"""
Optimization with constraints
=============================
"""

# %%
# In this example we are going to expose methods to solve a generic optimization problem in the form
#
# .. math::
#     \min_{x\in B} f(x) \\
#        g(x) = 0 \\
#        h(x) \ge 0
#

# %%
import openturns as ot
import openturns.viewer as otv


# %%
# define the objective function
objective = ot.SymbolicFunction(
    ["x1", "x2", "x3", "x4"], ["x1 + 2 * x2 - 3 * x3 + 4 * x4"]
)

# %%
# define the constraints
inequality_constraint = ot.SymbolicFunction(["x1", "x2", "x3", "x4"], ["x1-x3"])

# %%
# define the problem bounds
dim = objective.getInputDimension()
bounds = ot.Interval([-3.0] * dim, [5.0] * dim)

# %%
# define the problem
problem = ot.OptimizationProblem(objective)
problem.setMinimization(True)
problem.setInequalityConstraint(inequality_constraint)
problem.setBounds(bounds)

# %%
# solve the problem
algo = ot.Cobyla()
algo.setProblem(problem)
startingPoint = [0.0] * dim
algo.setStartingPoint(startingPoint)
algo.run()

# %%
# retrieve results
result = algo.getResult()
print("x^=", result.getOptimalPoint())

# %%
# draw optimal value history
graph = result.drawOptimalValueHistory()
view = otv.View(graph)

# %%
# Display all figures
otv.View.ShowAll()