LP duality - How is the dual model obtained analytically? Starting from a primal model through mathematical...
I have a LP model:
$$ Maxsum_{i=1}^n c_{j}x_{j}$$
S.t.
$$sum_{i=1}^n a_{i,j}x_{j} le b_{i}$$
$$ x_{j} ge 0$$
$$ i=1 cdots m$$
$$ j=1 cdots n$$
and I get this (Dual model):
$$ Minsum_{i=1}^m b_{i}y_{i}$$
S.t.
$$sum_{j=1}^m a_{i,j}y_{j} ge c_{i}$$
$$ y_{i} ge 0$$
$$ i=1 cdots m$$
$$ j=1 cdots n$$
using a kind of recipe.
I have reviewed some books, Dantzig, Gass, Taha and Lieberman, and the derivation of the Dual model is based on a recipe, or a small case example- Dantzig- using the conditions of Kunt & Tucker. I have a different explanation, I think, and I'm reviewing related works to see if what I have achieved is similar or different to make a publication.
I ask this question to get jobs related to the purpose of buying those jobs with mine and elaborate an article.
operations-research
asked Nov 18 at 23:01
José Dávila
11
add a comment |
I have a LP model:
$$ Maxsum_{i=1}^n c_{j}x_{j}$$
S.t.
$$sum_{i=1}^n a_{i,j}x_{j} le b_{i}$$
$$ x_{j} ge 0$$
$$ i=1 cdots m$$
$$ j=1 cdots n$$
and I get this (Dual model):
$$ Minsum_{i=1}^m b_{i}y_{i}$$
S.t.
$$sum_{j=1}^m a_{i,j}y_{j} ge c_{i}$$
$$ y_{i} ge 0$$
$$ i=1 cdots m$$
$$ j=1 cdots n$$
using a kind of recipe.
I have reviewed some books, Dantzig, Gass, Taha and Lieberman, and the derivation of the Dual model is based on a recipe, or a small case example- Dantzig- using the conditions of Kunt & Tucker. I have a different explanation, I think, and I'm reviewing related works to see if what I have achieved is similar or different to make a publication.
I ask this question to get jobs related to the purpose of buying those jobs with mine and elaborate an article.
operations-research
asked Nov 18 at 23:01
José Dávila
11
Please use the body of the Question to present the full problem statement. Attempting to rely solely on the title to state the problem is apt to cause confusion for Readers. Furthermore the body affords you space to explain what motivates the Question, or what makes it difficult or challenging to approach with your background.
– hardmath
Nov 18 at 23:15
add a comment |
I have a LP model:
$$ Maxsum_{i=1}^n c_{j}x_{j}$$
S.t.
$$sum_{i=1}^n a_{i,j}x_{j} le b_{i}$$
$$ x_{j} ge 0$$
$$ i=1 cdots m$$
$$ j=1 cdots n$$
and I get this (Dual model):
$$ Minsum_{i=1}^m b_{i}y_{i}$$
S.t.
$$sum_{j=1}^m a_{i,j}y_{j} ge c_{i}$$
$$ y_{i} ge 0$$
$$ i=1 cdots m$$
$$ j=1 cdots n$$
using a kind of recipe.
I have reviewed some books, Dantzig, Gass, Taha and Lieberman, and the derivation of the Dual model is based on a recipe, or a small case example- Dantzig- using the conditions of Kunt & Tucker. I have a different explanation, I think, and I'm reviewing related works to see if what I have achieved is similar or different to make a publication.
I ask this question to get jobs related to the purpose of buying those jobs with mine and elaborate an article.
operations-research
asked Nov 18 at 23:01
José Dávila
11
I have a LP model:
$$ Maxsum_{i=1}^n c_{j}x_{j}$$
S.t.
$$sum_{i=1}^n a_{i,j}x_{j} le b_{i}$$
$$ x_{j} ge 0$$
$$ i=1 cdots m$$
$$ j=1 cdots n$$
and I get this (Dual model):
$$ Minsum_{i=1}^m b_{i}y_{i}$$
S.t.
$$sum_{j=1}^m a_{i,j}y_{j} ge c_{i}$$
$$ y_{i} ge 0$$
$$ i=1 cdots m$$
$$ j=1 cdots n$$
using a kind of recipe.
I have reviewed some books, Dantzig, Gass, Taha and Lieberman, and the derivation of the Dual model is based on a recipe, or a small case example- Dantzig- using the conditions of Kunt & Tucker. I have a different explanation, I think, and I'm reviewing related works to see if what I have achieved is similar or different to make a publication.
I ask this question to get jobs related to the purpose of buying those jobs with mine and elaborate an article.
operations-research
operations-research
asked Nov 18 at 23:01
José Dávila
11
asked Nov 18 at 23:01
José Dávila
11
edited Nov 19 at 2:13
asked Nov 18 at 23:01
José Dávila
11
asked Nov 18 at 23:01
José Dávila
11
asked Nov 18 at 23:01
José Dávila
11
11
Please use the body of the Question to present the full problem statement. Attempting to rely solely on the title to state the problem is apt to cause confusion for Readers. Furthermore the body affords you space to explain what motivates the Question, or what makes it difficult or challenging to approach with your background.
– hardmath
Nov 18 at 23:15
add a comment |
Please use the body of the Question to present the full problem statement. Attempting to rely solely on the title to state the problem is apt to cause confusion for Readers. Furthermore the body affords you space to explain what motivates the Question, or what makes it difficult or challenging to approach with your background.
– hardmath
Nov 18 at 23:15
Please use the body of the Question to present the full problem statement. Attempting to rely solely on the title to state the problem is apt to cause confusion for Readers. Furthermore the body affords you space to explain what motivates the Question, or what makes it difficult or challenging to approach with your background.
– hardmath
Nov 18 at 23:15
Please use the body of the Question to present the full problem statement. Attempting to rely solely on the title to state the problem is apt to cause confusion for Readers. Furthermore the body affords you space to explain what motivates the Question, or what makes it difficult or challenging to approach with your background.
– hardmath
Nov 18 at 23:15
add a comment |
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
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%2f3004254%2flp-duality-how-is-the-dual-model-obtained-analytically-starting-from-a-primal%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
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%2f3004254%2flp-duality-how-is-the-dual-model-obtained-analytically-starting-from-a-primal%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
Please use the body of the Question to present the full problem statement. Attempting to rely solely on the title to state the problem is apt to cause confusion for Readers. Furthermore the body affords you space to explain what motivates the Question, or what makes it difficult or challenging to approach with your background.
– hardmath
Nov 18 at 23:15