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Setting Solver Tolerances

Tolerance refers to how small a parameter, such a mesh size, can become before the search is halted or changed in some way. You can specify the value of the following tolerances using optimoptions or the Optimization app:

  • Mesh tolerance — When the current mesh size is less than the value of Mesh tolerance, the algorithm halts.

  • X tolerance — After a successful poll, if the distance from the previous best point to the current best point is less than the value of X tolerance, the algorithm halts.

  • Function tolerance — After a successful poll, if the difference between the function value at the previous best point and function value at the current best point is less than the value of Function tolerance, the algorithm halts.

  • Nonlinear constraint tolerance — The algorithm treats a point to be feasible if constraint violation is less than ConstraintTolerance.

  • Bind tolerance — Bind tolerance applies to linearly constrained problems. It specifies how close a point must get to the boundary of the feasible region before a linear constraint is considered to be active. When a linear constraint is active, the pattern search polls points in directions parallel to the linear constraint boundary as well as the mesh points.

    Usually, you should set Bind tolerance to be at least as large as the maximum of Mesh tolerance, X tolerance, and Function tolerance.

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