# Nonlinear Least Squares Problem without Constraints

The nonlinear least squares problem without constraints can be described as follows:

where F(x) : Rn → R is a twice differentiable function in `Rn`. Solving of the nonlinear least squares problem is searching for the best approximation to vector y with model function `fi(x)`, which has nonlinear dependence on variables х. The best approximation means that the sum of squares of residuals `yi - fi(x)` is the lowest possible.

RCI TR Routines
Routine Name | Operation
--- | ---
dtrnlsp_init | Initializes the solver.
dtrnlsp_solve | Solves a nonlinear least squares problem on the basis of RCI using the Trust-Region algorithm.
dtrnlsp_get | Retrieves the number of iterations, stop criterion, initial residual, and final residual.
dtrnlsp_delete | Removes data.

- dtrnlsp_init
  Initializes the solver of nonlinear least squares problem.
- dtrnlsp_solve
  Solves a nonlinear least squares problem using the Trust-Region algorithm.
- dtrnlsp_get
  Retrieves the number of iterations, stop criterion, initial residual, and final residual.
- dtrnlsp_delete
  Removes the data object required by the TR solver.
- Examples of dtrnlsp Usage

Parent topic: Optimization Solver Routines