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onlinear programming with constraints

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i got some  questions,  if someone would answer them, I would appreciate it very much.

well there something called nonlinear programming with constraints and also without them, i've been searching in here how to solve this type of problem but what i found wasn't exactly what i was expecting.

 

for example: if i want to optimise (minimize or minimize o just find a solution that fits) a variable of  a single function, a system of equations or a system of differential equations.

 

How can i make it?  there is a sheet attached  with the different types of problem i mentioned.




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