# Coefficients of non-negative penalized generalized linear models for a given lambda for normal family

### Description

The function computes regression coefficients for a penalized generalized linear models subject to non-negativity constraints for a given lambda value for response variable following normal distribution.

### Usage

1 2 | ```
nnlasso.normal.lambda(n,p,x,y,xpx,xpy,beta.old,tau,
lambda1,tol,maxiter,xbeta.old,eps,SE)
``` |

### Arguments

`n` |
Number of observations |

`p` |
Number of predictors. |

`x` |
A n by p1 matrix of predictors. |

`y` |
A vector of n observations. |

`xpx` |
Matrix X'X |

`xpy` |
Vector X'y |

`beta.old` |
A vector of initial values of beta. |

`tau` |
Elastic net paramter. Default is 1 |

`lambda1` |
The value of lambda |

`tol` |
Tolerance criterion. Default is 10^-6 |

`maxiter` |
Maximum number of iterations. Default is 10000. |

`xbeta.old` |
A n by 1 vector of xbeta values. |

`eps` |
A small value below which a coefficient would be considered as zero. Default is eps=1e-6 |

`SE` |
Logical. If SE=TRUE, standard errors of the coefficients will be produced. Default is SE=FALSE |

### Details

This function is internal and used by nnlasso.normal function. User need not call this function.

### Value

A list with following components

`beta.new` |
Coefficient estimates |

`conv` |
"yes" means converged and "no" means did not converge |

`iter` |
Number of iterations to estimate the coefficients |

`ofv.new` |
Objective function value at solution |

`xbeta.new` |
xbeta values at solution |

`vcov` |
Variance-covariance matrix of the coefficient estimates |

### Author(s)

Baidya Nath Mandal and Jun Ma

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