Can someone please tell me how to go about optimizing this system of equations? It is weird because the residuals are computed with ##A = B*X_1+C*X_2## but X_1 and X_2 are computed in a separate function ##[X_1,X_2]=f(k1,k2,H0,G0)##, and what I am optimizing is a parameter in that second function.

I have this system of equations

H G K1 = HG

H G K2 = H2G

H0 = H + HG +2H2G

G0 = G + HG + H2G

HG, H2G, HG2, H, G are variables, and H2G represents 2H and G getting stuck together forming H2G.

In the last 2 equations H0, G0 are constants that represent the total H in the system (The H distributes itself to free H, HG, and H2G, so if you look at the H0 equation you see 2*H2G because H2G contains 2 H)

I can solve this system with a root finding algorithm like newtons method if I know K1, K2 and H0,G0.

The trouble is I don't really know K1 and K2, I want to solve for them.

I have 12 experiments represented as 12 equations :

##A_0H0_2 = A_1H + A_2HG + A_3H2G## with condition ##G0=G0_2##

##A_0H0_3 = A_1H + A_2HG + A_3H2G## with condition ##G0=G0_3##

##A_0H0_4 = A_1H + A_2HG + A_3H2G## with condition ##G0=G0_4##

and 9 more equations exactly like this.

Basically, these represent different experiments. The variables (H, G, HG, H2G) should all change because H0 and G0 change, but K1 and K2 should remain the same.

How can I optimize K1 and K2 (in a least squares sense)? Is there an algorithm that can update K1 and K2 using these 12 experiments which contain values computed by functions of K1 and K2?

I have this system of equations

H G K1 = HG

H G K2 = H2G

H0 = H + HG +2H2G

G0 = G + HG + H2G

HG, H2G, HG2, H, G are variables, and H2G represents 2H and G getting stuck together forming H2G.

In the last 2 equations H0, G0 are constants that represent the total H in the system (The H distributes itself to free H, HG, and H2G, so if you look at the H0 equation you see 2*H2G because H2G contains 2 H)

I can solve this system with a root finding algorithm like newtons method if I know K1, K2 and H0,G0.

The trouble is I don't really know K1 and K2, I want to solve for them.

I have 12 experiments represented as 12 equations :

##A_0H0_2 = A_1H + A_2HG + A_3H2G## with condition ##G0=G0_2##

##A_0H0_3 = A_1H + A_2HG + A_3H2G## with condition ##G0=G0_3##

##A_0H0_4 = A_1H + A_2HG + A_3H2G## with condition ##G0=G0_4##

and 9 more equations exactly like this.

Basically, these represent different experiments. The variables (H, G, HG, H2G) should all change because H0 and G0 change, but K1 and K2 should remain the same.

How can I optimize K1 and K2 (in a least squares sense)? Is there an algorithm that can update K1 and K2 using these 12 experiments which contain values computed by functions of K1 and K2?

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