org/downloads/).
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Once you have installed Julia , From the Julia REPL, type ] to enter the Pkg REPL mode and run
```Boscia
pkg > add Boscia

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```
or alternatively you can do this
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Add the Boscia stable release with:

```julia
Expand All @@ -35,6 +41,16 @@ import Pkg
Pkg.add(url="https://github.com/ZIB-IOL/Boscia.jl", rev="main")
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```

If you don't have SCIP , you can on go this link and add SCIP as instructed ['SCIP'](https://github.com/scipopt/SCIP.jl)
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**For Window Users** You need not to download whole SCIP binary instead you can follow **Custom Installation** mentioned on this page and download and link SCIP with your JULIA .






## Getting started

Here is a simple example to get started. For more examples, see the examples folder in the package.
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