Searching Solver for a convex seperable Integer programm
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I have given a problem of the form $min sum_{j=1}^n f_j(x_j)$, s.t. $sum_{j=1}^n g_j(x_j) leq b$. Both the $g_j$ and $f_j$ are convex functions and $x_j$ are integer, so its a convex seperable Integer programm.
Are there any solvers for this problem (preferably R or matlab, but ill take anything)?
Ive been googling but the only solution I found so far would be to transform the problem to a 0-1 knapsack problem and use an R solver. That would work, but I'd prefer a general solution without transforming the problem by hand first, because i have several problems of this type.
convex-optimization discrete-optimization
asked Nov 17 at 20:11
StefanWK
727
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up vote
0
down vote
favorite
I have given a problem of the form $min sum_{j=1}^n f_j(x_j)$, s.t. $sum_{j=1}^n g_j(x_j) leq b$. Both the $g_j$ and $f_j$ are convex functions and $x_j$ are integer, so its a convex seperable Integer programm.
Are there any solvers for this problem (preferably R or matlab, but ill take anything)?
Ive been googling but the only solution I found so far would be to transform the problem to a 0-1 knapsack problem and use an R solver. That would work, but I'd prefer a general solution without transforming the problem by hand first, because i have several problems of this type.
convex-optimization discrete-optimization
asked Nov 17 at 20:11
StefanWK
727
What is the range for $x_j$ (so an upper bound)? Any MINLP solver should be able to solve this.
– LinAlg
Nov 17 at 23:15
The upper bound depends on the specific problem (I have several of the same form) but I can calculate it for each problem. So MINLP solvers work also for a full integer NLP? Can you recommend one?
– StefanWK
Nov 18 at 11:35
Typically MINLP solvers do not work so well since solving the nonlinear problems to optimality is difficult. Due to the separability however, you may be lucky.
– LinAlg
Nov 18 at 13:43
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have given a problem of the form $min sum_{j=1}^n f_j(x_j)$, s.t. $sum_{j=1}^n g_j(x_j) leq b$. Both the $g_j$ and $f_j$ are convex functions and $x_j$ are integer, so its a convex seperable Integer programm.
Are there any solvers for this problem (preferably R or matlab, but ill take anything)?
Ive been googling but the only solution I found so far would be to transform the problem to a 0-1 knapsack problem and use an R solver. That would work, but I'd prefer a general solution without transforming the problem by hand first, because i have several problems of this type.
convex-optimization discrete-optimization
asked Nov 17 at 20:11
StefanWK
727
I have given a problem of the form $min sum_{j=1}^n f_j(x_j)$, s.t. $sum_{j=1}^n g_j(x_j) leq b$. Both the $g_j$ and $f_j$ are convex functions and $x_j$ are integer, so its a convex seperable Integer programm.
Are there any solvers for this problem (preferably R or matlab, but ill take anything)?
Ive been googling but the only solution I found so far would be to transform the problem to a 0-1 knapsack problem and use an R solver. That would work, but I'd prefer a general solution without transforming the problem by hand first, because i have several problems of this type.
convex-optimization discrete-optimization
convex-optimization discrete-optimization
asked Nov 17 at 20:11
StefanWK
727
asked Nov 17 at 20:11
StefanWK
727
asked Nov 17 at 20:11
StefanWK
727
asked Nov 17 at 20:11
StefanWK
727
asked Nov 17 at 20:11
StefanWK
727
727
What is the range for $x_j$ (so an upper bound)? Any MINLP solver should be able to solve this.
– LinAlg
Nov 17 at 23:15
The upper bound depends on the specific problem (I have several of the same form) but I can calculate it for each problem. So MINLP solvers work also for a full integer NLP? Can you recommend one?
– StefanWK
Nov 18 at 11:35
Typically MINLP solvers do not work so well since solving the nonlinear problems to optimality is difficult. Due to the separability however, you may be lucky.
– LinAlg
Nov 18 at 13:43
add a comment |
What is the range for $x_j$ (so an upper bound)? Any MINLP solver should be able to solve this.
– LinAlg
Nov 17 at 23:15
The upper bound depends on the specific problem (I have several of the same form) but I can calculate it for each problem. So MINLP solvers work also for a full integer NLP? Can you recommend one?
– StefanWK
Nov 18 at 11:35
Typically MINLP solvers do not work so well since solving the nonlinear problems to optimality is difficult. Due to the separability however, you may be lucky.
– LinAlg
Nov 18 at 13:43
What is the range for $x_j$ (so an upper bound)? Any MINLP solver should be able to solve this.
– LinAlg
Nov 17 at 23:15
What is the range for $x_j$ (so an upper bound)? Any MINLP solver should be able to solve this.
– LinAlg
Nov 17 at 23:15
The upper bound depends on the specific problem (I have several of the same form) but I can calculate it for each problem. So MINLP solvers work also for a full integer NLP? Can you recommend one?
– StefanWK
Nov 18 at 11:35
The upper bound depends on the specific problem (I have several of the same form) but I can calculate it for each problem. So MINLP solvers work also for a full integer NLP? Can you recommend one?
