How to describe this relation

Question

The constraint I want to place is $Mx_i-y_i<0$,that is to say when $y_i = 0$ ,then $x_i$ must equal to $0$. However the constraint is only needed when $a>b$ ($a,b$ are both the parameters).

Can I describe the constraint as below?

$$Mx_i-y_i < 0,\ a>b.$$

do you mean when and only when? – BCLC Jul 08 '16 at 05:13 — BCLC, Jul 08 '16 at 05:13
thank you for your responding,i mean only when. – frank-z Jul 08 '16 at 05:24 — frank-z, Jul 08 '16 at 05:24

Kuifje · Answer 1 · 2016-07-08T12:17:55.477

1

If $a$ and $b$ are parameters, then you can control which constraints you give to the solver. If $a>b$ add the following constraint: $$ x_i\le My_i $$ (If $x_i$ is binary, $M:=1$ is suitable)

If not, do not add the constraint. That's all there is to it.

edited Jul 08 '16 at 12:17

answered Jul 08 '16 at 01:45

Kuifje

9,584

Is the $M$ misplaced? – BCLC Jul 08 '16 at 05:13
1

$M$ is not misplaced: if $y_i=0$, $x_i\le0$. If $y_i=1$, $x_1\le M$ (the constraint is inactive). – Kuifje Jul 08 '16 at 11:49
sorry for confusing, in the constraint,Xi are binary variables. – frank-z Jul 08 '16 at 12:13
No problem, in this case set $M$ to $1$. – Kuifje Jul 08 '16 at 12:17
thank you very much!but,i still want to know how to describe this relation in an optimization model using mathematical symbols – frank-z Jul 08 '16 at 12:24
may i add a＞b behind the constraint? – frank-z Jul 08 '16 at 12:26
Not sure I understand what you want. This is an optimization model using symbols. You can add "if a>b" after the constraint, sure. – Kuifje Jul 08 '16 at 12:28

How to describe this relation

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