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Re: [Help-glpk] Linear Programming Relaxation

From: RC Loh
Subject: Re: [Help-glpk] Linear Programming Relaxation
Date: Thu, 3 Dec 2009 00:00:05 +0800 (SGT)

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 non-convex?
What is global optimum and local optimum?
Can you give me examples of global optimum, local optimum, convex and non-convex?
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 pre-maturely.
I gathered that using Simplex method does not work for me because I have more than 300 similar problems to be solved.


From: Michael Hennebry <address@hidden>
To: RC Loh <address@hidden>
Cc: Andrew Makhorin <address@hidden>; Jeffrey Kantor <address@hidden>; address@hidden
Sent: Wednesday, 2 December 2009 2:03:00
Subject: Re: [Help-glpk] Linear Programming Relaxation

On Tue, 1 Dec 2009, RC Loh wrote:

> Thank you for your suggestion. I am currently reading up on SOS1 and see whether it is applicable to my problem.

It is.

> According to Andrew, the SOS1 is implemented by a version of Simplex Method.
> Then what is the difference between using SOS1 with the Simplex Method compared to using Integer Programming?
> Integer Programming is also using the Simplex Method, isn't it?

Here be much conflation of problem type and solution method.

Integer programming is the solving of optimization problems
all of whose variables are required to be integers.
Mixed integer programming allows some variables to be real.
In either case, a simplex method might or might not be used.

SOS1 is a type of constraint.
It makes the feasible set non-convex.
Simplex methods find local optima.
That is global for a minimization problem
with a convex (e.g. linear) objective function.
It might not be good enough for a problem with an SOS constraint.

-- Michael  address@hidden
"Pessimist: The glass is half empty.
Optimist:  The glass is half full.
Engineer:  The glass is twice as big as it needs to be."

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