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I have this kind of optimization problem:

Variable to control: A=A=[a1;a2;...;am]

objective function to minimize: L=A*TL

where

L is a scalar

T is a matrix [1,m]

TL is a matrix [m,1]

constrain:

Dt>Dtv

where:

Dt=[dt1;dt2;...;dtn]

Dtv=[dtv1;dtv2;...;dtvn] is a constant matrix calcuted from other analysis.

dt1=a1*b11+a2*b12+...+am*b1m

dt2=a1*b21+a2*b22+...+am*b2m

dtn=a1*bn1+a2*bn2+...+am*bnm

where

B=[b11,b12,...,b1m;...;bn1,bn2,...,bnm] is the known matrix

A=[a1;a2;...;am]

since m is related to the test conditions, my aim is to reduce them. How can I find a subset of [a1;a2;...;am] that permits me to keep DT>DTV and in the meantime to not increase too much L? Any suggestion? Hopefully to have well explained my question, if no please tell me it.

thanks

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# Variable reduction on constrained optimization techniques

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