lp_box

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abs_normal: Solve a Linear Program With Box Constraints

Syntax

ok = lp_box (
      level , A , b , c , d , maxitr , xout
)

Prototype

template <class Vector>
bool lp_box(
   size_t        level   ,
   const Vector& A       ,
   const Vector& b       ,
   const Vector& c       ,
   const Vector& d       ,
   size_t        maxitr  ,
   Vector&       xout    )

Source

This following is a link to the source code for this example: lp_box.hpp .

Problem

We are given \(A \in \B{R}^{m \times n}\), \(b \in \B{R}^m\), \(c \in \B{R}^n\), \(d \in \B{R}^n\), This routine solves the problem

\[\begin{split}\begin{array}{rl} \R{minimize} & c^T x \; \R{w.r.t} \; x \in \B{R}^n \\ \R{subject \; to} & A x + b \leq 0 \; \R{and} \; - d \leq x \leq d \end{array}\end{split}\]

Vector

The type Vector is a simple vector with elements of type double .

level

This value is less that or equal two. If level == 0 , no tracing is printed. If level >= 1 , a trace of the lp_box operations is printed. If level >= 2 , the objective and primal variables \(x\) are printed at each simplex_method iteration. If level == 3 , the simplex tableau is printed at each simplex iteration.

A

This is a row-major representation of the matrix \(A\) in the problem.

b

This is the vector \(b\) in the problem.

c

This is the vector \(c\) in the problem.

d

This is the vector \(d\) in the problem. If \(d_j\) is infinity, there is no limit for the size of \(x_j\).

maxitr

This is the maximum number of newton iterations to try before giving up on convergence.

xout

This argument has size is n and the input value of its elements does no matter. Upon return it is the primal variables \(x\) corresponding to the problem solution.

ok

If the return value ok is true, an optimal solution was found.

Example

The file lp_box.cpp contains an example and test of lp_box .