lsi_ln

solve linear least square problem <code>min_x ||A*x-b||</code>
with inequality constraints <code>u%*%x &gt;= co</code>
If A is rank deficient, least norm solution <code>||mnorm%*%(x-x0)||</code> is used.
If the parameter mnorm is NULL, it is treated as an identity matrix.
If the vector x0 is NULL, it is treated as 0 vector.

We solve non linear least squares problems with optional
equality and/or inequality constraints. Non linear iterations are
globalized with back-tracking method. Linear problems are solved by
dense QR decomposition from 'LAPACK' which can limit the size of
treated problems. On the other side, we avoid condition number
degradation which happens in classical quadratic programming approach.
Inequality constraints treatment on each non
linear iteration is based on 'NNLS' method (by Lawson and Hanson).
We provide an original function 'lsi_ln' for solving linear least squares
problem with inequality constraints in least norm sens. Thus if Jacobian of
the problem is rank deficient a solution still can be provided.
However, truncation errors are probable in this case.
Equality constraints are treated by using a basis of Null-space.
User defined function calculating residuals must return a list having
residual vector (not their squared sum) and Jacobian. If Jacobian is
not in the returned list, package 'numDeriv' is used to calculated
finite difference version of Jacobian. The 'NLSIC' method was fist
published in Sokol et al. (2012) <doi:10.1093/bioinformatics/btr716>.

Serguei Sokol

nlsic

Non Linear Least Squares with Inequality Constraints

lsi_ln function

<dl><dt>a</dt>
<dd>dense matrix A or its QR decomposition</dd>
<dt>b</dt>
<dd>right hand side vector</dd>
<dt>u</dt>
<dd>dense matrix of inequality constraints</dd>
<dt>co</dt>
<dd>right hand side vector of inequality constraints</dd>
<dt>rcond</dt>
<dd>maximal condition number for determining rank deficient matrix</dd>
<dt>mnorm</dt>
<dd>norm matrix (can be dense or sparse) for which <code>%*%</code> operation with a dense vector is defined</dd>
<dt>x0</dt>
<dd>optional vector from which a least norm distance is searched for</dd></dl>

Arguments

Linear Least Squares with Inequality constraints, least norm solution — lsi_ln

<dl>

<dt>a</dt>
<dd>dense matrix A or its QR decomposition</dd>


<dt>b</dt>
<dd>right hand side vector</dd>


<dt>u</dt>
<dd>dense matrix of inequality constraints</dd>


<dt>co</dt>
<dd>right hand side vector of inequality constraints</dd>


<dt>rcond</dt>
<dd>maximal condition number for determining rank deficient matrix</dd>


<dt>mnorm</dt>
<dd>norm matrix (can be dense or sparse) for which <code>%*%</code> operation with a dense vector is defined</dd>


<dt>x0</dt>
<dd>optional vector from which a least norm distance is searched for</dd>

</dl>

lsi_ln: Linear Least Squares with Inequality constraints, least norm solution

Description

Usage

Value

Arguments

See Also