Modes overview
There are several ways to solve bilevel problems with BilevelJuMP. The main difference between them is the way the complementarity constraints are reformulated. The reformulation method is set with the mode option of the BilevelModel constructor.
The modes available are:
BilevelJuMP.SOS1Mode(): uses SOS1 constraints to model complementarity constraints and solve the problem with MIP solvers (Cbc, Xpress, Gurobi, CPLEX, SCIP).BilevelJuMP.IndicatorMode(): uses Indicator constraints to model complementarity constraints and solve the problem with MIP solvers (Cbc, Xpress, Gurobi, CPLEX, SCIP).BilevelJuMP.BigMMode(): uses the Fortuny-Amat and McCarl reformulation that requires a MIP solver with very basic functionality, i.e., just binary variables are needed. The main drawback of this method is that one must provide bounds for all primal and dual variables. However, if good bounds are provided, this method can be more efficient than the previous. Bound hints to compute the big-Ms can be passed with the methods:set_primal_(upper\lower)_bound_hint(variable, bound), for primals; andset_dual_(upper\lower)_bound_hint(constraint, bound)for duals. We can also callFortunyAmatMcCarlMode(primal_big_M = vp, dual_big_M = vd), wherevpandvdare, respectively, the big M fallback values for primal and dual variables, these are used when some variables have no given bounds, otherwise the given bounds are used instead.BilevelJuMP.ProductMode(): reformulates the complementarity constraints as products so that the problem can be solved by NLP (Ipopt, KNITRO) solvers or even MIP solvers with the aid of binary expansions (seeQuadraticToBinary.jl). Note that binary expansions require variables to have upper and lower bounds. Also, note that theGurobisolver supports products, but requires setting the"NonConvex"options.BilevelJuMP.MixedMode(default = mode): wheremodeis one of the other modes described above. With this method it is possible to set complementarity reformulations per constraint withBilevelJuMP.set_mode(constraint, mode), whereconstraintis a constraint of the bilevel problem andmodeis one of the modes described above. If no mode is set for a constraint, thedefaultmode is used instead. To set a mode to reformulate variables bounds use:BilevelJuMP.set_mode(variable, mode).BilevelJuMP.StrongDualityMode: this mode is not a complementarity reformulation method, instead, all complementarity constraints are replaced by constraints enforcing the strong duality. This mode is especially amenable for NLP solvers (Ipopt, KNITRO). MIP solvers can also be used but they will have to deal with the products of variables crated or the will have to be used in conjunction withQuadraticToBinary.jl.
The following example shows how to solve a classic bilevel problem.
We start loading all libraries needed for this example.
using BilevelJuMP, HiGHS, Ipopt, SCIPNow we create a bilevel model with the BilevelModel constructor with no solver nor mode specified.
