Nonlinear Least Squares - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English

The following options are supported.

Table 4.9 Table of Options for Nonlinear Least Squares.#

Option name

Type

Default

Description

Constraints

ralfit model

string

\(s=\) hybrid

NLLS model to solve.

\(s=\) gauss-newton, hybrid, quasi-newton, or tensor-newton.

print level

integer

\(i=1\)

Set level of verbosity for the solver: from 0, indicating no output, to 5, which is very verbose.

\(0 \le i \le 5\)

derivative test tol

real

\(r=10^{-4}\)

Tolerance used to check user-provided derivatives by finite-differences. If <print level> is 1, then only the entries with larger discrepancy are reported, and if print level is greater than or equal to 2, then all entries are printed.

\(0 < r \le 10\)

ralfit iteration limit

integer

\(i=100\)

Maximum number of iterations to perform.

\(1 \le i\)

lbfgsb memory limit

integer

\(i=11\)

Number of vectors to use for approximating the Hessian.

\(1 \le i \le 1000\)

lbfgsb iteration limit

integer

\(i=10000\)

Maximum number of iterations to perform.

\(1 \le i\)

coord iteration limit

integer

\(i=100000\)

Maximum number of iterations to perform.

\(1 \le i\)

monitoring frequency

integer

\(i=0\)

How frequently to call the user-supplied monitor function.

\(0 \le i\)

check derivatives

string

\(s=\) no

Check user-provided derivatives using finite-differences.

\(s=\) no, or yes.

ralfit nlls method

string

\(s=\) galahad

NLLS solver to use.

\(s=\) aint, galahad, linear solver, more-sorensen, or powell-dogleg.

optim method

string

\(s=\) lbfgsb

Select optimization solver to use.

\(s=\) bfgs, coord, lbfgs, lbfgsb, or ralfit.

ralfit convergence step size

real

\(r=\varepsilon/2\)

Absolute tolerance over the step size to declare convergence for the iterative optimization step. See details in optimization solver documentation.

\(0 < r < 1\)

coord restart

integer

\(i=\infty\)

Number of inner iterations to perform before requesting to perform a full evaluation of the step function.

\(0 \le i\)

ralfit convergence rel tol grd

real

\(r=10/21\sqrt{2\,\varepsilon}\)

Relative tolerance on the gradient norm to declare convergence for the iterative optimization step. See details in optimization solver documentation.

\(0 < r < 1\)

coord skip max

integer

\(i=100\)

Maximum times a coordinate can be skipped, after this the coordinate is checked.

\(10 \le i\)

coord skip min

integer

\(i=2\)

Minimum times a coordinate change is smaller than coord skip tol to start skipping.

\(2 \le i\)

check data

string

\(s=\) no

Check input data for NaNs prior to performing computation.

\(s=\) no, or yes.

storage order

string

\(s=\) column-major

Whether data is supplied and returned in row- or column-major order.

\(s=\) c, column-major, f, fortran, or row-major.

ralfit globalization method

string

\(s=\) trust-region

Globalization method to use. This parameter makes use of the regularization term and power option values.

\(s=\) reg, regularization, tr, or trust-region.

ralfit convergence abs tol fun

real

\(r=10/21\sqrt{2\,\varepsilon}\)

Absolute tolerance to declare convergence for the iterative optimization step. See details in optimization solver documentation.

\(0 < r < 1\)

print options

string

\(s=\) no

Print options list.

\(s=\) no, or yes.

debug

integer

\(i=0\)

Set debug level (internal use).

\(0 \le i \le 3\)

regularization term

real

\(r=0\)

Value of the regularization term. A value of 0 disables regularization.

\(0 \le r\)

finite differences step

real

\(r=10\;\sqrt{2\,\varepsilon}\)

Size of step to use for estimating derivatives using finite-differences.

\(0 < r < 10\)

lbfgsb convergence tol

real

\(r=\sqrt{2\,\varepsilon}\)

Tolerance of the projected gradient infinity norm to declare convergence.

\(0 < r < 1\)

lbfgsb progress factor

real

\(r=\frac{10}{\sqrt{2\,\varepsilon}}\)

The iteration stops when (f^k - f{k+1})/max{abs(fk);abs(f{k+1});1} <= factr*epsmch where epsmch is the machine precision. Typical values for type double: 10e12 for low accuracy; 10e7 for moderate accuracy; 10 for extremely high accuracy.

\(0 \le r\)

regularization power

string

\(s=\) quadratic

Value of the regularization power term.

\(s=\) cubic, or quadratic.

infinite bound size

real

\(r=10^{20}\)

Threshold value to take for +/- infinity.

\(1000 < r\)

time limit

real

\(r=10^6\)

Maximum time allowed to run (in seconds).

\(0 < r\)

coord convergence tol

real

\(r=50\;\sqrt{2\,\varepsilon}\)

Tolerance of the projected gradient infinity norm to declare convergence.

\(0 < r < 1\)

coord optimality tol

real

\(r=50\;\sqrt{2\,\varepsilon}\)

Tolerance to declare optimality, e.g. dual-gap, KKT conditions, etc.

\(0 \le r\)

ralfit convergence rel tol fun

real

\(r=10/21\sqrt{2\,\varepsilon}\)

Relative tolerance to declare convergence for the iterative optimization step. See details in optimization solver documentation.

\(0 < r < 1\)

coord skip tol

real

\(r=50\;\sqrt{2\,\varepsilon}\)

Coordinate skip tolerance, a given coordinate could be skipped if the change between two consecutive iterates is less than tolerance. Any negative value disables the skipping scheme.

\(-1 \le r\)

ralfit convergence abs tol grd

real

\(r=500\;\sqrt{2\,\varepsilon}\)

Absolute tolerance on the gradient norm to declare convergence for the iterative optimization step. See details in optimization solver documentation.

\(0 < r < 1\)