SOS1 for linearizing complementarity condition
0
$begingroup$
I am trying to linearize the complementarity condition
$0<a perp b>0$ with SOS1 method by the following formulation:
$p_1+p_2 = 1e5 label{1}tag{1}$
$a < p_1label{2}tag{2}$
$b < p_2label{3}tag{3}$
where, $p_1$ and $p_2$ are the SOS1 variables. If equation eqref{1} is set to 1, the problem becomes integer infeasible. If i set it to 1e5, both the variables attain values greater than 1. However, the definition of SOS1 says, at the most only 1 variable can take non zero value. Any clarification in this regard will be helpful.
optimization mixed-integer-programming
asked Dec 11 '18 at 2:28
S_ScouseS_Scouse
61
$endgroup$
|
show 1 more comment
0
$begingroup$
I am trying to linearize the complementarity condition
$0<a perp b>0$ with SOS1 method by the following formulation:
$p_1+p_2 = 1e5 label{1}tag{1}$
$a < p_1label{2}tag{2}$
$b < p_2label{3}tag{3}$
where, $p_1$ and $p_2$ are the SOS1 variables. If equation eqref{1} is set to 1, the problem becomes integer infeasible. If i set it to 1e5, both the variables attain values greater than 1. However, the definition of SOS1 says, at the most only 1 variable can take non zero value. Any clarification in this regard will be helpful.
optimization mixed-integer-programming
asked Dec 11 '18 at 2:28
S_ScouseS_Scouse
61
$endgroup$
$begingroup$
As i understand, the equality in eq. (1) causes the integer infeasibility. Hence, i reformed the equation to $p_1+p_2 < 1$. In this case,, after the solve $p_1$ is taking a value over 5000 and $p_2$ is taking a value just over 800.
$endgroup$
– S_Scouse
Dec 11 '18 at 11:21
$begingroup$
What are the domains of all the variables (lower and upper bounds, integral or not)? Also, do you mean <= in (2) and (3)? Math programs are generally intolerant of strict inequalities.
$endgroup$
– prubin
Dec 13 '18 at 0:07
$begingroup$
The variables a are indexed with different generation resources with their limits not exceeding 5950. b are Lagrangian dual variables with no upper bound and both a and b have their lower bound set to 0. There is no integral conditions involved. Yes, i meant <=, thank you for pointing that out. I tried big-M method but the optimization results vary depending on the M value.
$endgroup$
– S_Scouse
Dec 13 '18 at 20:20
$begingroup$
I agree that in an SOS1 constraint at most one variable should be nonzero. Is it possible that the solver you are using does not understand or support SOS1 constraints? If it does, I would have to guess that you entered the constraint incorrectly.
$endgroup$
– prubin
Dec 14 '18 at 21:12
$begingroup$
I am using cplex solver which from what I read supports sos1 constraints. Please let me know if that is the case. Also, is it possible that two variables in a sos1 set take positive values, where one of the sos1 variable value takes a higher value and the other takes a significant lower value which essentially set the constraint as binding. I am guessing this is far fetched but I am wondering if there is any truth behind it.
$endgroup$
– S_Scouse
Dec 14 '18 at 23:01
|
show 1 more comment
0
0
0
$begingroup$
I am trying to linearize the complementarity condition
$0<a perp b>0$ with SOS1 method by the following formulation:
$p_1+p_2 = 1e5 label{1}tag{1}$
$a < p_1label{2}tag{2}$
$b < p_2label{3}tag{3}$
where, $p_1$ and $p_2$ are the SOS1 variables. If equation eqref{1} is set to 1, the problem becomes integer infeasible. If i set it to 1e5, both the variables attain values greater than 1. However, the definition of SOS1 says, at the most only 1 variable can take non zero value. Any clarification in this regard will be helpful.
optimization mixed-integer-programming
asked Dec 11 '18 at 2:28
S_ScouseS_Scouse
61
$endgroup$
I am trying to linearize the complementarity condition
$0<a perp b>0$ with SOS1 method by the following formulation:
$p_1+p_2 = 1e5 label{1}tag{1}$
$a < p_1label{2}tag{2}$
$b < p_2label{3}tag{3}$
where, $p_1$ and $p_2$ are the SOS1 variables. If equation eqref{1} is set to 1, the problem becomes integer infeasible. If i set it to 1e5, both the variables attain values greater than 1. However, the definition of SOS1 says, at the most only 1 variable can take non zero value. Any clarification in this regard will be helpful.