model = BilevelModel()
@variable(Lower(model), x)
@variable(Upper(model), y)
@objective(Upper(model), Min, 3x + y)
@constraints(Upper(model), begin
x <= 5
y <= 8
y >= 0
end)
@objective(Lower(model), Min, -x)
@constraints(Lower(model), begin
c1, x + y <= 8
c2, 4x + y >= 8
c3, 2x + y <= 13
c4, 2x - 7y <= 0
end)(c1 : x + y ≤ 8, c2 : 4 x + y ≥ 8, c3 : 2 x + y ≤ 13, c4 : 2 x - 7 y ≤ 0)
BigMMode and HiGHS.Optimizer
set_optimizer(model, HiGHS.Optimizer)
BilevelJuMP.set_mode(model,
BilevelJuMP.BigMMode(primal_big_M = 100, dual_big_M = 100))
optimize!(model)
objective_value(model)
@assert abs(objective_value(model) - (3 * (7/2 * 8/15) + 8/15)) < 1e-1 # srcRunning HiGHS 1.5.1 [date: 1970-01-01, git hash: 93f1876e4]
Copyright (c) 2023 HiGHS under MIT licence terms
WARNING: Row 0 has infeasibility of 1 from [lower, value, upper] = [ -1; 0; -1]
WARNING: Row 2 has infeasibility of 8 from [lower, value, upper] = [ 8; 0; inf]
Solution has num max sum
Col infeasibilities 0 0 0
Integer infeasibilities 0 0 0
Row infeasibilities 4 13 30
Row residuals 0 0 0
Attempting to find feasible solution of continuous variables for user-supplied values of discrete variables
Presolving model
13 rows, 6 cols, 24 nonzeros
Problem status detected on presolve: Infeasible
Model status : Infeasible
Objective value : 0.0000000000e+00
HiGHS run time : 0.00
Presolving model
13 rows, 10 cols, 32 nonzeros
13 rows, 10 cols, 32 nonzeros
Solving MIP model with:
13 rows
10 cols (4 binary, 0 integer, 0 implied int., 6 continuous)
32 nonzeros
Nodes | B&B Tree | Objective Bounds | Dynamic Constraints | Work
Proc. InQueue | Leaves Expl. | BestBound BestSol Gap | Cuts InLp Confl. | LpIters Time
0 0 0 0.00% 0 inf inf 0 0 0 0 0.0s
R 0 0 0 0.00% 6.133333333 6.133333333 0.00% 0 0 0 5 0.0s
Solving report
Status Optimal
Primal bound 6.13333333333
Dual bound 6.13333333333
Gap 0% (tolerance: 0.01%)
Solution status feasible
6.13333333333 (objective)
0 (bound viol.)
0 (int. viol.)
0 (row viol.)
Timing 0.01 (total)
0.00 (presolve)
0.00 (postsolve)
Nodes 1
LP iterations 6 (total)
0 (strong br.)
0 (separation)
0 (heuristics)SOS1Mode and SCIP.Optimizer
set_optimizer(model, SCIP.Optimizer)
BilevelJuMP.set_mode(model, BilevelJuMP.SOS1Mode())
optimize!(model)
objective_value(model)
@assert abs(objective_value(model) - (3 * (3.5 * 8/15) + 8/15)) < 1e-1 # srcpresolving:
(round 1, fast) 0 del vars, 3 del conss, 0 add conss, 3 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 2, fast) 0 del vars, 3 del conss, 0 add conss, 5 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 3, fast) 0 del vars, 3 del conss, 0 add conss, 8 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 4, exhaustive) 0 del vars, 6 del conss, 0 add conss, 8 chg bounds, 3 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(0.0s) symmetry computation skipped: there exist constraints that cannot be handled by symmetry methods.
presolving (5 rounds: 5 fast, 2 medium, 2 exhaustive):
0 deleted vars, 6 deleted constraints, 0 added constraints, 8 tightened bounds, 0 added holes, 3 changed sides, 0 changed coefficients
0 implications, 0 cliques
presolved problem has 10 variables (0 bin, 0 int, 0 impl, 10 cont) and 10 constraints
4 constraints of type <SOS1>
6 constraints of type <linear>
Presolving Time: 0.00
time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl.
0.0s| 1 | 0 | 5 | - | 639k | 0 | 10 | 10 | 6 | 0 | 0 | 0 | 0 | 6.133333e+00 | -- | Inf | unknown
0.0s| 1 | 0 | 6 | - | 639k | 0 | 10 | 10 | 7 | 1 | 2 | 0 | 0 | 6.133333e+00 | -- | Inf | unknown
* 0.0s| 1 | 0 | 6 | - | LP | 0 | 10 | 10 | 7 | 1 | 4 | 0 | 0 | 6.133333e+00 | 6.133333e+00 | 0.00%| unknown
SCIP Status : problem is solved [optimal solution found]
Solving Time (sec) : 0.00
Solving Nodes : 1
Primal Bound : +6.13333333333333e+00 (1 solutions)
Dual Bound : +6.13333333333333e+00
Gap : 0.00 %SCIP requires a non-standard installation procedure in windows. See SCIP.jl for more details.
