A linear wirelength objective more effectively captures timing, congestion, and other global placement considerations than a squared wirelength objective. The GORDIAN-L cell placement tool [19] minimizes linear wirelength by first approximating the linear wirelength objective by a modified squared wirelength objective, then executing the following loop-1) minimize the current objective to yield some approximate solution and 2) use the resulting solution to construct a more accurate objective-until the solution converges. This paper shows how to apply a generalization [5], [6] of a 1937 algorithm due to Weiszfeld [22] to placement with a linear wirelength objective and that the main GORDIAN-L loop is actually a special case of this algorithm. We then propose applying a regularization parameter to the generalized Weiszfeld algorithm to control the tradeoff between convergence and solution accuracy; the GORDIAN-L iteration is equivalent to setting this regularization parameter to zero. We also apply novel numerical methods, such as the primal-Newton and primal-dual Newton iterations, to optimize the linear wirelength objective. Finally, we show both theoretically and empirically that the primal-dual Newton iteration stably attains quadratic convergence, while the generalized Weiszfeld iteration is linear convergent. Hence, primal-dual Newton is a superior choice for implementing a placer such as GORDIAN-L, or for any linear wirelength optimization.Index Terms-Analytic placement, GORDIAN-L, interconnect delay, linear placement, linear wirelength, Newton, primal dual, quadratic placement, Weiszfeld. include the design of efficient computational algorithms for large scale scientific computing (e.g., multigrid and domain decomposition algorithms, iterative methods, Krylov subspace methods, and parallel algorithms), VLSI circuit placement, and PDE methods for image processing.