– StefanWK
Nov 18 at 11:35
Typically MINLP solvers do not work so well since solving the nonlinear problems to optimality is difficult. Due to the separability however, you may be lucky.
– LinAlg
Nov 18 at 13:43
Typically MINLP solvers do not work so well since solving the nonlinear problems to optimality is difficult. Due to the separability however, you may be lucky.
– LinAlg
Nov 18 at 13:43
add a comment |
1 Answer
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1
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If the range of $x_j$ is limited, you can formulate the problems in terms of binary variables $y_{jk}$, where $y_{jk}=1$ if $x_j=k$. The problem is then:
$$min_{y in{0,1}^{ntimes K}} left{ sum_j sum_k y_{jk} f_j(k) mid sum_j sum_k y_{jk} g_j(k) leq b, sum_k y_{jk}=1 right}$$
The advantage of separability carries over, so I expect the relaxation to be efficiently solvable.
answered Nov 18 at 13:47
LinAlg
7,6791520
thanks for your answers so far, ive been thinking about it and have posted another question on the topic:math.stackexchange.com/questions/3004893/…
– StefanWK
Nov 19 at 12:55
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
If the range of $x_j$ is limited, you can formulate the problems in terms of binary variables $y_{jk}$, where $y_{jk}=1$ if $x_j=k$. The problem is then:
$$min_{y in{0,1}^{ntimes K}} left{ sum_j sum_k y_{jk} f_j(k) mid sum_j sum_k y_{jk} g_j(k) leq b, sum_k y_{jk}=1 right}$$
The advantage of separability carries over, so I expect the relaxation to be efficiently solvable.
answered Nov 18 at 13:47
LinAlg
7,6791520
thanks for your answers so far, ive been thinking about it and have posted another question on the topic:math.stackexchange.com/questions/3004893/…
– StefanWK
Nov 19 at 12:55
add a comment |
up vote
1
down vote
accepted
If the range of $x_j$ is limited, you can formulate the problems in terms of binary variables $y_{jk}$, where $y_{jk}=1$ if $x_j=k$. The problem is then:
$$min_{y in{0,1}^{ntimes K}} left{ sum_j sum_k y_{jk} f_j(k) mid sum_j sum_k y_{jk} g_j(k) leq b, sum_k y_{jk}=1 right}$$
The advantage of separability carries over, so I expect the relaxation to be efficiently solvable.
answered Nov 18 at 13:47
LinAlg
7,6791520
thanks for your answers so far, ive been thinking about it and have posted another question on the topic:math.stackexchange.com/questions/3004893/…
– StefanWK
Nov 19 at 12:55
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
If the range of $x_j$ is limited, you can formulate the problems in terms of binary variables $y_{jk}$, where $y_{jk}=1$ if $x_j=k$. The problem is then:
$$min_{y in{0,1}^{ntimes K}} left{ sum_j sum_k y_{jk} f_j(k) mid sum_j sum_k y_{jk} g_j(k) leq b, sum_k y_{jk}=1 right}$$
The advantage of separability carries over, so I expect the relaxation to be efficiently solvable.
answered Nov 18 at 13:47
LinAlg
7,6791520
If the range of $x_j$ is limited, you can formulate the problems in terms of binary variables $y_{jk}$, where $y_{jk}=1$ if $x_j=k$. The problem is then:
$$min_{y in{0,1}^{ntimes K}} left{ sum_j sum_k y_{jk} f_j(k) mid sum_j sum_k y_{jk} g_j(k) leq b, sum_k y_{jk}=1 right}$$
The advantage of separability carries over, so I expect the relaxation to be efficiently solvable.
answered Nov 18 at 13:47
LinAlg
7,6791520
answered Nov 18 at 13:47
LinAlg
7,6791520
answered Nov 18 at 13:47
LinAlg
7,6791520
answered Nov 18 at 13:47
LinAlg
7,6791520
7,6791520
thanks for your answers so far, ive been thinking about it and have posted another question on the topic:math.stackexchange.com/questions/3004893/…
– StefanWK
Nov 19 at 12:55
add a comment |
thanks for your answers so far, ive been thinking about it and have posted another question on the topic:math.stackexchange.com/questions/3004893/…
– StefanWK
Nov 19 at 12:55
thanks for your answers so far, ive been thinking about it and have posted another question on the topic:math.stackexchange.com/questions/3004893/…
– StefanWK
Nov 19 at 12:55
thanks for your answers so far, ive been thinking about it and have posted another question on the topic:math.stackexchange.com/questions/3004893/…
– StefanWK
Nov 19 at 12:55
add a comment |
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What is the range for $x_j$ (so an upper bound)? Any MINLP solver should be able to solve this.
– LinAlg
Nov 17 at 23:15
The upper bound depends on the specific problem (I have several of the same form) but I can calculate it for each problem. So MINLP solvers work also for a full integer NLP? Can you recommend one?
– StefanWK
Nov 18 at 11:35
Typically MINLP solvers do not work so well since solving the nonlinear problems to optimality is difficult. Due to the separability however, you may be lucky.
– LinAlg
Nov 18 at 13:43