In my problem there is exp(x), x is a variable that should be optimized. x can not be vary large, if it is very large, it will cause numerical issues. Is there a way to solve this problem?
Can you place an upper bound on x without cutting off the optimum? if not, can you change the units of x (i.e., re-scale)? Maybe you can take the log and avoid the exp, or use log_sum_exp if appropriate.
If you provide more specific and complete information, perhaps more specific recommendations can be made.