IndicatorMode and SCIP.Optimizer
set_optimizer(model, SCIP.Optimizer)
BilevelJuMP.set_mode(model, BilevelJuMP.IndicatorMode())
optimize!(model)
objective_value(model)
@assert abs(objective_value(model) - (3 * (3.5 * 8/15) + 8/15)) < 1e-1 # srcpresolving:
(round 1, fast) 8 del vars, 11 del conss, 0 add conss, 11 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 2, fast) 8 del vars, 11 del conss, 0 add conss, 14 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 3, fast) 8 del vars, 11 del conss, 0 add conss, 16 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(0.0s) probing cycle finished: starting next cycle
(round 4, exhaustive) 8 del vars, 11 del conss, 0 add conss, 17 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 46 impls, 3 clqs
(0.0s) probing cycle finished: starting next cycle
(0.0s) symmetry computation skipped: there exist constraints that cannot be handled by symmetry methods.
presolving (5 rounds: 5 fast, 2 medium, 2 exhaustive):
8 deleted vars, 11 deleted constraints, 0 added constraints, 17 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients
46 implications, 3 cliques
presolved problem has 14 variables (4 bin, 0 int, 0 impl, 10 cont) and 17 constraints
8 constraints of type <SOS1>
9 constraints of type <linear>
Presolving Time: 0.00
time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl.
0.0s| 1 | 0 | 18 | - | 754k | 0 | 14 | 17 | 9 | 0 | 0 | 0 | 0 | 6.133333e+00 | -- | Inf | unknown
0.0s| 1 | 0 | 20 | - | 761k | 0 | 14 | 17 | 11 | 2 | 1 | 0 | 0 | 6.133333e+00 | -- | Inf | unknown
0.0s| 1 | 0 | 21 | - | 765k | 0 | 14 | 17 | 12 | 3 | 2 | 0 | 0 | 6.133333e+00 | -- | Inf | unknown
0.0s| 1 | 0 | 22 | - | 766k | 0 | 14 | 17 | 13 | 4 | 4 | 0 | 0 | 6.133333e+00 | -- | Inf | unknown
r 0.0s| 1 | 0 | 22 | - |randroun| 0 | 14 | 17 | 13 | 0 | 4 | 0 | 0 | 6.133333e+00 | 6.133333e+00 | 0.00%| unknown
0.0s| 1 | 0 | 22 | - | 766k | 0 | 14 | 17 | 13 | 4 | 4 | 0 | 0 | 6.133333e+00 | 6.133333e+00 | 0.00%| unknown
SCIP Status : problem is solved [optimal solution found]
Solving Time (sec) : 0.00
Solving Nodes : 1
Primal Bound : +6.13333333333333e+00 (1 solutions)
Dual Bound : +6.13333333333333e+00
Gap : 0.00 %SCIP requires a non-standard installation procedure in windows. See SCIP.jl for more details.
ProductMode and Ipopt.Optimizer
set_optimizer(model, Ipopt.Optimizer)
BilevelJuMP.set_mode(model, BilevelJuMP.ProductMode())
optimize!(model)
objective_value(model)
@assert abs(objective_value(model) - (3 * (7/2 * 8/15) + 8/15)) < 1e-1 # srcThis is Ipopt version 3.14.4, running with linear solver MUMPS 5.4.1.
