Consider the following linear system y = A 1 </msub> x 1 <

cooloicons62

cooloicons62

Answered question

2022-07-15

Consider the following linear system
y = A 1 x 1 + A 2 x 2
subject to the linear constrains
C 1 x 1 + C 2 x 2 d
I am looking for a solution for the above linear system that gives more priority to the coordinates corresponding to x 1 compared to those of x 2 . This is what I precisely mean by priority
If x 1 alone can geenerated the given y while x 2 is kept at its minimum feasible value.
If there are infinite number of solutions for x 1 in step 1 then we take the minimum norm solution.
If x 1 alone cannot generate y then we allow x 2 to participate in generating y with the optimal x 1 obtained in step 1 and 2.
If there are infinite solutions for x 2 , then we take the minimum norm solution.
How to formuate the above described problem as an optimization problem for instance QP?

Answer & Explanation

ladaroh

ladaroh

Beginner2022-07-16Added 11 answers

I'm not sure I fully understand your problem, but I think what you want is to solve
max x 1 , x 2 x 1
subject to
{ A 1 x 1 + A 2 x 2 = y C 1 x 1 + C 2 x 2 d
This is straightforward with the simplex algorithm.

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