objective_coefficients.jl

"""
    set_dual_model_sense!(dual_model::MOI.ModelLike, model::MOI.ModelLike)

Set the dual model objective sense.
"""
function set_dual_model_sense(dual_model::MOI.ModelLike, primal_model::MOI.ModelLike)::Nothing where T
    # Get model sense
    primal_sense = MOI.get(primal_model, MOI.ObjectiveSense())
    if primal_sense == MOI.FEASIBILITY_SENSE
        error(primal_sense, " is not supported") # Feasibility should be supported?
    end
    # Set dual model sense
    dual_sense = (primal_sense == MOI.MIN_SENSE) ? MOI.MAX_SENSE : MOI.MIN_SENSE
    MOI.set(dual_model, MOI.ObjectiveSense(), dual_sense)
    return
end

function _scalar_quadratic_function(func::MOI.ScalarQuadraticFunction{T}, ::Type{T}) where T
    return MOIU.canonical(func)
end
function _scalar_quadratic_function(func::MOI.ScalarAffineFunction{T}, ::Type{T}) where T
    return _scalar_quadratic_function(
        SQF{T}(func.terms, MOI.ScalarQuadraticTerm{T}[], func.constant), T)
end
function _scalar_quadratic_function(func::MOI.SingleVariable, T::Type)
    return _scalar_quadratic_function(SAF{T}(func), T)
end

# Primals
"""
    PrimalObjective{T}

Primal objective is defined as a `MOI.ScalarAffineFunction`
"""
mutable struct PrimalObjective{T}
    obj::SQF{T}
    quad_cross_parameters::Dict{VI, Vector{MOI.ScalarAffineTerm{T}}}
    obj_parametric::Union{SQF{T},Nothing}

    function PrimalObjective{T}(obj) where T
        canonical_obj = _scalar_quadratic_function(obj, T)
        # if isempty(canonical_obj.terms)
        #     error("Dualization does not support models with no variables in the objective function.")
        # end
        # This was commented for now, because the current understanding is that
        # problems like {min 0*x} are well defined and have well defined dual problems.
        # Therefore, they present no issue to dualization as opposed to problems
        # with FEASIBILITY_SENSE that do not have a well defined dual problem.
        # Moreover, JuMP and MOI default is FEASIBILITY_SENSE, if a MIN_SENSE
        # is in the problem, it is because the user set it explicitly.
        # For more on the original discussion, see:
        # https://github.com/JuliaOpt/Dualization.jl/pull/64#discussion_r347484642
        quad_cross_parameters = Dict{VI, Vector{MOI.ScalarAffineTerm{T}}}()
        return new(canonical_obj,quad_cross_parameters,nothing)
    end
end

# Duals
"""
    DualObjective{T}

Dual objective is defined as a `MOI.ScalarAffineFunction`.
"""
mutable struct DualObjective{T}
    obj::SQF{T}

end

const Objective{T} = Union{PrimalObjective{T}, DualObjective{T}}

function get_raw_obj(objective::Objective{T}) where T
    return objective.obj
end
function get_affine_terms(objective::Objective{T}) where T
    return objective.obj.affine_terms
end

function get_primal_objective(primal_model::MOI.ModelLike, T::Type=Float64)
    F = MOI.get(primal_model, MOI.ObjectiveFunctionType())
    return _get_primal_objective(MOI.get(primal_model, MOI.ObjectiveFunction{F}()), T)
end

function _get_primal_objective(obj_fun, T::Type)
    return PrimalObjective{T}(obj_fun)
end

# allow removing variables from objective function
function get_primal_objective(primal_model::MOI.ModelLike, variable_parameters::Vector{VI}, T::Type)
    p_obj = get_primal_objective(primal_model, T)
    if length(variable_parameters) > 0
        vars_func, quad_cross_params, params_func = split_variables(p_obj.obj, variable_parameters)
        p_obj.obj = vars_func
        p_obj.quad_cross_parameters = quad_cross_params
        p_obj.obj_parametric = params_func
    end
    return p_obj
end

function split_variables(func::MOI.ScalarQuadraticFunction{T},
    variable_parameters::Vector{VI}) where T

    # linear part
    lin_params = MOI.ScalarAffineTerm{T}[]
    lin_vars = MOI.ScalarAffineTerm{T}[]
    for term in func.affine_terms
        if term.variable_index in variable_parameters
            push!(lin_params, term)
        else
            push!(lin_vars, term)
        end
    end

