It is a local search method. The approach rambles in the objective function from a start point into direction of most precipitous descent.
The increasing of the objective function at a actual matched point is determined by tactile steps. The exactly partial derivatives of the objective function depending on the optimization variables are also replaced by difference quotients. The used tactile step increment should be adapted to surface of the objective function. This step increment results normally at begin of optimization from 1/1000 of the given bounds (upper-lower) of a optimization variable. It must be also at least twice the accuracy of design parameter. This start step increments are influenced by changing of limits and accuracies of optimization variables.
The tactile steps are used to improve the solution point. At a tactile cycle, a discrete search cycle will be executed consecutively from a start vector in each coordinate direction. If a tactile step in one direction leads to no success (no improvement of fitness function), the contrarily direction will additionally be raster. If no further improvement of the objective function is archived, the optimization variable will be reset to old value.
After finish of a tactile phase, the extrapolation comes. A bigger tactile step will be executed in determined direction of most precipitous descent. If a improvement of the objective function is achieved, a re-extrapolation is double big like previous extrapolation. If the approach rubles over the most deep point, the step increments will be reduced stepwise for extrapolation. The optimization vector will be reset to old value for new tactile cycle.
If no improvement of the objective function at a longer time is achieved, the Hooke-Jeeves-method controls the start step increment down. This step increment get most the stochastic roughness of the objective function, the optimization get hanging at a point, which can be local optima or at a constraint limit. This should be more investigated.