Convex minlp problem and BARON solver memory

Archiver · August 26, 2015, 1:32pm

Hi Gams world,

I have a convex minlp model and it is very difficult to solve even though the model size is not very large (in total 238 binary variables and 136 continuous variables), and I am sure that the model is convex, the only nonlinear inequalities are:

x**1.85 + A*(1-y) + B =l= 0 ;

where x is positive variable, y is binary variable, A and B are parameters.

The model becomes very easy to solve if the inequalities become linear:

x + A*(1-y) + B =l= 0 ;

Therefore I guess the difficulty is not coming from the combination of binary variables.

On the other hand, the relaxed minlp problem is also very easy to solve since it is convex, which makes me wonder why it the so hard to solve this minlp problem.

Is there any efficient solver for convex minlp problem? Or is there any way to reformulate the nonlinear inequalities to make it easier to solve?

Besides, I am using BARON to solve a convex MINLP problem. While solving the problem, the solver suggests the memory requirement exceeds its estimation and request to provide more memory.

Later I tried the GAMS option ‘workspace’ and ‘workfactor’:

option workspace = 30 ;

However, both are recognized as invalid. How can I provide more memory to the solver?

Best regards,

Dylan

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Archiver · September 3, 2015, 10:31am

If you only have polynomial terms of the form

x^p + linear =1 + linear expressions, then you can reformulate it as an second order programming model (aka. conic quadratic programming model) then that is likely to solve much faster with MOSEK or one of the MISOCP codes.
The reformulation is exact as long as p is a rational number

Rewritting the problem to MISOCP form requires some tricks that you can find in the MOSEK modelling cookbook available

https://mosek.com/resources/doc

Here is a direct link

http://docs.mosek.com/modeling-cookbook/cqo.html#simple-polynomial-sets

and forward.

I am very interested in hearing about your expiriences with this if you try it out.

Erling

Den onsdag den 26. august 2015 kl. 13.35.53 UTC+2 skrev Dylan Lan:

Hi Gams world,

I have a convex minlp model and it is very difficult to solve even though the model size is not very large (in total 238 binary variables and 136 continuous variables), and I am sure that the model is convex, the only nonlinear inequalities are:

x**1.85 + A*(1-y) + B =l= 0 ;

where x is positive variable, y is binary variable, A and B are parameters.

The model becomes very easy to solve if the inequalities become linear:

x + A*(1-y) + B =l= 0 ;

Therefore I guess the difficulty is not coming from the combination of binary variables.

On the other hand, the relaxed minlp problem is also very easy to solve since it is convex, which makes me wonder why it the so hard to solve this minlp problem.

Is there any efficient solver for convex minlp problem? Or is there any way to reformulate the nonlinear inequalities to make it easier to solve?

Besides, I am using BARON to solve a convex MINLP problem. While solving the problem, the solver suggests the memory requirement exceeds its estimation and request to provide more memory.

Later I tried the GAMS option ‘workspace’ and ‘workfactor’:

option workspace = 30 ;

However, both are recognized as invalid. How can I provide more memory to the solver?

Best regards,

Dylan

–
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Archiver · September 3, 2015, 10:49am

Dylan,

Can you make your model available? If this is small, convex, and difficult this could be a good problem for the MINLP library (http://www.gamsworld.org/minlp/minlplib2/html/). There are ways to anonymize the model if you like. Please contact support@gams.com for details.

Best,
Michael Bussieck - GAMSWorld Coordinator

On Wednesday, August 26, 2015 at 7:35:53 AM UTC-4, Dylan Lan wrote:

Hi Gams world,

I have a convex minlp model and it is very difficult to solve even though the model size is not very large (in total 238 binary variables and 136 continuous variables), and I am sure that the model is convex, the only nonlinear inequalities are:

x**1.85 + A*(1-y) + B =l= 0 ;

where x is positive variable, y is binary variable, A and B are parameters.

The model becomes very easy to solve if the inequalities become linear:

x + A*(1-y) + B =l= 0 ;

Therefore I guess the difficulty is not coming from the combination of binary variables.

On the other hand, the relaxed minlp problem is also very easy to solve since it is convex, which makes me wonder why it the so hard to solve this minlp problem.