    # Quadratic part
    quad_params = MOI.ScalarQuadraticTerm{T}[]
    quad_vars = MOI.ScalarQuadraticTerm{T}[]
    quad_cross_params = Dict{VI, Vector{MOI.ScalarAffineTerm{T}}}()
    for term in func.quadratic_terms
        is_param_1 = term.variable_index_1 in variable_parameters
        is_param_2 = term.variable_index_2 in variable_parameters
        if is_param_1 && is_param_2
            push!(quad_params, term)
        elseif is_param_1
            push_affine_term(quad_cross_params, term, false)
        elseif is_param_2
            push_affine_term(quad_cross_params, term, true)
        else
            push!(quad_vars, term)
        end
    end

    variables_func = MOI.ScalarQuadraticFunction{T}(lin_vars, quad_vars, func.constant)
    parameters_func = MOI.ScalarQuadraticFunction{T}(lin_params, quad_params, zero(T))

    return variables_func, quad_cross_params, parameters_func
end

function push_affine_term(dic, term::MOI.ScalarQuadraticTerm{T}, var_is_first::Bool) where T
    variable = var_is_first ? term.variable_index_1 : term.variable_index_2
    parameter = var_is_first ? term.variable_index_2 : term.variable_index_1
    if haskey(dic, variable)
        push!(dic[variable],
            MOI.ScalarAffineTerm{T}(term.coefficient, parameter))
    else
        dic[variable] =
            [MOI.ScalarAffineTerm{T}(term.coefficient, parameter)]
    end
end

"""
    set_dual_objective(dual_model::MOI.ModelLike, dual_objective::DualObjective{T})::Nothing where T

Add the objective function to the dual model.
"""
function set_dual_objective(dual_model::MOI.ModelLike,
    dual_objective::DualObjective{T})::Nothing where T
    # Set dual model objective function
    raw_obj = get_raw_obj(dual_objective)
    if MOIU.number_of_quadratic_terms(T, raw_obj) > 0
        MOI.set(dual_model, MOI.ObjectiveFunction{SQF{T}}(), raw_obj)
    else
        MOI.set(dual_model, MOI.ObjectiveFunction{SAF{T}}(),
            SAF{T}(raw_obj.affine_terms, raw_obj.constant))
    end
    return
end

"""
    get_dual_objective(dual_model::MOI.ModelLike, dual_obj_affine_terms::Dict,
                       primal_objective::PrimalObjective{T})::DualObjective{T} where T

build the dual model objective function from the primal model.
"""
function get_dual_objective(dual_problem, dual_obj_affine_terms::Dict,
                            primal_objective::PrimalObjective{T},
                            con_types, scalar_affine_terms,
                            variable_parameters)::DualObjective{T} where T

    dual_model = dual_problem.dual_model
    map = dual_problem.primal_dual_map
    sense_change = MOI.get(dual_model, MOI.ObjectiveSense()) == MOI.MAX_SENSE ? -one(T) : one(T)

    # standard linear part
    num_objective_terms = length(dual_obj_affine_terms)
    lin_terms = MOI.ScalarAffineTerm{T}[]
    sizehint!(lin_terms, num_objective_terms)
    for var in keys(dual_obj_affine_terms) # Number of constraints of the primal model
        coef = dual_obj_affine_terms[var]
        push!(lin_terms, MOI.ScalarAffineTerm{T}(
            # Add positive terms bi if dual model sense is max
            sense_change * coef,
            # Variable index associated with term bi
            var
            ))
    end

    # standard quadratic part
    quad_terms = MOI.ScalarQuadraticTerm{T}[]
    sizehint!(quad_terms, length(primal_objective.obj.quadratic_terms))
    for term in primal_objective.obj.quadratic_terms
        push!(quad_terms, MOI.ScalarQuadraticTerm{T}(
            - MOI.coefficient(term),
            map.primal_var_dual_quad_slack[term.variable_index_1],
            map.primal_var_dual_quad_slack[term.variable_index_2]
            ))
    end

    # parametric part

    if nothing !== primal_objective.obj_parametric

        # linear
        for term in primal_objective.obj_parametric.affine_terms
            push!(lin_terms, MOI.ScalarAffineTerm{T}(
                MOI.coefficient(term),
                map.primal_parameter[term.variable_index]
                ))
        end

        # quadratic
        for term in primal_objective.obj_parametric.quadratic_terms
            push!(quad_terms, MOI.ScalarQuadraticTerm{T}(
                MOI.coefficient(term),
                map.primal_parameter[term.variable_index_1],
                map.primal_parameter[term.variable_index_2],
                ))
        end

        # crossed
        # TODO? set_dot
        for vi in variable_parameters
            param = map.primal_parameter[vi]
            for term in scalar_affine_terms[vi]
                push!(quad_terms, MOI.ScalarQuadraticTerm{T}(
                    sense_change * MOI.coefficient(term),
                    param,
                    term.variable_index,
                    ))
            end
        end
    end

    saf_dual_objective = MOI.ScalarQuadraticFunction{T}(
        lin_terms, quad_terms, MOI.constant(get_raw_obj(primal_objective)))
    return DualObjective{T}(saf_dual_objective)
end