Add error checks for set dimensions

[odow]

This fixes a TODO in Bridges and closes #967.

One point is up for debate: can you initialize a zero-dimensional set? What do we do in cases like

• Nonnegatives(0) => ??
• SecondOrderCone(1) => t <= 0?

[odow]

Tests are failing because of the following, which neatly summarizes my question:

MathOptInterface.jl/test/Bridges/Variable/rsoc_to_psd.jl

Lines 16 to 112 in 7923c60

	# Can come from a SOC of dimension 2 which makes more sense
	# FIXME should it be moved to contconic or is RSOC of dimension 2 too exotic ?
	@testset "RSOC of dimension 2" begin
	MOI.empty!(bridged_mock)
	xy, cxy = MOI.add_constrained_variables(
	bridged_mock,
	MOI.RotatedSecondOrderCone(2),
	)
	x, y = xy
	fx = MOI.SingleVariable(x)
	fy = MOI.SingleVariable(y)
	c = MOI.add_constraint(bridged_mock, 1.0fx + 1.0fy, MOI.LessThan(1.0))
	obj = 1.0fy
	MOI.set(bridged_mock, MOI.ObjectiveSense(), MOI.MAX_SENSE)
	MOI.set(bridged_mock, MOI.ObjectiveFunction{typeof(obj)}(), obj)
	mock.optimize! =
	(mock::MOIU.MockOptimizer) -> MOIU.mock_optimize!(
	mock,
	[0.0, 2.0],
	#(MOI.VectorOfVariables) => [0.0, 1.0],
	(MOI.ScalarAffineFunction{Float64}, MOI.LessThan{Float64}) =>
	[-1.0],
	)
	MOI.optimize!(bridged_mock)
	@test MOI.get(bridged_mock, MOI.ObjectiveValue()) == 1.0
	@test MOI.get(bridged_mock, MOI.DualObjectiveValue()) == 1.0
	@test MOI.get(bridged_mock, MOI.VariablePrimal(), xy) == [0.0, 1.0]
	@test MOI.get(bridged_mock, MOI.ConstraintPrimal(), cxy) == [0.0, 1.0]
	@test MOI.get(bridged_mock, MOI.ConstraintDual(), cxy) == [1.0, 0.0]
	@test MOI.get(bridged_mock, MOI.ConstraintPrimal(), c) == 1.0
	@test MOI.get(bridged_mock, MOI.ConstraintDual(), c) == -1.0
	MOI.set(mock, MOI.ConstraintName(), c, "c")
	@testset "Test mock model" begin
	var_names = ["a", "b"]
	MOI.set(
	mock,
	MOI.VariableName(),
	MOI.get(mock, MOI.ListOfVariableIndices()),
	var_names,
	)
	nonneg = MOI.get(
	mock,
	MOI.ListOfConstraintIndices{
	MOI.VectorOfVariables,
	MOI.Nonnegatives,
	}(),
	)
	@test length(nonneg) == 1
	MOI.set(mock, MOI.ConstraintName(), nonneg[1], "cab")
	s = """
	variables: a, b
	cab: [a, b] in MathOptInterface.Nonnegatives(2)
	c: a + 0.5b <= 1.0
	maxobjective: 0.5b
	"""
	model = MOIU.Model{Float64}()
	MOIU.loadfromstring!(model, s)
	MOIU.test_models_equal(mock, model, var_names, ["cab", "c"])
	end
	@testset "Test bridged model" begin
	var_names = ["x", "y"]
	MOI.set(
	bridged_mock,
	MOI.VariableName(),
	MOI.get(bridged_mock, MOI.ListOfVariableIndices()),
	var_names,
	)
	MOI.set(bridged_mock, MOI.ConstraintName(), cxy, "cxy")
	s = """
	variables: x, y
	cxy: [x, y] in MathOptInterface.RotatedSecondOrderCone(2)
	c: x + y <= 1.0
	maxobjective: 1.0y
	"""
	model = MOIU.Model{Float64}()
	MOIU.loadfromstring!(model, s)
	MOIU.test_models_equal(bridged_mock, model, var_names, ["cxy", "c"])
	end
	test_delete_bridged_variables(
	bridged_mock,
	xy,
	MOI.RotatedSecondOrderCone,
	2,
	(
	(MOI.VectorOfVariables, MOI.Nonnegatives, 0),
	(MOI.VectorOfVariables, MOI.PositiveSemidefiniteConeTriangle, 0),
	(MOI.SingleVariable, MOI.EqualTo{Float64}, 0),
	(MOI.ScalarAffineFunction{Float64}, MOI.EqualTo{Float64}, 0),
	(MOI.ScalarAffineFunction{Float64}, MOI.LessThan{Float64}, 1),
	),
	)
	end

[odow]

I've relaxed the restriction on the sets where it makes sense. So you can have RotatedSecondOrderCone(2) and NormOneCone(1). But you can't have matrix cones with zero dimensional matrices. And you can't have a 1-dimensional GeometricMeanCone (0th root of zero?).

Thoughts?

[odow]

@blegat how's this? Do they make sense?

[odow]

Bump @blegat