Reference

qp = QuadraticModel(c, Hrows, Hcols, Hvals; Arows = Arows, Acols = Acols, Avals = Avals, 
                    lcon = lcon, ucon = ucon, lvar = lvar, uvar = uvar, sortcols = false)

qp = QuadraticModel(c, H; A = A, lcon = lcon, ucon = ucon, lvar = lvar, uvar = uvar)

Create a Quadratic model $min ~\tfrac{1}{2} x^T H x + c^T x + c_0$ with optional bounds lvar ≦ x ≦ uvar and optional linear constraints lcon ≦ Ax ≦ ucon. The user should only give the lower triangle of H to the QuadraticModel constructor.

With the first constructor, if sortcols = true, then Hcols and Acols are sorted in ascending order (Hrows, Hvals and Arows, Avals are then sorted accordingly).

You can also use QPSReader.jl to create a Quadratic model from a QPS file:

using QPSReader
qps = readqps("QAFIRO.SIF")
qp = QuadraticModel(qps)

The instance of QuadraticModel{T, S, D} created contains the fields:

• meta of type NLPModels.NLPModelMeta from NLPModels.jl,
• data, of type QuadraticModels.QPData depending on the input types of the A and H matrices.
• counters of type NLPModels.Counters from NLPModels.jl.

Using NLPModelsModifiers.SlackModel from NLPModelsModifiers.jl with a QuadraticModel based on a QPData with dense matrices will convert the field data to a QPData with SparseMatricesCOO.

Its in-place variant SlackModel! specific to QuadraticModels will only work with a QuadraticModel based on a QPData with SparseMatricesCOO.

QuadraticModel(nlp, x)

Creates a quadratic Taylor model of nlp around x.

new_ncon = empty_rows!(Arows, lcon, ucon, ncon, row_cnt, empty_rows, Arows_s)

Removes the empty rows of A, and the corresponding elements in lcon and ucon that are in empty_rows. Arows_s is a view of Arows sorted in ascending order. row_cnt is a vector of the number of elements per row.

Returns the new number of constraints new_ncon and updates in-place Arows, lcon, ucon.

x, y, s_l, s_u = postsolve(qm::QuadraticModel{T, S}, psqm::PresolvedQuadraticModel{T, S}, 
                           x_in::S, y_in::S,
                           s_l_in::SparseVector{T, Int},
                           s_u_in::SparseVector{T, Int}) where {T, S}

Retrieve the solution x, y, s_l, s_u of the original QP qm given the solution of the presolved QP (psqm) x_in, y_in, s_l_in, s_u_in.

stats_ps = presolve(qm::QuadraticModel{T, S}; kwargs...)

Apply a presolve routine to qm and returns a GenericExecutionStats from the package SolverCore.jl. The presolve operations currently implemented are:

• empty_rows! : remove empty rows
• singleton_rows! : remove singleton rows
• remove_ifix! : remove fixed variables

The PresolvedQuadraticModel{T, S} <: AbstractQuadraticModel{T, S} is located in the solver_specific field:

psqm = stats_ps.solver_specific[:presolvedQM]

and should be used to call postsolve.

If the presolved problem has 0 variables, stats_ps.solution contains a solution of the primal problem, stats_ps.multipliers is a zero SparseVector, and, if we define

s = qm.data.c + qm.data.H * stats_ps.solution

stats_ps.multipliers_L is the positive part of s and stats_ps.multipliers_U is the opposite of the negative part of s.

xrm, c0ps, nvarrm = remove_ifix!(ifix, Hrows, Hcols, Hvals, nvar, 
                                 Arows, Acols, Avals, c, c0, 
                                 lvar, uvar, lcon, ucon)

Remove rows and columns in H, columns in A, and elements in lcon and ucon corresponding to fixed variables, that are in ifix (They should be the indices i where lvar[i] == uvar[i]).

Returns the removed elements of lvar (or uvar), the constant term in the QP objective c0ps resulting from the fixed variables, and the new number of variables nvarrm. Hrows, Hcols, Hvals, Arows, Acols, Avals, c, lvar, uvar, lcon and ucon are updated in-place.

new_ncon = singleton_rows!(Arows, Acols, Avals, lcon, ucon,
                           lvar, uvar, nvar, ncon, row_cnt, singl_rows)

Removes the singleton rows of A, and the corresponding elements in lcon and ucon that are in singl_rows. row_cnt is a vector of the number of elements per row.

Returns the new number of constraints new_ncon and updates in-place Arows, Acols, Avals, lcon, ucon, lvar, uvar.