0
$\begingroup$

Let $$f(x) = \left\{ \begin{array}{l} {a_1}x + {b_1} & if\,0 \le {x_1} \le x \le {x_2}\\ {a_2}x + {b_2} & if\,{x_2} < x \le {x_3}\\ \vdots \\ {a_n}x + {b_n} & if\,{x_{n - 1}} < x \le {x_n} \end{array} \right.$$ be a piecewise continuous function and $0\leq a_1\leq a_2\leq \cdots \leq a_n$.

Formulate the problem of miniimizing $f(x)$ in terms of linear programming

$\endgroup$

closed as unclear what you're asking by Thomas Klimpel, Jan, Christian Clason, Godric Seer, Bill Barth Oct 8 '13 at 19:09

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 3
    $\begingroup$ Is this problem a homework problem? $\endgroup$ – Geoff Oxberry Sep 30 '13 at 17:30
1
$\begingroup$

Note that $f(x)=\max_{i} a_{i}x+b_{i}$. You can then reformulate the problem as

$\min_{t,x} t $

subject to

$ t \geq a_{i}x + b_{i}$, $i=1, 2, \ldots, n$.

$\endgroup$
  • $\begingroup$ but optimal point may not lying in the intervals. can you give an example (for n=2) $\endgroup$ – SKMohammadi Sep 30 '13 at 15:44
  • 1
    $\begingroup$ Your comment doesn't make sense as a sentence in English, so I'm not sure what you're asking. If you're concerned that the minimum of the LP might be outside of the interval $[x_{1},x_{n}]$, you can simply add the constraints $x \geq x_{1}$ and $x \leq x_{n}$. Pick any numbers that you want for $a_{1}$, $b_{1}$, $a_{2}$, and $b_{2}$ and try it. $\endgroup$ – Brian Borchers Sep 30 '13 at 16:14
  • $\begingroup$ Maybe a feasible point do not satisfy all restrictions! Please give an simple example. $\endgroup$ – SKMohammadi Oct 2 '13 at 5:46

Not the answer you're looking for? Browse other questions tagged or ask your own question.