Is there any efficient solver for convex minlp problem? Or is there any way to reformulate the nonlinear inequalities to make it easier to solve?

Besides, I am using BARON to solve a convex MINLP problem. While solving the problem, the solver suggests the memory requirement exceeds its estimation and request to provide more memory.

Later I tried the GAMS option ‘workspace’ and ‘workfactor’:

option workspace = 30 ;

However, both are recognized as invalid. How can I provide more memory to the solver?

Best regards,

Dylan

–
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Archiver · September 3, 2015, 10:52am

Dylan,

BARON shines for non-convex problems and guarantees global optimality (or proven gaps) If you know your problem is convex, solvers like DICOPT, SBB, AlphaECP, and Bonmin might be more efficient.

Best,
Michael Bussieck - GAMSWorld Coordinator

On Thursday, September 3, 2015 at 4:49:20 AM UTC-4, Michael Bussieck wrote:

Dylan,

Can you make your model available? If this is small, convex, and difficult this could be a good problem for the MINLP library (http://www.gamsworld.org/minlp/minlplib2/html/). There are ways to anonymize the model if you like. Please contact support@gams.com for details.

Best,
Michael Bussieck - GAMSWorld Coordinator

On Wednesday, August 26, 2015 at 7:35:53 AM UTC-4, Dylan Lan wrote:

Hi Gams world,

I have a convex minlp model and it is very difficult to solve even though the model size is not very large (in total 238 binary variables and 136 continuous variables), and I am sure that the model is convex, the only nonlinear inequalities are:

x**1.85 + A*(1-y) + B =l= 0 ;

where x is positive variable, y is binary variable, A and B are parameters.

The model becomes very easy to solve if the inequalities become linear:

x + A*(1-y) + B =l= 0 ;

Therefore I guess the difficulty is not coming from the combination of binary variables.

On the other hand, the relaxed minlp problem is also very easy to solve since it is convex, which makes me wonder why it the so hard to solve this minlp problem.

Is there any efficient solver for convex minlp problem? Or is there any way to reformulate the nonlinear inequalities to make it easier to solve?

Besides, I am using BARON to solve a convex MINLP problem. While solving the problem, the solver suggests the memory requirement exceeds its estimation and request to provide more memory.

Later I tried the GAMS option ‘workspace’ and ‘workfactor’:

option workspace = 30 ;

However, both are recognized as invalid. How can I provide more memory to the solver?

Best regards,

Dylan

–
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Archiver · September 5, 2015, 3:52am

Hi Michael,

Thank you very much for your reply. I will try to contact the support group.

In fact I used DICOPT and SBB for solution at the beginning, but neither found integer solution.

Later I tried BARON and SCIP, both are able to find optimal solution in about 2700 s and 1200 s, respective. Is the solution time typical for a convex minlp model of this size (in total 238 binary variables and 136 continuous variables)?

Best regards,

Dylan

åœ¨ 2015å¹´9æœˆ3æ—¥æ˜ŸæœŸå›› UTC+8ä¸‹åˆ4:49:20ï¼ŒMichael Bussieckå†™é“ï¼š

Dylan,

Can you make your model available? If this is small, convex, and difficult this could be a good problem for the MINLP library (http://www.gamsworld.org/minlp/minlplib2/html/). There are ways to anonymize the model if you like. Please contact sup...@gams.com for details.

Best,
Michael Bussieck - GAMSWorld Coordinator

On Wednesday, August 26, 2015 at 7:35:53 AM UTC-4, Dylan Lan wrote:

Hi Gams world,

I have a convex minlp model and it is very difficult to solve even though the model size is not very large (in total 238 binary variables and 136 continuous variables), and I am sure that the model is convex, the only nonlinear inequalities are:

x**1.85 + A*(1-y) + B =l= 0 ;

where x is positive variable, y is binary variable, A and B are parameters.

The model becomes very easy to solve if the inequalities become linear:

x + A*(1-y) + B =l= 0 ;

Therefore I guess the difficulty is not coming from the combination of binary variables.

On the other hand, the relaxed minlp problem is also very easy to solve since it is convex, which makes me wonder why it the so hard to solve this minlp problem.

Is there any efficient solver for convex minlp problem? Or is there any way to reformulate the nonlinear inequalities to make it easier to solve?

