If then condition on mixed linear integer programming - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T03:46:15Z http://mathoverflow.net/feeds/question/104717 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/104717/if-then-condition-on-mixed-linear-integer-programming If then condition on mixed linear integer programming ashade 2012-08-14T20:24:01Z 2012-08-14T20:57:52Z <p>Hi all. Let $a$ and $b$ be two real variables such that $0 \le a \le a_{max}$ and $0 \le b \le b_{max}$. I must write the following if-then-else condition with linear inequalities:</p> <p>if $a &lt; a_{max}$ then $b = 0$ else $b \ge 0$.</p> <p>Is it possible by adding a single binary variable $y$?</p> http://mathoverflow.net/questions/104717/if-then-condition-on-mixed-linear-integer-programming/104721#104721 Answer by Gilead for If then condition on mixed linear integer programming Gilead 2012-08-14T20:57:52Z 2012-08-14T20:57:52Z <p>Yes.</p> <p>$a_{\text{max}} y \leq a \leq (1-y)(a_{\text{max}} - \epsilon) + a_{\text{max}}y$</p> <p>$0 \leq b \leq b_{\text{max}} y$</p> <p>where $y \in \{{0,1\}}$ and $\epsilon$ is a small positive real.</p>