Is there a Hessian-free optimization algorithm?

I need to do some constrained optimization work on a function which is actually a Simulink model involving hundreds of variables. Each function evaluation takes about 6 or 7 seconds. So, lowering the number of function evaluations is critical to me.

I've looked into the available algorithms with fmincon (interior-point, sqp, active-set, trust-region-reflective) and they all require Hessian calculation.

Is there any algorithm available in MATLAB that can optimize the function via only function or gradient evaluation? (and does not require the time-consuming Hessian calculation)

Answer 1

[Sean de Wolski]

In the Global Optimization Toolbox:

doc patternsearch

perhaps

Answer 2

[Mary Fenelon]

If your functions are smooth, a gradient-based solver such as fmincon may take fewer function evaluation overall. Some of its algorithms do not calculate the Hessian using finite differences but use an approximation to the Hessian; see more here . You might also want to review the docs on choosing an appropriate step size when optimizing a simulation to help decide between a gradient-based solver and patternsearch but it's hard to predict so if possible give them both a try.