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Added some IIS documentation
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‎docs/make.jl‎

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* *
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* This file is part of the HiGHS linear optimization suite *
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* *
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* Written and engineered 2008-2024 by Julian Hall, Ivet Galabova, *
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* Leona Gottwald and Michael Feldmeier *
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* *
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* Available as open-source under the MIT License *
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* *
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* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *=#
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"structures/classes/HighsSparseMatrix.md",
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"structures/classes/HighsLp.md",
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"structures/classes/HighsHessian.md",
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"structures/classes/HighsModel.md"
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"structures/classes/HighsModel.md",
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"structures/classes/HighsIis.md"
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],
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"Structures" => Any[
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"structures/structs/index.md",

‎docs/src/guide/advanced.md‎

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yield a specific row or column of ``B^{-1}A``. In all cases,
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HiGHS can return the number and indices of the nonzeros in the result.
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## Irreducible infeasibility system (IIS) detection(@id highs-iis)
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An Irreducible infeasibility system (IIS) consists of a set of
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variables and a set of constraints in a model, together with
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variable/constraint bound information, that cannot be satisfied (so is
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infeasible). It is irreducible in that if any constraint or variable
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bound is removed, then the system can be satisfied (so is feasible).
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HiGHS has an IIS facility that is under development. Currently it can only be used for LPs.
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## IIS-related methods in the `Highs` class
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- `const HighsLp& getIisLp()`: Return a const reference to the internal IIS LP instance
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- `HighsStatus getIis(HighsIis& iis)`: Try to find an IIS for the incumbent model. Gets the internal [`HighsIis`](@ref highs-iis-class) instance, returning `HighsStatus::kError` if the calculation failed. Note that if the incumbent model is found to be feasible, this is a "success", and `HighsStatus::kOk` is returned.
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- ` HighsStatus writeIisModel(const std::string& filename = "")`: Write out the internal IIS LP instance to a file.
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‎docs/src/guide/further.md‎

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Multi-objective optimization in HiGHS is defined by the following methods
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- [addLinearObjective](@ref Multi-objective-optimization] - Add a single `HighsLinearObjective` instance to any already stored in HiGHS
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- [clearLinearObjectives](@ref Multi-objective-optimization] - Clears any linear objectives stored in HiGHS
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- [addLinearObjective](@ref Multi-objective-optimization) - Add a single `HighsLinearObjective` instance to any already stored in HiGHS
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- [clearLinearObjectives](@ref Multi-objective-optimization) - Clears any linear objectives stored in HiGHS
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When there is at least one `HighsLinearObjective` instance in HiGHS,
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the `col_cost_` data in the incumbent model is ignored.

‎docs/src/structures/classes/HighsHessian.md‎

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A Hessian matrix is communicated via an instance of the HighsHessian class.
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- dim_: Scalar of type integer - Dimension of the Hessian
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- format\_: Scalar of [HessianFormat](@ref) type - Format of the Hessian
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- start\_: Vector of integer type - Start of each compressed column in the Hessian
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- index\_: Vector of integer type - Indices of the nonzeros in the Hessian
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- value\_: Vector of double type - Values of the nonzeros in the Hessian
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- `dim_`: Scalar of type integer - Dimension of the Hessian
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- `format\_`: Scalar of [HessianFormat](@ref) type - Format of the Hessian
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- `start\_`: Vector of integer type - Start of each compressed column in the Hessian
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- `index\_`: Vector of integer type - Indices of the nonzeros in the Hessian
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- `value\_`: Vector of double type - Values of the nonzeros in the Hessian

‎docs/src/structures/classes/HighsIis.md‎

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# [HighsIis](@id highs-iis-class)
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Irreducible infeasibility system (IIS) data are communicated via an instance of the `HighsIis` class.
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- `valid\_`: The data in the HighsIis instance is valid
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- `strategy\_`: The IIS strategy used
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- `col\_index\_`: The indices of model columns in the IIS
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- `row\_index\_`: The indices of model rows in the IIS
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- `col\_bound\_`: The bounds on each column that define the IIS
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- `row\_bound\_`: The bounds on each row that define the IIS
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- `col\_status\_`: Indicates whether a column in the model is in an IIS, may be in an IIS, or is not in an IIS
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- `row\_status\_`: Indicates whether a row in the model is in an IIS, may be in an IIS, or is not in an IIS
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- `info\_`: Data on the time and number of simplex iterations required to form the IIS
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- `model\_`: A `HighsModel` consisting of the variables, constraints and bounds in the IIS. Currently only its `HighsLp` instance is relevant
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‎docs/src/structures/classes/HighsLp.md‎

