A Spline Smoothing Newton Method for 𝐿_∞ Distance Regression with Bound Constraints

Table 1

Test result for the example, 𝑥⁰=(0,0,−2,2,−2,1), 𝑡=10⁻⁵.

𝑚	Method	𝑥^∗	𝑓(𝑥^∗)	Time
	SN	(−0.156746,−0.124595,…,1.732075)	0.744533	1.891536
20000	TSN	(−0.156611,−0.123928,…,1.736362)	0.743643	3.878818
	SQP	(−0.155824,−0.126803,…,1.760751)	0.927184	31.302830
	SN	(−0.156984,−0.125677,…,1.732449)	0.851957	4.166439
50000	TSN	(−0.155253,−0.123374,…,1.733202)	0.851803	10.761201
	SQP	(−0.155824,−0.126194,…,1.760880)	0.971305	33.716271
	SN	(−0.155158,−0.124954,…,1.736343)	0.856780	16.437595
100000	TSN	(−0.155159,−0.124956,…,1.736346)	0.856767	37.235130
	SQP	(−0.157418,−0.125016,…,1.761221)	1.025103	101.817872