Number of nonzeros in equality constraint Jacobian...: 4
Number of nonzeros in inequality constraint Jacobian.: 30
Number of nonzeros in Lagrangian Hessian.............: 8
Total number of variables............................: 6
variables with only lower bounds: 1
variables with lower and upper bounds: 0
variables with only upper bounds: 3
Total number of equality constraints.................: 1
Total number of inequality constraints...............: 11
inequality constraints with only lower bounds: 2
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 9
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 0.0000000e+00 8.00e+00 1.25e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 1.1715810e+00 6.47e+00 7.43e+00 -1.0 4.20e+00 - 2.30e-02 1.94e-01h 1
2 3.3572931e+00 3.62e+00 7.92e+00 -1.0 3.51e+00 - 1.78e-01 4.34e-01h 1
3 4.0212202e+00 2.75e+00 7.49e+00 -1.0 1.98e+00 - 3.33e-01 2.33e-01h 1
4 5.0194310e+00 1.45e+00 2.08e+01 -1.0 1.53e+00 - 2.24e-01 4.53e-01h 1
5 5.4214626e+00 9.28e-01 1.48e+01 -1.0 8.61e-01 - 2.39e-01 3.24e-01h 1
6 5.5118789e+00 8.11e-01 1.01e+02 -1.0 4.61e+00 - 8.91e-02 7.14e-02H 1
7 5.8180392e+00 4.11e-01 1.05e+03 -1.0 1.38e+01 - 5.31e-02 1.21e-01f 4
8 5.8109187e+00 4.20e-01 1.01e+03 -1.0 1.08e+00 0.0 1.00e+00 4.07e-02h 1
9 6.1545183e+00 5.33e-02 1.99e+03 -1.0 1.31e+00 -0.5 1.00e+00 9.94e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 6.1580596e+00 6.24e-02 5.04e+03 -1.0 3.56e-01 -1.0 1.00e+00 1.25e-01h 1
11 6.1546734e+00 4.75e-02 4.15e+03 -1.0 7.14e-01 - 1.00e+00 6.44e-01h 1
12 6.1446716e+00 2.01e-02 9.53e+03 -1.0 1.21e+00 - 1.00e+00 5.79e-01h 1
13 6.1404036e+00 9.88e-03 2.21e+04 -1.0 9.75e-01 - 1.00e+00 5.87e-01h 1
14 6.1376399e+00 4.50e-03 5.26e+04 -1.0 9.21e-01 - 1.00e+00 5.88e-01h 1
15 6.1361150e+00 2.11e-03 1.25e+05 -1.0 7.41e-01 - 1.00e+00 5.91e-01h 1
16 6.1351608e+00 9.63e-04 2.89e+05 -1.0 5.95e-01 - 1.00e+00 5.98e-01h 1
17 6.1345596e+00 4.31e-04 6.32e+05 -1.0 4.38e-01 - 1.00e+00 6.15e-01h 1
18 6.1344562e+00 3.57e-04 2.89e+06 -1.0 3.08e-01 - 1.00e+00 1.64e-01f 3
19 6.1339299e+00 6.40e-05 5.29e+05 -1.0 3.58e-01 - 1.00e+00 9.04e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 6.1339131e+00 5.84e-05 5.21e+06 -1.0 2.91e-02 - 1.00e+00 3.48e-01f 2
21 6.1336199e+00 1.02e-05 3.75e+05 -1.0 1.00e-01 - 1.00e+00 1.00e+00h 1
22 6.1335417e+00 4.72e-06 1.16e+06 -1.0 2.95e-02 - 1.00e+00 6.66e-01h 1
23 6.1334913e+00 2.46e-06 3.69e+06 -1.0 2.73e-02 - 1.00e+00 3.97e-01f 2
24 6.1334055e+00 4.88e-07 5.89e+05 -1.0 1.34e-02 - 1.00e+00 1.00e+00h 1
25 6.1333506e+00 1.59e-08 8.75e+04 -1.0 8.26e-03 - 1.00e+00 1.00e+00h 1
26 6.1333604e+00 5.74e-08 3.18e+05 -1.0 4.19e-03 - 1.00e+00 3.61e-01f 2
27 6.1333559e+00 3.78e-08 2.30e+05 -1.0 6.97e-04 - 1.00e+00 8.11e-01h 1
28 6.1333447e+00 3.25e-09 1.96e+06 -1.0 2.95e-03 - 1.00e+00 4.96e-01f 2
29 6.1333430e+00 0.00e+00 2.44e+03 -1.0 2.20e-04 - 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
30 6.1333427e+00 0.00e+00 3.07e+03 -2.5 3.24e-05 - 1.00e+00 1.00e+00f 1
31 6.1333393e+00 0.00e+00 2.13e+01 -2.5 3.73e-05 4.0 1.00e+00 1.00e+00f 1
Cannot call restoration phase at point that is almost feasible (violation 0.000000e+00).
