Variable reduction on constrained optimization techniques

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SUMMARY

This discussion focuses on variable reduction techniques for constrained optimization problems, specifically minimizing the objective function L=A*TL while adhering to the constraint Dt>Dtv. The variables A consist of elements [a1;a2;...;am], and the matrix B is defined as [b11,b12,...,b1m;...;bn1,bn2,...,bnm]. The user seeks methods to identify a subset of variables that maintain the constraint without significantly increasing the scalar L. Effective strategies for variable selection in this context are essential for optimizing performance.

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  • Understanding of constrained optimization techniques
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Researchers, data scientists, and optimization engineers working on constrained optimization problems who need to reduce variables while maintaining performance metrics.

serbring
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Hi all,

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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