[Help-glpk] [Fwd: Re: Objective function defined with max, min.]

[Andrew Makhorin]

-------- Forwarded Message --------
From: Alexey Karakulov <address@hidden>
To: Michael Hennebry <address@hidden>
Cc: Andrew Makhorin <address@hidden>, address@hidden
Subject: Re: [Help-glpk] Objective function defined with max, min.
Date: Fri, 6 Jan 2017 00:09:00 +0200

Michael, thanks.


This seems to work for me, but it's only for maximizing "crop(s)", not
minimizing, right? I have "crop(s[i])" with both positive and negative
signs for different "i", so I should do some fiddling to get it working.

On Thu, Jan 5, 2017 at 8:39 PM, Michael Hennebry
<address@hidden> wrote:
        The objective function includes  crop(s) = median(0, s, 1)
        where the range of s includes both negative values and values >
        1 .
        
        The set defined is not convex and so cannot be defined purely
        with
        linear constraints.
        One can get around the need for a binary by using optimality.
        
        Add nonnegative auxillary variables p0, n0, p1 and n1.
        s = p0-n0
        s = p1-n1+1
        Adjust the objective to ensure that p0 or n0 is zero
        at optimality and that p1 or n1 is zero at optimality.
        
        0<=crop(s)<=1
        crop(s)<=p0
        crop(s)>=1-n1
        
        -- 
        Michael   address@hidden
        "Sorry but your password must contain an uppercase letter, a
        number,
        a haiku, a gang sign, a heiroglyph, and the blood of a virgin."
                                                                     --
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