Support objective constants in MPS

[odow]

Reported on Discourse: https://discourse.julialang.org/t/mathoptformat-jl-error-when-reading-mps-file-objective-functions-with-constant-terms/55683

CPLEX supports objective constants in MPS: https://www.ibm.com/support/knowledgecenter/SSSA5P_20.1.0/ilog.odms.cplex.help/CPLEX/FileFormats/topics/MPS_records.html

You can also declare an objective offset for a model in the RHS section of a file in MPS format. To do so, use the negative value of the offset, and declare it as the RHS of the objective function. For example, the following line declares an objective offset of 3.1415 (as in the example in the LP file format):
rhs obj -3.1415
Notice particularly the reversal of the sign from 3.1415 to -3.1415.

The writing code should be modified here:

MathOptInterface.jl/src/FileFormats/MPS/MPS.jl

Lines 347 to 371 in 4aebdf3

	function _write_rhs(io, model, S, sense_char)
	for index in MOI.get(
	model,
	MOI.ListOfConstraintIndices{MOI.ScalarAffineFunction{Float64},S}(),
	)
	row_name = MOI.get(model, MOI.ConstraintName(), index)
	set = MOI.get(model, MOI.ConstraintSet(), index)
	println(
	io,
	Card(
	f2 = "rhs",
	f3 = row_name,
	f4 = sprint(print_shortest, value(set)),
	),
	)
	end
	end
	function write_rhs(io::IO, model::Model)
	println(io, "RHS")
	for (set_type, sense_char) in SET_TYPES
	_write_rhs(io, model, set_type, sense_char)
	end
	return
	end

The reading code should be modified here:

MathOptInterface.jl/src/FileFormats/MPS/MPS.jl

Lines 1012 to 1021 in 4aebdf3

	function parse_single_rhs(
	data,
	row_name::String,
	value::Float64,
	items::Vector{String},
	)
	row = get(data.name_to_row, row_name, nothing)
	if row === nothing
	error("ROW name $(row_name) not recognised. Is it in the ROWS field?")
	end