optim_doc: nonlin_min

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### 1.1 Frontend nonlin_min for scalar non-linear optimization

Function File: [p, objf, cvg, outp] = nonlin_min (f, pin)
Function File: [p, objf, cvg, outp] = nonlin_min (f, pin, settings)

  Frontend for nonlinear minimization of a scalar objective function.

  The functions supplied by the user have a minimal interface; any additionally needed constants can be supplied by wrapping the user functions into anonymous functions.

  The following description applies to usage with vector-based parameter handling. Differences in usage for structure-based parameter handling will be explained separately.

  f: objective function. It gets a column vector of real parameters as argument. In gradient determination, this function may be called with an informational second argument, whose content depends on the function for gradient determination.

  pin: real column vector of initial parameters.

  settings: structure whose fields stand for optional settings referred to below. The fields can be set by `optimset()`.

  The returned values are the column vector of final parameters p, the final value of the objective function objf, an integer cvg indicating if and how optimization succeeded or failed, and a structure outp with additional information, curently with possible fields: `niter`, the number of iterations, `nobjf`, the number of objective function calls (indirect calls by gradient function not counted), `lambda`, the lambda of constraints at the result, and `user_interaction`, information on user stops (see settings). The backend may define additional fields. cvg is greater than zero for success and less than or equal to zero for failure; its possible values depend on the used backend and currently can be `0` (maximum number of iterations exceeded), `1` (success without further specification of criteria), `2` (parameter change less than specified precision in two consecutive iterations), `3` (improvement in objective function less than specified), `-1` (algorithm aborted by a user function), or `-4` (algorithm got stuck).

#### Settings

The fields of the settings structure can be set with (octave)optimset.

For settings common to all frontends (including these for statistics) see Common frontend options.

For additional settings common to all optimization frontends see Common optimization options.

#### Specific defaults:

`Algorithm`: | "lm_feasible"

#### Additional settings:

`objf_grad`

  Function computing the gradient of the objective function with respect to the parameters. Default: real finite differences. Will be called with the column vector of parameters and an informational structure as arguments. If `dfdp` was specified by the user, the informational structure has the fields `f`: value of objective function for current parameters, `fixed`: logical vector indicating which parameters are not optimized, so these partial derivatives need not be computed and can be set to zero, `diffp`, `diff_onesided`, `lbound`, `ubound`: identical to the user settings of this name, `plabels`: 1-dimensional cell-array of column-cell-arrays, each column with labels for all parameters; the first column contains the numerical indices of the parameters; the second and third columns, present for structure based parameter handling, see Parameter structures, contain the names of the parameters and the subindices of the parameters, see Non-scalar parameters, respectively. The default gradient function will call the objective function with the second argument set with fields `f`: as the `f` passed to the gradient function, `plabels`: cell-array of 1x1 cell-arrays with the entries of the column-cell-arrays of `plabels` as passed to the jacobian function corresponding to current parameter, `side`: `0` for one-sided interval, `1` or `2`, respectively, for the sides of a two-sided interval, and `parallel`: logical scalar indicating parallel computation of partial derivatives. This information can be useful if the model function can omit some computations depending on the currently computed partial derivative.

`objf_hessian`

  Function computing the Hessian of the objective function with respect to the parameters. The default is backend specific. Will be called with the column vector of parameters as argument.

`inverse_hessian`

  Logical scalar, indicating whether the Hessian function passed by the user actually returns the inverse of the Hessian.

`complex_step_derivative_objf`

  Logical scalar, default: `false`. Estimate gradient of objective function with complex step derivative approximation. Use only if you know that your objective function is suitable for this. No user function for the gradient (`objf_grad`) must be specified.

`save_state`

  String with path to a file which will be created for periodical saving of the state of optimization. Useful for very long optimizations which might get interrupted. The format of the saved state will be backend-specific. Currently, only the `"siman"` backend honours this option. Default: empty string, meaning no saving of state.

`recover_state`

  String with path to a file created due to option `save_state`, which is used to recover a saved state before starting optimization. Default: empty string, meaning no recovering of state.

#### Structure based parameter handling

Please see Parameter structures.

#### Backend information

Please see Scalar optimization and choose backend from menu.

Next: lm_feasible, Up: Scalar optimization [Index]