DEQ
Weiszfeld, geometric median
Computes the geometic median of random 2D points UNDER CONSTRUCTION
2025.Sep.22 08:12:56
Points Number of points in region.
Width, height Regin width and height.
Algorithm   Algorithm to find g.-median.
Tolerance Convergence tolerance.
Method           Method of multivariable minimization.
Trials (N), seed    → Monte Carlo trials, seed.
Simul. y-, x-axis bounds Simulation: axes bound in plot.
Plot points Simulation: n. of plot points.
Show values Show graph coordinates.

Computes the geometric median, (in a rectangular region) by minimum total distance (numerically): either by multivariate minimization or by the Weiszfeld algorithm.

Minimization methods: (1) NM=Nelder-Mead, (2) Pow=Powell, (3) CG, (4) BFGS, (5) LB=L-BFGS-B, (6) TNC, (7) CL=COBYLA, (8) CQ=COBYQA, (9) SL=SLSQP.

Shows the graphical results: # (a) region with random points, and centroid as larger circle and g. median as smaller circle; and (b) random behavior of simulated variable.
ODEs Fig. 1
References: Plate: Weiszfeld

• Optimization (scipy.optimize), The SciPy community. • 'minimize' (methods)

• Vászonyi, Andrew (Weiszfeld)

• The Dantzig Library (ORMS Today)

• CISTI'2026, 17–19 June (to be confirmed) 2026, Santiago de Compostela (Spain).

• 1913-09-02: Gel'fand, Israil Moisyeevich (Израиль Моисеевич Гельфанд) (†2009-10-05, 96 yrs.).

 
 
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Created: 2025-09-01 — Last modified: 2025-09-06