optimization mixed-integer-programming
optimization mixed-integer-programming
asked Dec 11 '18 at 2:28
S_ScouseS_Scouse
61
asked Dec 11 '18 at 2:28
S_ScouseS_Scouse
61
asked Dec 11 '18 at 2:28
S_ScouseS_Scouse
61
asked Dec 11 '18 at 2:28
S_ScouseS_Scouse
61
asked Dec 11 '18 at 2:28
S_ScouseS_Scouse
61
61
$begingroup$
As i understand, the equality in eq. (1) causes the integer infeasibility. Hence, i reformed the equation to $p_1+p_2 < 1$. In this case,, after the solve $p_1$ is taking a value over 5000 and $p_2$ is taking a value just over 800.
$endgroup$
– S_Scouse
Dec 11 '18 at 11:21
$begingroup$
What are the domains of all the variables (lower and upper bounds, integral or not)? Also, do you mean <= in (2) and (3)? Math programs are generally intolerant of strict inequalities.
$endgroup$
– prubin
Dec 13 '18 at 0:07
$begingroup$
The variables a are indexed with different generation resources with their limits not exceeding 5950. b are Lagrangian dual variables with no upper bound and both a and b have their lower bound set to 0. There is no integral conditions involved. Yes, i meant <=, thank you for pointing that out. I tried big-M method but the optimization results vary depending on the M value.
$endgroup$
– S_Scouse
Dec 13 '18 at 20:20
$begingroup$
I agree that in an SOS1 constraint at most one variable should be nonzero. Is it possible that the solver you are using does not understand or support SOS1 constraints? If it does, I would have to guess that you entered the constraint incorrectly.
$endgroup$
– prubin
Dec 14 '18 at 21:12
$begingroup$
I am using cplex solver which from what I read supports sos1 constraints. Please let me know if that is the case. Also, is it possible that two variables in a sos1 set take positive values, where one of the sos1 variable value takes a higher value and the other takes a significant lower value which essentially set the constraint as binding. I am guessing this is far fetched but I am wondering if there is any truth behind it.
$endgroup$
– S_Scouse
Dec 14 '18 at 23:01
|
show 1 more comment
$begingroup$
As i understand, the equality in eq. (1) causes the integer infeasibility. Hence, i reformed the equation to $p_1+p_2 < 1$. In this case,, after the solve $p_1$ is taking a value over 5000 and $p_2$ is taking a value just over 800.
$endgroup$
– S_Scouse
Dec 11 '18 at 11:21
$begingroup$
What are the domains of all the variables (lower and upper bounds, integral or not)? Also, do you mean <= in (2) and (3)? Math programs are generally intolerant of strict inequalities.
$endgroup$
– prubin
Dec 13 '18 at 0:07
$begingroup$
The variables a are indexed with different generation resources with their limits not exceeding 5950. b are Lagrangian dual variables with no upper bound and both a and b have their lower bound set to 0. There is no integral conditions involved. Yes, i meant <=, thank you for pointing that out. I tried big-M method but the optimization results vary depending on the M value.
$endgroup$
– S_Scouse
Dec 13 '18 at 20:20
$begingroup$
I agree that in an SOS1 constraint at most one variable should be nonzero. Is it possible that the solver you are using does not understand or support SOS1 constraints? If it does, I would have to guess that you entered the constraint incorrectly.
$endgroup$
– prubin
Dec 14 '18 at 21:12
$begingroup$
I am using cplex solver which from what I read supports sos1 constraints. Please let me know if that is the case. Also, is it possible that two variables in a sos1 set take positive values, where one of the sos1 variable value takes a higher value and the other takes a significant lower value which essentially set the constraint as binding. I am guessing this is far fetched but I am wondering if there is any truth behind it.
$endgroup$
– S_Scouse
Dec 14 '18 at 23:01
$begingroup$
As i understand, the equality in eq. (1) causes the integer infeasibility. Hence, i reformed the equation to $p_1+p_2 < 1$. In this case,, after the solve $p_1$ is taking a value over 5000 and $p_2$ is taking a value just over 800.
$endgroup$
– S_Scouse
Dec 11 '18 at 11:21
$begingroup$
As i understand, the equality in eq. (1) causes the integer infeasibility. Hence, i reformed the equation to $p_1+p_2 < 1$. In this case,, after the solve $p_1$ is taking a value over 5000 and $p_2$ is taking a value just over 800.
