Main Content

Linear Least Squares

Solve linear least-squares problems with bounds or linear constraints

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.

Linear least-squares solves min||C*x - d||2, possibly with bounds or linear constraints.

For the problem-based approach, create problem variables, and then represent the objective function and constraints in terms of these symbolic variables. 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 lsqlin or, for nonnegative least squares, you can also use lsqnonneg.


expand all

evaluateEvaluate optimization expression
infeasibilityConstraint violation at a point
optimproblemCreate optimization problem
optimvarCreate optimization variables
solveSolve optimization problem or equation problem
lsqlinSolve constrained linear least-squares problems
lsqnonnegSolve nonnegative linear least-squares problem
mldivide, \Solve systems of linear equations Ax = B for x

Live Editor Tasks

OptimizeOptimize or solve equations in the Live Editor


Problem-Based Linear Least Squares

Shortest Distance to a Plane

Shows how to solve a linear least-squares problem using the problem-based approach.

Nonnegative Linear Least Squares, Problem-Based

Shows how to solve a nonnegative linear least-squares problem using the problem-based approach and several solvers.

Large-Scale Constrained Linear Least-Squares, Problem-Based

Solves an optical deblurring problem using the problem-based approach.

Solver-Based Linear Least Squares

Optimize Live Editor Task with lsqlin Solver

Example showing the Optimize Live Editor task and linear least squares.

Nonnegative Linear Least Squares, Solver-Based

This example shows how to use several algorithms to solve a linear least-squares problem with the bound constraint that the solution is nonnegative.

Jacobian Multiply Function with Linear Least Squares

Example showing how to save memory in a large structured linear least-squares problem.

Large-Scale Constrained Linear Least-Squares, Solver-Based

Solves an optical deblurring problem using the solver-based approach.

Problem-Based Algorithms

Write Objective Function for Problem-Based Least Squares

Syntax rules for problem-based least squares.

Problem-Based Optimization Algorithms

How the optimization functions and objects solve optimization problems.

Supported Operations on Optimization Variables and Expressions

Lists all available mathematical and indexing operations on optimization variables and expressions.

Algorithms and Options

Least-Squares (Model Fitting) Algorithms

Minimizing a sum of squares in n dimensions with only bound or linear constraints.

Optimization Options Reference

Explore optimization options.