Chavtal-Gomory inequalities.
up vote
0
down vote
favorite
Let $X = {x in {0,1}^n | x_i + x_j leq 1 forall i not = j}$. Clearly, the inequalities $x_1 + ldots + x_k leq 1$ are all valid inequalities for $X$(for each $k geq 3$). How can we obtain these inequalities using the CG procedure?
My attempt:
I tried to start with $k = 3$ first and we get $x_1 + x_2 + x_3 leq 1$. Then following the CG procedure, I would take the floor of the whole inequality and we would be able to use induction to prove for a more general case, however, I don't know if this is the right way to obtain the inequalities using the CG procedure.
optimization
asked Nov 15 at 5:16
HD5450
11
add a comment |
up vote
0
down vote
favorite
Let $X = {x in {0,1}^n | x_i + x_j leq 1 forall i not = j}$. Clearly, the inequalities $x_1 + ldots + x_k leq 1$ are all valid inequalities for $X$(for each $k geq 3$). How can we obtain these inequalities using the CG procedure?
My attempt:
I tried to start with $k = 3$ first and we get $x_1 + x_2 + x_3 leq 1$. Then following the CG procedure, I would take the floor of the whole inequality and we would be able to use induction to prove for a more general case, however, I don't know if this is the right way to obtain the inequalities using the CG procedure.
optimization
asked Nov 15 at 5:16
HD5450
11
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $X = {x in {0,1}^n | x_i + x_j leq 1 forall i not = j}$. Clearly, the inequalities $x_1 + ldots + x_k leq 1$ are all valid inequalities for $X$(for each $k geq 3$). How can we obtain these inequalities using the CG procedure?
My attempt:
I tried to start with $k = 3$ first and we get $x_1 + x_2 + x_3 leq 1$. Then following the CG procedure, I would take the floor of the whole inequality and we would be able to use induction to prove for a more general case, however, I don't know if this is the right way to obtain the inequalities using the CG procedure.
optimization
asked Nov 15 at 5:16
HD5450
11
Let $X = {x in {0,1}^n | x_i + x_j leq 1 forall i not = j}$. Clearly, the inequalities $x_1 + ldots + x_k leq 1$ are all valid inequalities for $X$(for each $k geq 3$). How can we obtain these inequalities using the CG procedure?
My attempt:
I tried to start with $k = 3$ first and we get $x_1 + x_2 + x_3 leq 1$. Then following the CG procedure, I would take the floor of the whole inequality and we would be able to use induction to prove for a more general case, however, I don't know if this is the right way to obtain the inequalities using the CG procedure.
optimization
optimization
asked Nov 15 at 5:16
HD5450
11
asked Nov 15 at 5:16
HD5450
11
asked Nov 15 at 5:16
HD5450
11
asked Nov 15 at 5:16
HD5450
11
asked Nov 15 at 5:16
HD5450
11
11
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2999250%2fchavtal-gomory-inequalities%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