$endgroup$
– S_Scouse
Dec 11 '18 at 11:21
$begingroup$
What are the domains of all the variables (lower and upper bounds, integral or not)? Also, do you mean <= in (2) and (3)? Math programs are generally intolerant of strict inequalities.
$endgroup$
– prubin
Dec 13 '18 at 0:07
$begingroup$
What are the domains of all the variables (lower and upper bounds, integral or not)? Also, do you mean <= in (2) and (3)? Math programs are generally intolerant of strict inequalities.
$endgroup$
– prubin
Dec 13 '18 at 0:07
$begingroup$
The variables a are indexed with different generation resources with their limits not exceeding 5950. b are Lagrangian dual variables with no upper bound and both a and b have their lower bound set to 0. There is no integral conditions involved. Yes, i meant <=, thank you for pointing that out. I tried big-M method but the optimization results vary depending on the M value.
$endgroup$
– S_Scouse
Dec 13 '18 at 20:20
$begingroup$
The variables a are indexed with different generation resources with their limits not exceeding 5950. b are Lagrangian dual variables with no upper bound and both a and b have their lower bound set to 0. There is no integral conditions involved. Yes, i meant <=, thank you for pointing that out. I tried big-M method but the optimization results vary depending on the M value.
$endgroup$
– S_Scouse
Dec 13 '18 at 20:20
$begingroup$
I agree that in an SOS1 constraint at most one variable should be nonzero. Is it possible that the solver you are using does not understand or support SOS1 constraints? If it does, I would have to guess that you entered the constraint incorrectly.
$endgroup$
– prubin
Dec 14 '18 at 21:12
$begingroup$
I agree that in an SOS1 constraint at most one variable should be nonzero. Is it possible that the solver you are using does not understand or support SOS1 constraints? If it does, I would have to guess that you entered the constraint incorrectly.
$endgroup$
– prubin
Dec 14 '18 at 21:12
$begingroup$
I am using cplex solver which from what I read supports sos1 constraints. Please let me know if that is the case. Also, is it possible that two variables in a sos1 set take positive values, where one of the sos1 variable value takes a higher value and the other takes a significant lower value which essentially set the constraint as binding. I am guessing this is far fetched but I am wondering if there is any truth behind it.
$endgroup$
– S_Scouse
Dec 14 '18 at 23:01
$begingroup$
I am using cplex solver which from what I read supports sos1 constraints. Please let me know if that is the case. Also, is it possible that two variables in a sos1 set take positive values, where one of the sos1 variable value takes a higher value and the other takes a significant lower value which essentially set the constraint as binding. I am guessing this is far fetched but I am wondering if there is any truth behind it.
$endgroup$
– S_Scouse
Dec 14 '18 at 23:01
|
show 1 more comment
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$begingroup$
As i understand, the equality in eq. (1) causes the integer infeasibility. Hence, i reformed the equation to $p_1+p_2 < 1$. In this case,, after the solve $p_1$ is taking a value over 5000 and $p_2$ is taking a value just over 800.
$endgroup$
– S_Scouse
Dec 11 '18 at 11:21
$begingroup$
What are the domains of all the variables (lower and upper bounds, integral or not)? Also, do you mean <= in (2) and (3)? Math programs are generally intolerant of strict inequalities.
$endgroup$
– prubin
Dec 13 '18 at 0:07
$begingroup$
The variables a are indexed with different generation resources with their limits not exceeding 5950. b are Lagrangian dual variables with no upper bound and both a and b have their lower bound set to 0. There is no integral conditions involved. Yes, i meant <=, thank you for pointing that out. I tried big-M method but the optimization results vary depending on the M value.
$endgroup$
– S_Scouse
Dec 13 '18 at 20:20
$begingroup$
I agree that in an SOS1 constraint at most one variable should be nonzero. Is it possible that the solver you are using does not understand or support SOS1 constraints? If it does, I would have to guess that you entered the constraint incorrectly.
$endgroup$
– prubin
Dec 14 '18 at 21:12
$begingroup$
I am using cplex solver which from what I read supports sos1 constraints. Please let me know if that is the case. Also, is it possible that two variables in a sos1 set take positive values, where one of the sos1 variable value takes a higher value and the other takes a significant lower value which essentially set the constraint as binding. I am guessing this is far fetched but I am wondering if there is any truth behind it.
$endgroup$
– S_Scouse
Dec 14 '18 at 23:01