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Mesh Adaptive Direct Search (MASH) is an algorithm for black box optimization

I want to understand an implement this method to solve some 2D multivariate blackbox function $f(x,y)$, but am having trouble understanding the algorithm.

What I understand so far:

  1. Start with some initial trial value $x_0, y_0$
  2. Create the 'Mesh'
  3. Search a finite number of points on the mesh
  4. If the search fails, perform a 'Poll' step $P_k = x_k + \Delta_k d$

Where I am confused

  1. How do we 'create' the Mesh? How does the mesh change with each iteration?

  2. How do we perform a search step? How do we choose which points on the mesh to search?

  3. What does it mean to perform a poll step? How should $\Delta_k$ change? What is meant by $d$?

Thanks in advance for an help

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  • $\begingroup$ Shouldn't it be Mesh Adaptive Direct Search (MADS)? $\endgroup$ – Remis Mar 29 '18 at 6:35

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