Abort in line search due to no other fall back.
Number of Iterations....: 31
(scaled) (unscaled)
Objective...............: 6.1333392656866677e+00 6.1333392656866677e+00
Dual infeasibility......: 2.1310536983443171e+01 2.1310536983443171e+01
Constraint violation....: 0.0000000000000000e+00 0.0000000000000000e+00
Variable bound violation: 4.4274786760585229e-09 4.4274786760585229e-09
Complementarity.........: 3.1439668442150119e-03 3.1439668442150119e-03
Overall NLP error.......: 1.6855608441038162e-02 2.1310536983443171e+01
Number of objective function evaluations = 65
Number of objective gradient evaluations = 33
Number of equality constraint evaluations = 65
Number of inequality constraint evaluations = 65
Number of equality constraint Jacobian evaluations = 33
Number of inequality constraint Jacobian evaluations = 33
Number of Lagrangian Hessian evaluations = 32
Total seconds in IPOPT = 0.014
EXIT: Error in step computation!StrongDualityMode and Ipopt.Optimizer
set_optimizer(model, Ipopt.Optimizer)
BilevelJuMP.set_mode(model, BilevelJuMP.StrongDualityMode())
optimize!(model)
objective_value(model)
@assert abs(objective_value(model) - (3 * (7/2 * 8/15) + 8/15)) < 1e-1 # srcThis is Ipopt version 3.14.4, running with linear solver MUMPS 5.4.1.
Number of nonzeros in equality constraint Jacobian...: 4
Number of nonzeros in inequality constraint Jacobian.: 35
Number of nonzeros in Lagrangian Hessian.............: 8
Total number of variables............................: 6
variables with only lower bounds: 1
variables with lower and upper bounds: 0
variables with only upper bounds: 3
Total number of equality constraints.................: 1
Total number of inequality constraints...............: 9
inequality constraints with only lower bounds: 3
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 6
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 0.0000000e+00 8.00e+00 1.37e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 6.9373007e-01 7.10e+00 4.04e+00 -1.0 4.21e+00 - 2.29e-02 1.15e-01h 1
2 4.1458199e+00 2.60e+00 3.57e+00 -1.0 3.84e+00 - 1.18e-01 6.25e-01h 1
3 4.8949366e+00 1.62e+00 3.58e+00 -1.0 1.45e+00 - 9.38e-01 3.62e-01h 1
4 5.7107572e+00 6.46e-01 1.78e+00 -1.0 1.27e+00 - 3.22e-01 6.17e-01h 1
5 5.9360287e+00 3.84e-01 4.61e+00 -1.0 8.08e-01 - 7.52e-01 4.57e-01h 1
6 6.0003610e+00 1.73e-01 7.61e-01 -1.0 5.81e+00 - 2.74e-01 3.48e-01h 1
7 6.1244252e+00 1.29e-01 6.99e-01 -1.7 1.39e+00 - 8.70e-01 9.43e-01h 1
8 6.1300137e+00 8.68e-02 1.19e+02 -1.7 4.08e-01 -2.0 1.00e+00 3.26e-01h 1
