Decision Optimization

Hi,

I am trying to optimize for the Shannon entropy of a system. This would mean the objective function is (summing over i) Σx_i*log(x_i).  The problem is linearly constrained.

I am not sure if there is anyway to get CPLEX to solve for this directly? Preferably using the C API as that is what I have a decent amount of experience using. Any help would be appreciated!

Thanks in advance

------------------------------
Patrick
------------------------------

Hi,

you can either use CPO

using CP;

int scale=1000;

dvar int scalex in 1..1000000;
dexpr float x=scalex/scale;

maximize x;

subject to
{
log(x)<=2.5;
}

execute
{
writeln("x=",x);
}

works fine and you can do that in C++ too

or you can linearize and then use CPLEX MIP





------------------------------
ALEX FLEISCHER
------------------------------

Original Message:
Sent: Wed November 04, 2020 05:09 PM
From: Patrick Kreitzber
Subject: Can CPLEX solve a problem with a logarithm in the objective function (e.g. optimize entropy)

Hi,

I am trying to optimize for the Shannon entropy of a system. This would mean the objective function is (summing over i) Σx_i*log(x_i).  The problem is linearly constrained.

I am not sure if there is anyway to get CPLEX to solve for this directly? Preferably using the C API as that is what I have a decent amount of experience using. Any help would be appreciated!

Thanks in advance

------------------------------
Patrick
------------------------------

You could linearize the function x -> xlog(x), that is approximate it with a piecewise linear function F.
then you define new variables yj == F(xj) and minimize the sum of yj.
As Alex mentioned, this will introduce binary variables and change the nature of your problem to MILP.

------------------------------
Philippe Couronne
------------------------------

Original Message:
Sent: Thu November 05, 2020 10:32 AM
From: ALEX FLEISCHER
Subject: Can CPLEX solve a problem with a logarithm in the objective function (e.g. optimize entropy)

Hi,

you can either use CPO

using CP;

int scale=1000;

dvar int scalex in 1..1000000;
dexpr float x=scalex/scale;

maximize x;

subject to
{
log(x)<=2.5;
}

execute
{
writeln("x=",x);
}

works fine and you can do that in C++ too

or you can linearize and then use CPLEX MIP





------------------------------
ALEX FLEISCHER

Original Message:
Sent: Wed November 04, 2020 05:09 PM
From: Patrick Kreitzber
Subject: Can CPLEX solve a problem with a logarithm in the objective function (e.g. optimize entropy)

Hi,

I am trying to optimize for the Shannon entropy of a system. This would mean the objective function is (summing over i) Σx_i*log(x_i).  The problem is linearly constrained.

I am not sure if there is anyway to get CPLEX to solve for this directly? Preferably using the C API as that is what I have a decent amount of experience using. Any help would be appreciated!

Thanks in advance

------------------------------
Patrick
------------------------------

May I know, why the constraint become log(x)<=2.5?

------------------------------
Farahanim Misni
------------------------------

Original Message:
Sent: Thu November 05, 2020 10:32 AM
From: ALEX FLEISCHER
Subject: Can CPLEX solve a problem with a logarithm in the objective function (e.g. optimize entropy)

Hi,

you can either use CPO

using CP;

int scale=1000;

dvar int scalex in 1..1000000;
dexpr float x=scalex/scale;

maximize x;

subject to
{
log(x)<=2.5;
}

execute
{
writeln("x=",x);
}

works fine and you can do that in C++ too

or you can linearize and then use CPLEX MIP





------------------------------
ALEX FLEISCHER

Original Message:
Sent: Wed November 04, 2020 05:09 PM
From: Patrick Kreitzber
Subject: Can CPLEX solve a problem with a logarithm in the objective function (e.g. optimize entropy)

Hi,

I am trying to optimize for the Shannon entropy of a system. This would mean the objective function is (summing over i) Σx_i*log(x_i).  The problem is linearly constrained.

I am not sure if there is anyway to get CPLEX to solve for this directly? Preferably using the C API as that is what I have a decent amount of experience using. Any help would be appreciated!

Thanks in advance

------------------------------
Patrick
------------------------------

Hi,

what do you mean ? With CPOptimizer within CPLEX you can use log and as an example I wrote

log(x)<=2.5;​

------------------------------
[Alex] [Fleischer]
[EMEA CPLEX Optimization Technical Sales]
[IBM]
------------------------------

Original Message:
Sent: Thu November 19, 2020 08:36 AM
From: Farahanim Misni
Subject: Can CPLEX solve a problem with a logarithm in the objective function (e.g. optimize entropy)

May I know, why the constraint become log(x)<=2.5?

------------------------------
Farahanim Misni

Original Message:
Sent: Thu November 05, 2020 10:32 AM
From: ALEX FLEISCHER
Subject: Can CPLEX solve a problem with a logarithm in the objective function (e.g. optimize entropy)

Hi,

you can either use CPO

using CP;

int scale=1000;

dvar int scalex in 1..1000000;
dexpr float x=scalex/scale;

maximize x;

subject to
{
log(x)<=2.5;
}

execute
{
writeln("x=",x);
}

works fine and you can do that in C++ too

or you can linearize and then use CPLEX MIP





------------------------------
ALEX FLEISCHER

Original Message:
Sent: Wed November 04, 2020 05:09 PM
From: Patrick Kreitzber
Subject: Can CPLEX solve a problem with a logarithm in the objective function (e.g. optimize entropy)

Hi,

I am trying to optimize for the Shannon entropy of a system. This would mean the objective function is (summing over i) Σx_i*log(x_i).  The problem is linearly constrained.

I am not sure if there is anyway to get CPLEX to solve for this directly? Preferably using the C API as that is what I have a decent amount of experience using. Any help would be appreciated!

Thanks in advance

------------------------------
Patrick
------------------------------