16.3.3  Derivative-free constrained optimization

The fMin and fMax commands find local minima and maxima of a multivariate function, possibly subject to constraints (either equalities or inequalities), by using the COBYLA algorithm.

• fMax and fMin take four mandatory and two optional arguments:
  • expr, an expression with several variables, which does not need to be differentiable.
  • constr, a list of constraints (equalities and/or inequalities).
  • vars, a list of the variables.
  • init, an initial guess, which must be a list of nonzero reals representing a starting point (not necessarily feasible).
  • Optionally, ε, the precision. If this is not given, the default epsilon value is used (see Section 2.5.7, item 2.5.7).
  • Optionally, N, the maximum number of iterations.
• fMin(expr,constr,vars,init ⟨,ε,N ⟩) (and analogously with fMax) returns a point that minimizes (maximizes) expr subject to constr.
• If there are several feasible local minima/maxima, then the return value depends on the initial point.

Examples