Besides, I am using BARON to solve a convex MINLP problem. While solving the problem, the solver suggests the memory requirement exceeds its estimation and request to provide more memory.

Later I tried the GAMS option ‘workspace’ and ‘workfactor’:

option workspace = 30 ;

However, both are recognized as invalid. How can I provide more memory to the solver?

Best regards,

Dylan

–
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Archiver · September 5, 2015, 10:37am

Hi Michael,

Should I send my model to you or to the support group?

Best regards,

Dylan

åœ¨ 2015å¹´9æœˆ3æ—¥æ˜ŸæœŸå›› UTC+8ä¸‹åˆ4:49:20ï¼ŒMichael Bussieckå†™é“ï¼š

Dylan,

Can you make your model available? If this is small, convex, and difficult this could be a good problem for the MINLP library (http://www.gamsworld.org/minlp/minlplib2/html/). There are ways to anonymize the model if you like. Please contact sup...@gams.com for details.

Best,
Michael Bussieck - GAMSWorld Coordinator

On Wednesday, August 26, 2015 at 7:35:53 AM UTC-4, Dylan Lan wrote:

Hi Gams world,

I have a convex minlp model and it is very difficult to solve even though the model size is not very large (in total 238 binary variables and 136 continuous variables), and I am sure that the model is convex, the only nonlinear inequalities are:

x**1.85 + A*(1-y) + B =l= 0 ;

where x is positive variable, y is binary variable, A and B are parameters.

The model becomes very easy to solve if the inequalities become linear:

x + A*(1-y) + B =l= 0 ;

Therefore I guess the difficulty is not coming from the combination of binary variables.

On the other hand, the relaxed minlp problem is also very easy to solve since it is convex, which makes me wonder why it the so hard to solve this minlp problem.

Is there any efficient solver for convex minlp problem? Or is there any way to reformulate the nonlinear inequalities to make it easier to solve?

Besides, I am using BARON to solve a convex MINLP problem. While solving the problem, the solver suggests the memory requirement exceeds its estimation and request to provide more memory.

Later I tried the GAMS option ‘workspace’ and ‘workfactor’:

option workspace = 30 ;

However, both are recognized as invalid. How can I provide more memory to the solver?

Best regards,

Dylan

–
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Archiver · September 5, 2015, 6:49pm

Dylan, What ever you prefer. Michael

On Saturday, September 5, 2015 at 12:43:51 PM UTC-4, Dylan Lan wrote:

Hi Michael,

Should I send my model to you or to the support group?

Best regards,

Dylan

åœ¨ 2015å¹´9æœˆ3æ—¥æ˜ŸæœŸå›› UTC+8ä¸‹åˆ4:49:20ï¼ŒMichael Bussieckå†™é“ï¼š

Dylan,

Can you make your model available? If this is small, convex, and difficult this could be a good problem for the MINLP library (http://www.gamsworld.org/minlp/minlplib2/html/). There are ways to anonymize the model if you like. Please contact sup...@gams.com for details.

Best,
Michael Bussieck - GAMSWorld Coordinator

On Wednesday, August 26, 2015 at 7:35:53 AM UTC-4, Dylan Lan wrote:

Hi Gams world,

I have a convex minlp model and it is very difficult to solve even though the model size is not very large (in total 238 binary variables and 136 continuous variables), and I am sure that the model is convex, the only nonlinear inequalities are:

x**1.85 + A*(1-y) + B =l= 0 ;

where x is positive variable, y is binary variable, A and B are parameters.

The model becomes very easy to solve if the inequalities become linear:

x + A*(1-y) + B =l= 0 ;

Therefore I guess the difficulty is not coming from the combination of binary variables.

On the other hand, the relaxed minlp problem is also very easy to solve since it is convex, which makes me wonder why it the so hard to solve this minlp problem.

Is there any efficient solver for convex minlp problem? Or is there any way to reformulate the nonlinear inequalities to make it easier to solve?

Besides, I am using BARON to solve a convex MINLP problem. While solving the problem, the solver suggests the memory requirement exceeds its estimation and request to provide more memory.

Later I tried the GAMS option ‘workspace’ and ‘workfactor’:

option workspace = 30 ;

However, both are recognized as invalid. How can I provide more memory to the solver?

Best regards,

Dylan

–
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