Optimal Chebyshev FIR filters
The Chebyshev criterion minimizes the maximum weighted absolute error:

$$\epsilon=\max_{\omega\in\Omega}W(\omega)|H(\omega)-D(\omega)|\tag{1}$$

where $\Omega$ is the union of all frequency bands of interest, $W(\omega)$ is a positive weight function, $H(\omega)$ is the filter's complex frequency response, and $D(\omega)$ is the complex desired frequency response.

Note that in general, $(1)$ is a complex approximation problem, because $H(\omega)$ and $D(\omega)$ are generally complex-valued. However, in the special case of linear phase FIR filters, $(1)$ can be rewritten as a real approximation problem, for which a very efficient algorithm exists (the Remez exchange algorithm used in the Parks-McClellan method). In the general case of non-linear phase FIR filters or IIR filters, $(1)$ can be solved by (much) more complex general optimization algorithms. For FIR filters, the problem is still a lot easier than for IIR filters, and several algorithms have been suggested (cf. the thesis linked here and the references therein). One of the algorithms is implemented in Matlab's signal processing toolbox: cfirpm.m