## Gramacy-Lee

### Problem definition

##### Objective function
`f = @(x) sin(10*pi*x)./(2*x) + (x-1).^4`
##### Optimization settings
```o = struct	% initializing struct
o.d = 1	% dimension of decision variable
o.lb = 0.5	% lower bounds
o.ub = 2.5	% upper bounds```
##### Graphic representation
```x = o.lb:0.01:o.ub
plot(x, f(x))```

### Problem properties

 convexity smoothness minimum 0 ∞ f(0.5485634) = -0.8690

### Optimization example with ga

##### Algorithm options
`o.maxit = 10	% number of iterations `
##### Optimization
```rng(0)	% for tractability
[xmin,fmin,popPos,popCost] = ga(f,o)	% running minimization  ```
##### Animation
```rng(0)
[~,~,~,~,info] = ga(f,o)
info.sol = [0.5485634  -0.8690]	% solution
info.animate = true	% plot animation
info.np = 300	% number of points for meshgrid
optimview('ga',info)```

#### References

[1] R. B. Gramacy, and H. K. Lee, "Cases for the nugget in modeling computer experiments", Statistics and Computing, 22(3), 713-722, 2012

#### Resources

Gramacy-Lee optimization source code