9 6.1336984e+00 2.63e-02 1.44e+02 -1.7 2.77e+00 - 1.00e+00 6.20e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 6.1317629e+00 9.14e-03 2.51e+02 -1.7 1.45e+01 - 6.09e-01 3.74e-01h 1
11 6.1326207e+00 8.08e-03 3.75e+02 -1.7 7.78e+01 - 5.24e-01 3.34e-01f 1
12 6.1330471e+00 4.49e-03 5.42e+02 -1.7 5.06e+01 - 5.84e-01 4.01e-01H 1
13 6.1330042e+00 4.19e-03 2.38e+02 -1.7 2.41e+02 - 3.12e-01 4.80e-01F 1
14 6.1332031e+00 4.03e-03 2.43e+02 -1.7 3.17e+02 - 3.74e-01 3.74e-01H 1
15 6.1332221e+00 6.18e-04 7.32e+02 -1.7 5.37e+02 - 5.47e-01 4.62e-01H 1
16 6.1332962e+00 6.48e-04 5.28e+02 -1.7 9.70e+02 - 4.48e-01 4.99e-01H 1
17 6.1333059e+00 6.51e-03 1.37e+04 -1.7 1.92e+03 - 7.43e-01 3.38e-01f 2
18 6.1333095e+00 6.49e-03 3.75e+04 -1.7 3.05e+03 - 6.23e-01 1.25e-01h 4
19 6.1333111e+00 6.32e-03 7.22e+04 -1.7 4.20e+03 - 7.09e-01 6.25e-02h 5
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 6.1333127e+00 6.18e-03 1.06e+05 -1.7 4.53e+03 - 6.98e-01 6.25e-02h 5
21 6.1333141e+00 6.05e-03 1.40e+05 -1.7 4.98e+03 - 7.11e-01 6.25e-02h 5
22 6.1333155e+00 5.93e-03 1.73e+05 -1.7 5.43e+03 - 7.12e-01 6.25e-02h 5
23 6.1333167e+00 5.81e-03 2.06e+05 -1.7 5.95e+03 - 7.18e-01 6.25e-02h 5
24 6.1333179e+00 5.70e-03 2.39e+05 -1.7 6.52e+03 - 7.21e-01 6.25e-02h 5
25 6.1333190e+00 5.60e-03 2.71e+05 -1.7 7.14e+03 - 7.25e-01 6.25e-02h 5
26 6.1333200e+00 5.50e-03 3.03e+05 -1.7 7.81e+03 - 7.28e-01 6.25e-02h 5
27 6.1333348e+00 6.40e-02 2.04e+04 -1.7 8.54e+03 - 7.31e-01 1.00e+00w 1
28 6.1333342e+00 1.11e-02 1.79e+05 -1.7 4.04e+03 - 1.00e+00 8.78e-01w 1
29 6.1333333e+00 8.74e-03 1.16e+05 -1.7 6.41e+03 - 1.00e+00 5.31e-01w 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
30 6.1333204e+00 5.39e-03 3.47e+05 -1.7 3.50e+03 - 7.31e-01 3.12e-02h 5
31 6.1333209e+00 5.28e-03 3.91e+05 -1.7 9.06e+03 - 7.54e-01 3.12e-02h 6
32 6.1333211e+00 5.22e-03 4.39e+05 -1.7 9.36e+03 - 7.46e-01 1.56e-02h 7
33 6.1333213e+00 5.15e-03 4.87e+05 -1.7 9.68e+03 - 7.64e-01 1.56e-02h 7
34 6.1333214e+00 5.13e-03 5.38e+05 -1.7 9.81e+03 - 7.57e-01 3.91e-03h 9
35 6.1333222e+00 5.08e-03 5.53e+05 -1.7 9.95e+03 - 7.71e-01 6.25e-02h 5
36 6.1333230e+00 5.01e-03 5.65e+05 -1.7 1.05e+04 - 7.30e-01 6.25e-02h 5
37 6.1333237e+00 4.95e-03 5.79e+05 -1.7 1.17e+04 - 7.55e-01 6.25e-02h 5
38 6.1333244e+00 4.88e-03 5.92e+05 -1.7 1.27e+04 - 7.45e-01 6.25e-02h 5
39 6.1333250e+00 4.81e-03 6.05e+05 -1.7 1.39e+04 - 7.55e-01 6.25e-02h 5
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
40 6.1333340e+00 6.12e-02 1.79e+04 -1.7 1.51e+04 - 7.55e-01 1.00e+00w 1
