(Generalized) Benders Decomposition of MINLP Leads to Linear Master and Sub Problem
$begingroup$
I have a mixed-integer nonlinear program (MINLP) which I want to apply (Generalized) Benders Decomposition (GBD) to.
The nonlinearities exclusively originate from products of first-stage decision variables and second-stage decision variables. Consequently, the decomposition of the original MINLP into master problem and sub problem yields two linear programmes (MILP and LP).
My question: Will solving this work using the regular Benders decomposition algorithm for MILP?
I currently don't see a reason why it should not; but I am also far from sure about this. I take it that the dual multipliers of the sub problem satisfy strong duality conditions and that since it is linear it is convex.
optimization nonlinear-optimization mixed-integer-programming
asked Dec 3 '18 at 12:03
Fabian NeumannFabian Neumann
12
$endgroup$
add a comment |
$begingroup$
I have a mixed-integer nonlinear program (MINLP) which I want to apply (Generalized) Benders Decomposition (GBD) to.
The nonlinearities exclusively originate from products of first-stage decision variables and second-stage decision variables. Consequently, the decomposition of the original MINLP into master problem and sub problem yields two linear programmes (MILP and LP).
My question: Will solving this work using the regular Benders decomposition algorithm for MILP?
I currently don't see a reason why it should not; but I am also far from sure about this. I take it that the dual multipliers of the sub problem satisfy strong duality conditions and that since it is linear it is convex.
optimization nonlinear-optimization mixed-integer-programming
asked Dec 3 '18 at 12:03
Fabian NeumannFabian Neumann
12
$endgroup$
add a comment |
$begingroup$
I have a mixed-integer nonlinear program (MINLP) which I want to apply (Generalized) Benders Decomposition (GBD) to.
The nonlinearities exclusively originate from products of first-stage decision variables and second-stage decision variables. Consequently, the decomposition of the original MINLP into master problem and sub problem yields two linear programmes (MILP and LP).
My question: Will solving this work using the regular Benders decomposition algorithm for MILP?
I currently don't see a reason why it should not; but I am also far from sure about this. I take it that the dual multipliers of the sub problem satisfy strong duality conditions and that since it is linear it is convex.
optimization nonlinear-optimization mixed-integer-programming
asked Dec 3 '18 at 12:03
Fabian NeumannFabian Neumann
12
$endgroup$
I have a mixed-integer nonlinear program (MINLP) which I want to apply (Generalized) Benders Decomposition (GBD) to.
The nonlinearities exclusively originate from products of first-stage decision variables and second-stage decision variables. Consequently, the decomposition of the original MINLP into master problem and sub problem yields two linear programmes (MILP and LP).
My question: Will solving this work using the regular Benders decomposition algorithm for MILP?
I currently don't see a reason why it should not; but I am also far from sure about this. I take it that the dual multipliers of the sub problem satisfy strong duality conditions and that since it is linear it is convex.
optimization nonlinear-optimization mixed-integer-programming
optimization nonlinear-optimization mixed-integer-programming
asked Dec 3 '18 at 12:03
Fabian NeumannFabian Neumann
12
asked Dec 3 '18 at 12:03
Fabian NeumannFabian Neumann
12
asked Dec 3 '18 at 12:03
Fabian NeumannFabian Neumann
12
asked Dec 3 '18 at 12:03
Fabian NeumannFabian Neumann
12
asked Dec 3 '18 at 12:03
Fabian NeumannFabian Neumann
12
12
add a comment |
add a comment |
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