Optimization function needs to integrated in problem

Hi,

I have a function σ=σ_W+kT/(rS_W )* ln⁡((1-Ka_s)/(1-Ka_s (1-C) ))

here, the value of r , K ,C needs to be sorted out by optimization .

sigma is the surface tension , S_W = 10^-19 , k = 1.38*10^-23 , T=298 K ; a_s= needs to take value from excel file.

my constraints are : 0<K<1 , C>0 and no constraints for r .

i was suggested to use fmincon function to do this ... but i don't have clear idea of this .

Could someone please help ?

Answer 1

[Matt J]

No, it's just a linear equation. Expand the ln() into two terms and rewrite as

σ=σ_W+kT/(rS_W )* ln⁡((1-Ka_s) - kT/(rS_W )*ln(1-Ka_s (1-C) ))

=Known1 +A*Known2+B

where A=k/r and B=kT/(rS_W )*ln(1-Ka_s (1-C) )). This is an unconstrained linear equation in A and B.