Suppose that you are trying to solve the optimization problem: <mtable columnalign="left left l

vaganzahi

vaganzahi

Answered question

2022-05-26

Suppose that you are trying to solve the optimization problem:
maximize v x subject to A x b A R m × n
(i.e. trying to solve an optimization problem in n variables with m linear inequality constraints).
This problem can be reduced to running a solution finding algorithm on a different system of linear equations in k variables. What is the smallest value of k for which this can be done.

Answer & Explanation

Julien Carrillo

Julien Carrillo

Beginner2022-05-27Added 13 answers

The answer is m + n. The idea is that you need to solve for the given inequalities and for the dual as well. The given inequalities will have n variables, the dual will have m, so all in all, you will need to solve for m + n variables!

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