Yes. Unlike l_\infty, sums of exponentials are smooth everywhere, and smooth functions are easier to optimize. But geometrically, the two can be brought arbitrarily close together by adjusting the exponents with a multiplicative constant.
That's TeX for "l" with subscript infinity. It's a vector norm, and is equal to the element of the vector with maximal absolute value. It's also called the max-norm and sup-norm (for the infinite dimensional generalization, e.g., where the vector becomes a real-valued function of a single real variable).
A norm (meaning a definition of "length") where the length of a vector is defined as the largest absolute value of any of its components. Its one of the standard lp norms, you get a norm for every p in the closed interval [1,infinity]. The standard Euclidian norm is the case p=2.
