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Difference between the "FindMinimum" and "Minimization" ?

Posted 6 years ago

Could any one please explain with example what is the difference between the "Find Minimum" and "Minimization" functions in Mathematica?

POSTED BY: Amir Khan
3 Replies

Read this tutorial on optimization in WMA

POSTED BY: Neil Singer
Posted 6 years ago

Thanks for the details. This is still not a definite answer. The problem is that if I have a multivariable function and I have to fit for one variable to find its minimum, while all other variables are mixed; some are kept free and some are constrained. How would I have to decide that I should use "Find minimum" or "Minimize". If both functions give different results, how would I decide which one is correct and which is wrong? For the single parameter function, it is fine that "Minimize" will give the global minimum while for "Find Minimum" will give the local minimum, but how about for the multivariable function, can this application still hold? Thanks!

POSTED BY: Amir Khan

FindMinimum is the oldest function, dating back to 1988. It implements numerical algorithms and will output a floating point result. Minimize is newer (2003), and it uses symbolic methods with exact results. They have distinct purposes and applicability. The confusing names are due to historical accident.

For example

Minimize[x + 2 (x^2 - 1)^2, x] // N

will find the global minimum, while

FindMinimum[x + 2 (x^2 - 1)^2, x]

will find a local, but not global, minimum. On the other hand, Minimize can fail to give an answer for complicated functions:

Minimize[Exp[Cos[x]] + 2 (x^2 - 1)^2, x]

while FindMinimum will give something useful:

FindMinimum[Exp[Cos[x]] + 2 (x^2 - 1)^2, x]
POSTED BY: Gianluca Gorni
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