What Is Direct Search?
Direct search is a method for solving optimization problems
that does not require any information about the gradient of the objective
function. Unlike more traditional optimization methods that use information
about the gradient or higher derivatives to search for an optimal
point, a direct search algorithm searches a set of points around the
current point, looking for one where the value of the objective function
is lower than the value at the current point. You can use direct search
to solve problems for which the objective function is not differentiable,
or is not even continuous.
Genetic Algorithm and Direct Search Toolbox functions include
two direct search algorithms called the generalized pattern search
(GPS) algorithm and the mesh adaptive search (MADS) algorithm. Both
are pattern search algorithms that compute a
sequence of points that approach an optimal point. At each step, the
algorithm searches a set of points, called a mesh,
around the current point—the point computed
at the previous step of the algorithm. The mesh is formed by adding
the current point to a scalar multiple of a set of vectors called
a pattern. If the pattern search algorithm finds
a point in the mesh that improves the objective function at the current
point, the new point becomes the current point at the next step of
the algorithm.
The MADS algorithm is a modification of the GPS algorithm. The
algorithms differ in how the set of points forming the mesh is computed.
The GPS algorithm uses fixed direction vectors, whereas the MADS algorithm
uses a random selection of vectors to define the mesh.
 | Getting Started with Direct Search | | Performing a Pattern Search |  |
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