paralp: A solver for parameterized LP problems
In fastclime: A Fast Solver for Parameterized LP Problems, Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation and Dantzig Selector

Description Usage Arguments Details Value Author(s) See Also Examples

A parameterized linear programming solver using parametric simplex method

1	paralp(obj,mat,rhs,obj_bar,rhs_bar,lambda=0)

`obj`	The objective vector of the coefficient with length n.
`mat`	The constraint matrix of the linear programming with dimension m*n. Note this argument must be in matrix form even it is a vector.
`rhs`	The right hand side vector of the constraint with length m.
`obj_bar`	The vector used to time the parameter and added to the objective vector, with length n. This pertubation vector must be nonnegative.
`rhs_bar`	The vector used to time the parameter and added to the right hand side vector, with length m. This pertubation vector must be nonnegative.
`lambda`	The parametric simplex method will stop when the calculated paramter is smaller than lambda. The default value is zero and it corresponds to the optimal value.

This function is used to solve a general linear programming in standard inequality form: "maximize obj*x+obj_bar*lambda, subject to: mat*x<=rhs+rhs_bar*lambda, x>=0"

The optimal value will be returned if it exists with a proper value of chosen lambda. Otherwise the function will indicate the problem is infeasible or unbounded.

Haotian Pang, Han Liu and Robert Vanderbei
Maintainer: Haotan Pang<hpang@princeton.edu>

fastclime and fastclime-package

#generate an LP problem and solve it
A=matrix(c(-1,-1,0,1,-2,1),nrow=3)
b=c(-1,-2,1)
c=c(-2,3)
b_bar=c(1,1,1)
c_bar=c(1,1)
paralp(c,A,b,c_bar,b_bar)

Loading required package: lattice
Loading required package: igraph

Attaching package: 'igraph'

The following objects are masked from 'package:stats':

    decompose, spectrum

The following object is masked from 'package:base':

    union

Loading required package: MASS
Loading required package: Matrix
optimal solution found! 
[1] 1.3333333 0.3333333