41 6.1333339e+00 1.21e-02 1.51e+05 -1.7 1.00e+04 - 1.00e+00 8.38e-01w 1
42 6.1333333e+00 1.17e-02 4.61e+05 -1.7 1.60e+04 - 1.00e+00 7.32e-01w 1
43 6.1333335e+00 2.88e-03 1.85e+05 -1.7 6.33e+03 - 1.00e+00 8.91e-01h 1
44 6.1333334e+00 2.97e-07 3.08e-02 -1.7 1.80e-03 -2.5 1.00e+00 1.00e+00f 1
45 6.1333333e+00 5.94e-08 1.57e+00 -8.6 2.63e-01 - 1.00e+00 1.00e+00h 1
46 6.1333333e+00 0.00e+00 4.62e+02 -8.6 3.21e+00 - 9.95e-01 1.00e+00h 1
In iteration 46, 1 Slack too small, adjusting variable bound
47 6.1333333e+00 3.64e-12 2.79e-01 -8.6 5.59e-08 -3.0 1.00e+00 9.99e-01h 1
48 6.1333333e+00 6.89e-04 3.75e+00 -8.6 2.25e+04 - 4.67e-01 1.00e+00h 1
49 6.1333333e+00 0.00e+00 1.19e-08 -8.6 3.22e-05 -3.4 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
50 6.1333333e+00 3.08e-04 4.13e-02 -9.0 1.78e+04 - 8.51e-01 1.00e+00h 1
51 6.1333333e+00 2.52e-04 6.84e-01 -9.0 6.87e+04 - 6.60e-01 1.00e+00h 1
52 6.1333333e+00 2.29e-04 4.52e-01 -9.0 9.58e+04 - 8.64e-01 2.72e-01h 2
53 6.1333333e+00 1.05e-03 4.74e-01 -9.0 2.54e+06 - 4.38e-02 3.12e-02h 6
54 6.1333333e+00 6.98e-04 3.14e-01 -9.0 5.97e-04 -3.9 1.00e+00 3.37e-01h 2
55 6.1333333e+00 5.39e-04 2.25e-01 -9.0 7.13e+04 - 1.00e+00 2.43e-01h 2
56 6.1333333e+00 2.30e-05 4.05e-02 -9.0 1.95e+04 - 1.00e+00 1.00e+00h 1
57 6.1333333e+00 3.20e-06 2.46e-04 -9.0 5.39e+03 - 1.00e+00 1.00e+00h 1
58 6.1333333e+00 1.20e-08 4.72e-06 -9.0 7.70e+02 - 1.00e+00 1.00e+00h 1
59 6.1333333e+00 0.00e+00 1.29e-06 -9.0 5.09e+02 - 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
60 6.1333333e+00 1.16e-10 5.39e-06 -9.0 1.04e+03 - 1.00e+00 1.00e+00h 1
61 6.1333333e+00 0.00e+00 4.44e-07 -9.0 2.98e+02 - 1.00e+00 1.00e+00h 1
62 6.1333333e+00 0.00e+00 1.10e-07 -9.0 1.48e+02 - 1.00e+00 1.00e+00h 1
63 6.1333333e+00 0.00e+00 1.04e-06 -9.0 8.86e+02 - 1.00e+00 5.00e-01h 2
64 6.1333333e+00 2.33e-10 1.55e-06 -9.0 5.56e+02 - 1.00e+00 1.00e+00h 1
65 6.1333333e+00 1.16e-10 4.47e-06 -9.0 9.43e+02 - 1.00e+00 1.00e+00h 1
66 6.1333333e+00 1.16e-10 2.33e-06 -9.0 6.81e+02 - 1.00e+00 1.00e+00h 1
67 6.1333333e+00 0.00e+00 1.37e-06 -9.0 4.06e+02 - 1.00e+00 5.00e-01h 2
68 6.1333333e+00 0.00e+00 6.94e-07 -9.0 3.72e+02 - 1.00e+00 1.00e+00h 1
69 6.1333333e+00 1.16e-10 1.40e-09 -9.0 1.67e+01 - 1.00e+00 1.00e+00h 1
Number of Iterations....: 69
(scaled) (unscaled)
Objective...............: 6.1333332729116652e+00 6.1333332729116652e+00
Dual infeasibility......: 1.3969838619232178e-09 1.3969838619232178e-09
Constraint violation....: 1.1641532182693481e-10 1.1641532182693481e-10
