Saddle Point Maximization
My question is that in general, is there a case where saddle point be the global max of a function?
I am solving a game theory question which the optimal solution is the saddle point. Can I conclude that the optimal solution is at the boundaries?
optimization
asked Jan 4 at 18:30
user3425989user3425989
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My question is that in general, is there a case where saddle point be the global max of a function?
I am solving a game theory question which the optimal solution is the saddle point. Can I conclude that the optimal solution is at the boundaries?
optimization
asked Jan 4 at 18:30
user3425989user3425989
11
New contributor
user3425989 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I thought saddles were by definition neither max nor min.
– Randall
Jan 4 at 18:32
What game theory question?
– cgiovanardi
Jan 5 at 0:02
add a comment |
My question is that in general, is there a case where saddle point be the global max of a function?
I am solving a game theory question which the optimal solution is the saddle point. Can I conclude that the optimal solution is at the boundaries?
optimization
asked Jan 4 at 18:30
user3425989user3425989
11
New contributor
user3425989 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
My question is that in general, is there a case where saddle point be the global max of a function?
I am solving a game theory question which the optimal solution is the saddle point. Can I conclude that the optimal solution is at the boundaries?
optimization
optimization
asked Jan 4 at 18:30
user3425989user3425989
11
New contributor
user3425989 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 18:30
user3425989user3425989
11
New contributor
user3425989 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 18:30
user3425989user3425989
11
New contributor
user3425989 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 18:30
user3425989user3425989
11
asked Jan 4 at 18:30
user3425989user3425989
11
11
New contributor
user3425989 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user3425989 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user3425989 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I thought saddles were by definition neither max nor min.
– Randall
Jan 4 at 18:32
What game theory question?
– cgiovanardi
Jan 5 at 0:02
add a comment |
I thought saddles were by definition neither max nor min.
– Randall
Jan 4 at 18:32
What game theory question?
– cgiovanardi
Jan 5 at 0:02
I thought saddles were by definition neither max nor min.
– Randall
Jan 4 at 18:32
I thought saddles were by definition neither max nor min.
– Randall
Jan 4 at 18:32
What game theory question?
– cgiovanardi
Jan 5 at 0:02
What game theory question?
– cgiovanardi
Jan 5 at 0:02
add a comment |
2 Answers
2
active
oldest
votes
By definition, a saddle point is
- a local min in some directions and
- a local max in other directions at the same time.
Since it is a local min in at least one direction, there are more optimal points for maximization. Ditto minimization from the other directions...
answered Jan 4 at 18:32
gt6989bgt6989b
33.3k22452
Thanks, So can we say that is is only boundary solutions?
– user3425989
Jan 4 at 18:40
@user3425989 if no relative extrema lie inside the region, then all candidates for the optimal solutions will come from the boundary.
– gt6989b
Jan 6 at 5:29
add a comment |
It is a common misunderstanding in optimization how a saddle point may be the optimal point. The saddle point that is the optimal solution is the saddle point for the Lagrange function $L(x,u,v)$, not the saddle point for the objective function itself.
answered Jan 4 at 18:39
A.Γ.A.Γ.
22.6k32656
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
By definition, a saddle point is
- a local min in some directions and
- a local max in other directions at the same time.
Since it is a local min in at least one direction, there are more optimal points for maximization. Ditto minimization from the other directions...
answered Jan 4 at 18:32
gt6989bgt6989b
33.3k22452
Thanks, So can we say that is is only boundary solutions?
– user3425989
Jan 4 at 18:40
@user3425989 if no relative extrema lie inside the region, then all candidates for the optimal solutions will come from the boundary.
– gt6989b
Jan 6 at 5:29
add a comment |
By definition, a saddle point is
- a local min in some directions and
- a local max in other directions at the same time.
Since it is a local min in at least one direction, there are more optimal points for maximization. Ditto minimization from the other directions...
answered Jan 4 at 18:32
gt6989bgt6989b
33.3k22452
Thanks, So can we say that is is only boundary solutions?
– user3425989
Jan 4 at 18:40
@user3425989 if no relative extrema lie inside the region, then all candidates for the optimal solutions will come from the boundary.
– gt6989b
Jan 6 at 5:29
add a comment |
By definition, a saddle point is
- a local min in some directions and
- a local max in other directions at the same time.
Since it is a local min in at least one direction, there are more optimal points for maximization. Ditto minimization from the other directions...
answered Jan 4 at 18:32
gt6989bgt6989b
33.3k22452
By definition, a saddle point is
- a local min in some directions and
- a local max in other directions at the same time.
Since it is a local min in at least one direction, there are more optimal points for maximization. Ditto minimization from the other directions...
answered Jan 4 at 18:32
gt6989bgt6989b
33.3k22452
answered Jan 4 at 18:32
gt6989bgt6989b
33.3k22452
answered Jan 4 at 18:32
gt6989bgt6989b
33.3k22452
answered Jan 4 at 18:32
gt6989bgt6989b
33.3k22452
33.3k22452
Thanks, So can we say that is is only boundary solutions?
– user3425989
Jan 4 at 18:40
@user3425989 if no relative extrema lie inside the region, then all candidates for the optimal solutions will come from the boundary.
– gt6989b
Jan 6 at 5:29
add a comment |
Thanks, So can we say that is is only boundary solutions?
– user3425989
Jan 4 at 18:40
@user3425989 if no relative extrema lie inside the region, then all candidates for the optimal solutions will come from the boundary.
– gt6989b
Jan 6 at 5:29
Thanks, So can we say that is is only boundary solutions?
– user3425989
Jan 4 at 18:40
Thanks, So can we say that is is only boundary solutions?
– user3425989
Jan 4 at 18:40
@user3425989 if no relative extrema lie inside the region, then all candidates for the optimal solutions will come from the boundary.
– gt6989b
Jan 6 at 5:29
@user3425989 if no relative extrema lie inside the region, then all candidates for the optimal solutions will come from the boundary.
– gt6989b
Jan 6 at 5:29
add a comment |
It is a common misunderstanding in optimization how a saddle point may be the optimal point. The saddle point that is the optimal solution is the saddle point for the Lagrange function $L(x,u,v)$, not the saddle point for the objective function itself.
answered Jan 4 at 18:39
A.Γ.A.Γ.
22.6k32656
add a comment |
It is a common misunderstanding in optimization how a saddle point may be the optimal point. The saddle point that is the optimal solution is the saddle point for the Lagrange function $L(x,u,v)$, not the saddle point for the objective function itself.
answered Jan 4 at 18:39
A.Γ.A.Γ.
22.6k32656
add a comment |
It is a common misunderstanding in optimization how a saddle point may be the optimal point. The saddle point that is the optimal solution is the saddle point for the Lagrange function $L(x,u,v)$, not the saddle point for the objective function itself.
answered Jan 4 at 18:39
A.Γ.A.Γ.
22.6k32656
It is a common misunderstanding in optimization how a saddle point may be the optimal point. The saddle point that is the optimal solution is the saddle point for the Lagrange function $L(x,u,v)$, not the saddle point for the objective function itself.
answered Jan 4 at 18:39
A.Γ.A.Γ.
22.6k32656
answered Jan 4 at 18:39
A.Γ.A.Γ.
22.6k32656
answered Jan 4 at 18:39
A.Γ.A.Γ.
22.6k32656
answered Jan 4 at 18:39
A.Γ.A.Γ.
22.6k32656
22.6k32656
add a comment |
add a comment |
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I thought saddles were by definition neither max nor min.
– Randall
Jan 4 at 18:32
What game theory question?
– cgiovanardi
Jan 5 at 0:02