Linearly Constrained Least-Squares ProblemsLeast-Squares > Definitions >> [ LS | Regularized LS | Constrained LS ] | Solution | Sensitivity | Limitations
Linearly constrained least-squaresDefinitionAn interesting variant of the ordinary least-squares problem involves equality constraints on the decision variable ![]() where Examples: SolutionWe can express the solution by first computing the nullspace of ![]() where Expressing ![]() where Minimum-norm solution to linear equationsA special case of linearly constrained LS is ![]() in which we implicitly assume that the linear equation in The above problem allows to select a particular solution to a linear equation, in the case when there are possibly many, that is, the linear system As seen here, when ![]() Examples: Control positioning of a mass. |