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I am looking for an open source implementation of a method doing constrained optimization for nonlinear multivariable function in Java.
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You can have a look at Choco, a framework for constraint programming implemented in java.
IPOPT is the most robust solver I know of.
It has a Java interface although I have no idea how good that is, I only use the C++ API.
There are several open source java implementations that can do this, such as:
I recently ported Michael Powells' COBYLA2 derivative-free optimizer for nonlinear objective functions and constraints to Java. You'll find the source code here.