simplifying an algebraic expression in 6 variables

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Az.Sa 2022-6-7

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编辑： Torsten 2022-6-8

采纳的回答： Torsten

hello,

can you please help me with the following , I am trying to write matlab code to simplyfy this expression :

0.95 x1 -0.85 x2-0.14 x3+0.13 x4 -0.88 x5 -1.52 x6 - 1.64 * sqrt{ ( 0.100 x1 + 0.06 x2 + 1.03 x3 + 0.88 x4+0.02 x5 +0.19x6) ^2 + (0.04 x1 -0.05 x2+0.057 x3+0.15 x4-0.01 x5 -0.08 x6) ^2 }

I want to combine all x1 together and x2 as well ..etc

Thank you in advance

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Torsten 2022-6-7

编辑：Torsten 2022-6-7

I'm surprised that the expression under curly brackets is not squared.

Just use lsqnonlin or lsqcurvefit and set up the model function as is (with the square root). No simplification is possible (and needed).

Az.Sa 2022-6-7

编辑：Az.Sa 2022-6-7

I am sorry can you give me a clue how to setup my optimization problem correctly. I am not sure how to construct the code corresponding to the above equation. Also, You are right the expression suppose to be squared if I am applying least square. However, If I want to use least absolute deviation insted of least square how can I deal with that ?

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采纳的回答

Torsten 2022-6-7

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https://ww2.mathworks.cn/matlabcentral/answers/1735550-simplifying-an-algebraic-expression-in-6-variables#answer_980995

编辑：Torsten 2022-6-8

在 MATLAB Online 中打开

fun = @(x) sum( (y - A.'*x - K*sqrt((B.'*x).^2 + (C.'*x).^2) ).^2 );
Aeq = ones(1,6);
beq = 1;
lb = zeros(1,6);
ub = ones(1,6);
x0 = ones(1,6)/6;
x = fmincon(fun,x0,[],[],Aeq,beq,lb,ub)