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# HighsLp
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An LP model is communicated via an instance of the HighsLp class
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An LP model is communicated via an instance of the `HighsLp` class
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- num\_col\_: Scalar of type integer - Number of columns in the model
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- num\_row\_: Scalar of type integer - Number of rows in the model
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- col\_cost\_: Vector of type double - Coefficients of the linear term in the objective function
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- col\_lower\_: Vector of type double - Lower bounds on the variables
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- col\_upper\_: Vector of type double - Upper bounds on the variables
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- row\_lower\_: Vector of type double - Lower bounds on the constraints
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- row\_upper\_: Vector of type double - Upper bounds on the constraints
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- a\_matrix\_: Instance of [HighsSparseMatrix](@ref) class - Constraint matrix
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- sense\_: Scalar of type [ObjSense](@ref) - Optimization sense of the model
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- offset\_: Scalar of type double - Constant term in the objective function
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- model\_name\_: Scalar of type string - Name of the model
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- objective\_name\_: Scalar of type string - Name of the objective function
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- col\_names\_: Vector of type string - Names of the variables
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- row\_names\_: Vector of type string - Names of the constraints
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- integrality\_: Vector of type [HighsVarType](@ref) - Type of each variable
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- `num\_col\_`: Scalar of type integer - Number of columns in the model
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- `num\_row\_`: Scalar of type integer - Number of rows in the model
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- `col\_cost\_`: Vector of type double - Coefficients of the linear term in the objective function
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- `col\_lower\_`: Vector of type double - Lower bounds on the variables
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- `col\_upper\_`: Vector of type double - Upper bounds on the variables
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- `row\_lower\_`: Vector of type double - Lower bounds on the constraints
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- `row\_upper\_`: Vector of type double - Upper bounds on the constraints
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- `a\_matrix\_`: Instance of [HighsSparseMatrix](@ref) class - Constraint matrix
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- `sense\_`: Scalar of type [ObjSense](@ref) - Optimization sense of the model
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- `offset\_`: Scalar of type double - Constant term in the objective function
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- `model\_name\_`: Scalar of type string - Name of the model
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- `objective\_name\_`: Scalar of type string - Name of the objective function
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- `col\_names\_`: Vector of type string - Names of the variables
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- `row\_names\_`: Vector of type string - Names of the constraints
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- `integrality\_`: Vector of type [HighsVarType](@ref) - Type of each variable

‎docs/src/structures/classes/HighsModel.md‎

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A QP model is communicated via an instance of the HighsModel class
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- lp\_: Instance of [HighsLp](@ref) class - LP components of the model
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- hessian\_: Instance of [HighsHessian](@ref) class - Hessian matrix
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- `lp\_`: Instance of [HighsLp](@ref) class - LP components of the model
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- `hessian\_`: Instance of [HighsHessian](@ref) class - Hessian matrix

‎docs/src/structures/classes/HighsSparseMatrix.md‎

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The constraint matrix of an LP model is communicated via an instance of the HighsSparseMatrix class
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- format\_: Scalar of [MatrixFormat](@ref) type - Format of the matrix
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- num\_col\_ : Scalar of integer type - Number of columns in the matrix
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- num\_row\_: Scalar of integer type - Number of rows in the matrix
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- start\_: Vector of integer type - Start of each compressed vector in the matrix
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- index\_: Vector of integer type - Indices of the nonzeros in the matrix
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- value\_: Vector of double type - Values of the nonzeros in the matrix
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- `format\_`: Scalar of [MatrixFormat](@ref) type - Format of the matrix
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- `num\_col\_ `: Scalar of integer type - Number of columns in the matrix
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- `num\_row\_`: Scalar of integer type - Number of rows in the matrix
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- `start\_`: Vector of integer type - Start of each compressed vector in the matrix
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- `index\_`: Vector of integer type - Indices of the nonzeros in the matrix
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- `value\_`: Vector of double type - Values of the nonzeros in the matrix

‎highs/lp_data/IIS.md‎

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# HiGHS Irreducible infeasibility system (IIS) facility
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Further to documentation
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