
From:  Meketon, Marc 
Subject:  RE: [Helpglpk] Linear Programming Relaxation 
Date:  Wed, 2 Dec 2009 14:15:17 0500 
To the best of my knowledge (which
admittedly is not uptodate), none of the research into using interior point
algorithms for solving integer programs has ever been used commercially, nor
has there been any convincing arguments to use interior point algorithms for
integer programming. On the cases where interior point
algorithms converge to the initial relaxed linear program of an integer program
much more quickly than the simplex does, an extra step is needed to take that solution
and create an extreme point solution. Often, “reallife” linear
programs are dual degenerate which means that there are multiple optimal
solutions. Interior point solutions tend to be far away from the extreme
points of the convex optimal surface, and getting to any extreme point often
takes a lot of computations. To get to the extreme points, you need the
simplex. So by the time you find an optimal extreme point with the
combination of interior point and simplex, you might as well just used the
simplex. The extreme points tend to be more “integer”.
More importantly, an extreme point is necessary for the simplex algorithm
used in the branch and bound (and branch and cut) procedures. The simplex
works well since it can be warmstarted – only a relatively few simplex
iterations are needed to resolve. But a consistently working warmstart
strategy for interior points is elusive, leaving the simplex as the only real
method for resolving a linear program after a branch or a cutting plan is added. As I mentioned above, my knowledge is a
bit old. I would like hear from anyone else if there are advances in
using interior point algorithms for integer programming. Marc From:
address@hidden
[mailto:address@hidden On Behalf Of RC Loh Hi Andrew, Michael, Jeffrey, Ali, Thank you very much for all your information and advice. So from what I gathered from all of you are that: 1) An Integer program can be solved using Interior Point
method too. Not necessary solving an Integer program using Simplex method. 2) Simplex method under certain conditions also runs in
polynomial time. Some of the terms used by Michael confused me. Sorry that I
am very new to this area. So I am not familiar with most of the terms. What is convex and nonconvex? What is global optimum and local optimum? Can you give me examples of global optimum, local optimum,
convex and nonconvex? Hi Ali, To answer your question, yes, I faced computational
time problem when I have 2000 binary structural variables using Simplex
method. It took more than 4 hours and still I could not obtain a result.
So I terminated the execution prematurely. I gathered that using Simplex method does not work for me
because I have more than 300 similar problems to be solved. Rdgs, Paul
From: Michael Hennebry
<address@hidden> New
Email names for you! This email and any attachments may be confidential or legally privileged. If you received this message in error or are not the intended recipient, you should destroy the email message and any attachments or copies, and you are prohibited from retaining, distributing, disclosing or using any information contained herein. Please inform us of the erroneous delivery by return email. Thank you for your cooperation.  
[Prev in Thread]  Current Thread  [Next in Thread] 