Optimization‏ FIR filter
I'm not sure if I understand your question correctly, but I'll try to make a few things clear. First of all, note that windowing and frequency sampling are not iterative. On the other hand, the Remez exchange algorithm (used in the ParksMcClellan program) is iterative.

All methods for the design of linear phase FIR filters impose the linear phase constraint in the formulation of the design problem, i.e., the filters are always guaranteed to have a linear phase. The difference between the different methods is either the way the optimal solution is computed, or the design criterion, i.e., the way the error to be minimized is defined. Some common design criteria are the least squared error criterion (used in the Matlab function firls.m), or the maximum (Chebyshev) error criterion, where the maximum error is minimized (used in the Matlab function firpm.m).