constrainedWeightedSolution

Solve weighted least squares with optional linear constraints.

Developer documentation: this item describes internal implementation details.

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Declaration

 [xi,systemMatrix] = constrainedWeightedSolution(normalMatrix,rhs,Aeq,beq,Aineq,bineq)

Parameters

• normalMatrix weighted normal-equation matrix
• rhs weighted right-hand side
• Aeq equality-constraint matrix
• beq equality-constraint right-hand side
• Aineq inequality-constraint matrix
• bineq inequality-constraint right-hand side

Returns

• xi fitted coefficient vector
• systemMatrix solved system matrix or quadratic Hessian proxy

Discussion

If only equality constraints are present, this forms and solves the KKT system

\[\begin{bmatrix} N & A_{\mathrm{eq}}^T \\ A_{\mathrm{eq}} & 0 \end{bmatrix} \begin{bmatrix} \xi \\ \lambda \end{bmatrix} = \begin{bmatrix} r \\ b_{\mathrm{eq}} \end{bmatrix}.\]

If inequality constraints are also present, the method switches to quadprog and solves the equivalent convex quadratic program with Hessian N.