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Here is my understanding:
Let’s assume that you are long equities, long bonds, short Euro.
factor push: what would happen if equities fell by 10% (though there could be some other factors, not just individual sector)
worst-case scenario: equities go down, bonds go down, Euro goes up.
maximum-loss optimization: what’s the maximum loss within certain parameters. For example, loss based on 10% fall and equities and bonds and Euro goes up by 5% (if your parameters are 10%, 10% and 5%).

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