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August 19th, 2019, 05:39 PM   #1
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Question Optimization Problem with Exponential Form (double terms)

Hello, Could anybody help me with this optimization problem?

I want to minimize

sum(s=1,S) a_s * exp(b_s*x_s) + c_s * exp(d_s*x_s)

subject to the constraint:

sum(s=1,S) x_s = A

I am supposed to find x_s which makes the statement minimized. a_s, b_s, c_s, d_s, and A values are constants in the problem.

Example: it is like finding the minimum value for x^a-x^b+4x+3 by finding the proper x based on other constants. (a and b)

Thank you very much for your attention and time!
navidsina2004 is offline  
 
August 19th, 2019, 06:25 PM   #2
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There was a similar question not too long ago.

Replace x_S with [A - sum(s=1,S-1) x_s]. Now it's just minimising a single function with respect to S-1 variables. Long and tedious, but straightforward. (That's what computers are for. )
DarnItJimImAnEngineer is offline  
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