What is a good optimization algorithm/tool for otimization on Partially Ordered set?

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Actually I'm interested to minimize following kind of functions:

$f: U \rightarrow V$

where:

$U$ is a vector space and $V$ is a Ordered vector space, i mean Partially Ordered Vector space.

Special Case : $U$ is any set and $V$ is a Partially Ordered set.

What kind of Optimization algorithm works here? What is the starting point. Is there any ready made optimization toolbox available for this?

Thanks in advance !!!

FYI:

After googling a lot. I found this[http://en.wikipedia.org/wiki/Vector_optimization] is the closest thing I'm searching for. The references given in that page are really helpful.