Nonlinear Least Squares (Curve Fitting)

Nonlinear least-squares is solving the problem min(∑||F(x_i) - y_i||²), where F(x_i) is a nonlinear function and y_i is data. The problem can have bounds, linear constraints, or nonlinear constraints. These problems come from fitting curves to experimental data, estimating parameters for physical models, and others.

Before you begin to solve an optimization problem, you must choose the appropriate approach: problem-based or solver-based. For details, see First Choose Problem-Based or Solver-Based Approach.

For the problem-based approach, create problem variables, and then represent the objective function and constraints in terms of these symbolic variables. To formulate a least-squares problem, follow the instructions in Write Objective Function for Problem-Based Least Squares. For the problem-based steps to take, see Problem-Based Optimization Workflow. To solve the resulting problem, use solve.

For the solver-based steps to take, including defining the objective function and constraints, and choosing the appropriate solver, see Solver-Based Optimization Problem Setup. To solve the resulting problem, use lsqcurvefit or lsqnonlin.