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 9.0909101251615372e-10 9.0909101251615372e-10
Overall NLP error.......: 1.3969838619232178e-09 1.3969838619232178e-09
Number of objective function evaluations = 212
Number of objective gradient evaluations = 70
Number of equality constraint evaluations = 212
Number of inequality constraint evaluations = 212
Number of equality constraint Jacobian evaluations = 70
Number of inequality constraint Jacobian evaluations = 70
Number of Lagrangian Hessian evaluations = 69
Total seconds in IPOPT = 0.029
EXIT: Optimal Solution Found.MixedMode and SCIP.Optimizer
set_optimizer(model, SCIP.Optimizer)
BilevelJuMP.set_mode(model, BilevelJuMP.MixedMode(default = BilevelJuMP.SOS1Mode()))
BilevelJuMP.set_mode(c1, BilevelJuMP.IndicatorMode())
BilevelJuMP.set_mode(c3, BilevelJuMP.SOS1Mode())
optimize!(model)
objective_value(model)
@assert abs(objective_value(model) - (3 * (3.5 * 8/15) + 8/15)) < 1e-1 # srcpresolving:
(round 1, fast) 2 del vars, 5 del conss, 0 add conss, 5 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 2, fast) 2 del vars, 5 del conss, 0 add conss, 8 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 3, fast) 2 del vars, 5 del conss, 0 add conss, 10 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 4, exhaustive) 2 del vars, 7 del conss, 0 add conss, 10 chg bounds, 2 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(0.0s) probing cycle finished: starting next cycle
(0.0s) symmetry computation skipped: there exist constraints that cannot be handled by symmetry methods.
presolving (5 rounds: 5 fast, 2 medium, 2 exhaustive):
2 deleted vars, 7 deleted constraints, 0 added constraints, 10 tightened bounds, 0 added holes, 2 changed sides, 0 changed coefficients
7 implications, 0 cliques
presolved problem has 11 variables (1 bin, 0 int, 0 impl, 10 cont) and 12 constraints
5 constraints of type <SOS1>
7 constraints of type <linear>
Presolving Time: 0.00
time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl.
p 0.0s| 1 | 0 | 5 | - | locks| 0 | 11 | 12 | 7 | 0 | 0 | 0 | 0 | 0.000000e+00 | 6.133333e+00 | Inf | unknown
0.0s| 1 | 0 | 10 | - | 641k | 0 | 11 | 11 | 7 | 0 | 0 | 0 | 0 | 6.133333e+00 | 6.133333e+00 | 0.00%| unknown
SCIP Status : problem is solved [optimal solution found]
Solving Time (sec) : 0.00
Solving Nodes : 1
Primal Bound : +6.13333333333333e+00 (1 solutions)
Dual Bound : +6.13333333333333e+00
Gap : 0.00 %SCIP requires a non-standard installation procedure in windows. See SCIP.jl for more details.
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