Add test for Luksan-Vlcek Problem 10 in test_lukvle10.py

Author: yemine0x01

tests/test_lukvle10.py

@@ -0,0 +1,49 @@
+import pytest
+
+import pyoptinterface as poi
+from pyoptinterface import ipopt, nl
+
+
+def test_nlp_lukvle10(nlp_model_ctor):
+    # LUKSAN-VLCEK Problem 10
+    #
+    # min  sum[i=1..n] (x[2i]^2)^(x[2i+1]^2 + 1) + (x[2i+1]^2)^(x[2i]^2 + 1)
+    # s.t. (3 - 2*x[i+1])*x[i+1] + 1 - x[i] - 2*x[i+2] = 0,  i = 1,...,2n-2
+    #
+    # Starting point: x[2i] = 1, x[2i+1] = -1
+    model = nlp_model_ctor()
+    if isinstance(model, ipopt.Model):
+        pytest.skip("lukvle10 is too large to be supported with IPOPT")
+
+    n = 100000
+    x = model.add_m_variables(2 * n, name="x")
+
+    for i in range(2 * n - 2):
+        model.add_quadratic_constraint(
+            (3 - 2 * x[i + 1]) * x[i + 1] + 1 - x[i] - 2 * x[i + 2],
+            poi.ConstraintSense.Equal,
+            0.0,
+            name=f"c{i}",
+        )
+
+    with nl.graph():
+        for i in range(n):
+            x_sq_2i = x[2 * i] * x[2 * i]
+            x_sq_2ip1 = x[2 * i + 1] * x[2 * i + 1]
+            model.add_nl_objective(
+                nl.pow(x_sq_2i, x_sq_2ip1 + 1) + nl.pow(x_sq_2ip1, x_sq_2i + 1)
+            )
+
+    for i in range(n):
+        model.set_variable_attribute(x[2 * i], poi.VariableAttribute.PrimalStart, 1.0)
+        model.set_variable_attribute(
+            x[2 * i + 1], poi.VariableAttribute.PrimalStart, -1.0
+        )
+
+    model.optimize()
+
+    termination_status = model.get_model_attribute(poi.ModelAttribute.TerminationStatus)
+    assert (
+        termination_status == poi.TerminationStatusCode.LOCALLY_SOLVED
+        or termination_status == poi.TerminationStatusCode.OPTIMAL
+    )