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I am using the following algorithm to solve an optimization problem I have. I was wondering if there is a proper name for this algorithm in the literature.

Let $f(x)$ be my objective function.

I guess some $x_0$ and see have it performs.

Next, I randomly generate around $x_0$, some $\{x_k \}$ for $k \in [1:K]$ and see how the compare to $x_0$. If I find $x_n$ that perform better than $x_0$. I perform the same procedure again with $x_n$.

I am only starting to learn about algorithms and would be grateful if you point me to the name and some reference on similar algorithms

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    $\begingroup$ I don't recall seeing a precise name for the particular variant you have, but it's a type of Random Search - essentially a Local Search where you select elements from the neighbourhood at random. $\endgroup$
    – Luke Mathieson
    Aug 9, 2015 at 1:24

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This is a form of local search. It is similar to hill climbing. It's also reminiscent of stochastic hill climbing, as @Juho suggests.

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  • $\begingroup$ I think this is actually stochastic hill climbing, if you want to find a more exact name. $\endgroup$
    – Juho
    Aug 9, 2015 at 8:36

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