My Math Forum Optimization Problem with Exponential Form (double terms)

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 August 19th, 2019, 05:39 PM #1 Newbie   Joined: Aug 2019 From: US Posts: 1 Thanks: 0 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!
 August 19th, 2019, 06:25 PM #2 Senior Member   Joined: Jun 2019 From: USA Posts: 213 Thanks: 90 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. )

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