TOMLAB OPTIMIZATION ENVIRONMENT: lsei

lsei

Purpose

MEX interface for lsei

For solving linearly constrained least squares problems with both equality and inequality constraints.

Syntax

  [x, rNormE, rNormL, mode, Cov, eqRank, rlsRank] = lsei ( ...
     A, b, E, f, G, h, CompCov, ScaleCov, ColScale, D, epsEQ, epsRank)

Description

lsei solves a linearly constrained least squares problem with both equality and inequality constraints.

May return a covariance matrix of the solution parameters.

Given dense matrices E, A and G of respective dimensions mE by N, mA by N and mG by N, and vectors f, b and h of respective lengths ME, MA and MG. This subroutine solves the linearly constrained least squares problem formulated as:

    min   || A x  - b || subject to

             E x  = f    Equations to be exactly satisfied
             G x >= h    Inequality constraints

In case the equality constraints cannot be satisfied, a generalized inverse solution residual vector length is obtained for f-Ex. This is the minimal length possible for f-Ex.

Any number of rows in A, E and G are permitted.

Input Parameters

At least 2 input parameters needed

   A         mA x n dense matrix
   b         mA x 1 dense vector
   E         mE x n dense matrix
   f         mE x 1 dense vector
   G         mG x n dense matrix
   h         mG x 1 dense vector
   CompCov   If > 0 compute covariance matrix. Default 0
   ScaleCov  If > 0 scale covariance matrix. Default 1
   ColScale  If > 0 column scaling of full matrix W. Default 0
   D         If nonempty, n x 1 dense vector with diagonal scaling of columns
   epsEQ     Linear equality feasibility tolerance
   epsRank   Rank tolerance in least squares part

Output Parameters

   x         Solution x
   rNormE    ||Ex-f||
   rNormL    ||Ax-b||
   mode      Exit status:      
             0  Both equality and inequality constraints are compatible 
                and have been satisfied.
             1  Equality constraints are contradictory.
                A generalized inverse solution of Ex=f was used
                to minimize the residual vector length f-Ex.
             2  Inequality constraints are contradictory.
             3  Both equality and inequality constraints are contradictory.
             4  Usage error occurred. This should not occur.

   Cov       Covariance matrix, if CompCov > 0
   eqRank    Rank of E matrix part
   rlsRank   Rank of A matrix part

See Also

lseiTL