Consider a set of 500 equations in 100 variables: Ax\le b, given by a_{i}^{T}x\le b_{i}. Suppose that these are not feasible, i.e., there is no solution that satisfies all of them. Show that in fact, there must be a subset of at most 101 which are not feasible. (Hint: Use duality and complementary slackness, E.g., what is the LP that finds the minimum value of slack s we have to put into Ax−1s≤b to make it feasible? The dual of such an LP could then be useful, and complementary slackness can relate variables and constraints between the two.).
Consider a set of 500 equations in 100 variables: Ax\le b, given by a_{i}^{T}x\le b_{i}. Suppose that these are not feasible, i.e., there is no solution that satisfies all of them. Show that in fact, there must be a subset of at most 101 which are not feasible. (Hint: Use duality and complementary slackness, E.g., what is the LP that finds the minimum value of slack s we have to put into Ax−1s≤b to make it feasible? The dual of such an LP could then be useful, and complementary slackness can relate variables and constraints between the two.).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Consider a set of 500 equations in 100 variables: Ax\le b, given by a_{i}^{T}x\le b_{i}. Suppose that these are not feasible, i.e., there is no solution that satisfies all of them. Show that in fact, there must be a subset of at most 101 which are not feasible. (Hint: Use duality and complementary slackness, E.g., what is the LP that finds the minimum value of slack s we have to put into Ax−1s≤b to make it feasible? The dual of such an LP could then be useful, and complementary slackness can relate variables and constraints between the two.).
AI-Generated Solution
AI-generated content may present inaccurate or offensive content that does not represent bartleby’s views.
Unlock instant AI solutions
Tap the button
to generate a solution
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
