# Optimization using NLoptΒΆ

In this example we are going to explore optimization using the interface to the NLopt library.

```import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt

ot.Log.Show(ot.Log.NONE)
```

List available algorithms

```for algo in ot.NLopt.GetAlgorithmNames():
print(algo)
```
```AUGLAG
AUGLAG_EQ
GD_MLSL
GD_MLSL_LDS
GN_CRS2_LM
GN_DIRECT
GN_DIRECT_L
GN_DIRECT_L_NOSCAL
GN_DIRECT_L_RAND
GN_DIRECT_L_RAND_NOSCAL
GN_DIRECT_NOSCAL
GN_ESCH
GN_ISRES
GN_MLSL
GN_MLSL_LDS
GN_ORIG_DIRECT
GN_ORIG_DIRECT_L
G_MLSL
G_MLSL_LDS
LD_AUGLAG
LD_AUGLAG_EQ
LD_CCSAQ
LD_LBFGS
LD_MMA
LD_SLSQP
LD_TNEWTON
LD_TNEWTON_PRECOND
LD_TNEWTON_PRECOND_RESTART
LD_TNEWTON_RESTART
LD_VAR1
LD_VAR2
LN_AUGLAG
LN_AUGLAG_EQ
LN_BOBYQA
LN_COBYLA
LN_NEWUOA
LN_SBPLX
```

More details on NLopt algorithms are available here .

The optimization algorithm is instantiated from the NLopt name

```algo = ot.NLopt("LD_SLSQP")
```

define the problem

```objective = ot.SymbolicFunction(["x1", "x2"], ["100*(x2-x1^2)^2+(1-x1)^2"])
inequality_constraint = ot.SymbolicFunction(["x1", "x2"], ["x1-2*x2"])
dim = objective.getInputDimension()
bounds = ot.Interval([-3.0] * dim, [5.0] * dim)
problem = ot.OptimizationProblem(objective)
problem.setMinimization(True)
problem.setInequalityConstraint(inequality_constraint)
problem.setBounds(bounds)
```

solve the problem

```algo.setProblem(problem)
startingPoint = [0.0] * dim
algo.setStartingPoint(startingPoint)
algo.run()
```

retrieve results

```result = algo.getResult()
print("x^=", result.getOptimalPoint())
```
```x^= [0.517441,0.258721]
```

draw optimal value history

```graph = result.drawOptimalValueHistory()
view = viewer.View(graph)
plt.show()
```