maximising with dynamic parameters

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econgrad 2013-8-1

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https://ww2.mathworks.cn/matlabcentral/answers/83764-maximising-with-dynamic-parameters

The function I have looks like this: ln(1+a*x1+b*x2). I need to maximise this with respect to x1 and x2 but for each choice of x1 and x2 the values of a and b would also change. For example if x1=1 and x2=2 then a=2 and b=3 , x1=2 and x2=2 then a=1 and b=4 and so on. Please suggest if this can be done and how it can be approached.

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Roger Stafford 2013-8-2

You wrote "and so on" way too soon. You need to explain the relationship between the x1,x2 pair values and the corresponding a,b pair values in much greater detail before any useful advice can be given as to how to maximize your function value.

econgrad 2013-8-11

thank you so much for your reply and sorry for being late. let me give you the detail description: a and b are implicit functions i.e. a=a(x1,x2,c1,c2) and b=b(x1,x2,c1,c2). When x1 and x2 changes, c1 and c2 would also change and that change has to obtained by finding the fixed points of a(x1,x2,c1,c2) and b(x1,x2,c1,c2). After finding the new c1,c2 by fixed point iteration, I get a new a(x1,x2,c1,c2) & b(x1,x2,c1,c2).

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