# Optimization: Trust region method

I am trying to optimize a 6-D objective function using Trust region method. I am using Matlab's inbuilt function fmincon which requires me to calculate finite difference gradient and Hessian. The issue is that when I fixed three of the six parameters and optimized the 3-D function, a finite difference step length of $\Delta x= 10^{-2}$ gave marvelous results. However when I am trying to optimize in 6-D (i.e. keeping all the six parameters as variable), any finite difference step length below 1 does not solve the problem well, $\Delta x=1$ however works nicely in 6-D. Anyone who could help me figure out a possible explanation for this observation?

Details of my code:-

1) I use numerical simulation to evaluate objective function (Quasi Monte Carlo Method)

2) Objective function, $f = \mathrm{func}(V)$, where $V= (\mu_1+\sigma_1\cdot s_1)\cdot a + (\mu_2+\sigma_2\cdot s_2)\cdot b + (\mu_3+\sigma_3\cdot s_3)\cdot c$, $\{\mu_1,\mu_2,\mu_3,\sigma_1,\sigma_2,\sigma_3\}$ are the six parameters; $\{s_1,s_2,s_3\}$ are quasi-random numbers in $(0,1)$;
$a$, $b$, $c$ are observed values

3) In 6-D case, $V= (\mu_1+\sigma_1\cdot s_1)\cdot a + (\mu_2+\sigma_2\cdot s_2)\cdot b + (\mu_3+\sigma_3\cdot s_3)\cdot c$ => inaccuracy in objective function value due to random numbers

In 3-D case, $V = \mu_1\cdot a + \mu_2\cdot b + \mu_3\cdot c$
=> no random numbers involved

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