A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum Functions

Table 3

𝑥₀=(1,1)^𝑇𝜎₁=0.01,𝜎₂=1 and computes 𝑑_𝑘 by (3.3).

Step	(𝑥1,𝑥2)^𝑇	𝐹(𝑥)
19	(0.00989,1.0000)^𝑇	1.0𝑒−004∗(0.9784,0.9784)^𝑇
20	(0.0095,1.0000)^𝑇	1.0𝑒−004∗(0.9087,0.9087)^𝑇
21	(0.0092,1.0000)^𝑇	1.0𝑒−004∗(0.8481,0.8481)^𝑇
22	(0.0089,1.0000)^𝑇	1.0𝑒−004∗(0.7951,0.7951)^𝑇
23	(0.0087,1.0000)^𝑇	1.0𝑒−004∗(0.7483,0.7483)^𝑇
24	(0.0084,1.0000)^𝑇	1.0𝑒−004∗(0.7066,0.7066)^𝑇
25	(0.0082,1.0000)^𝑇	1.0𝑒−004∗(0.6693,0.6693)^𝑇
26	(0.00797,1.0000)^𝑇	1.0𝑒−004∗(0.6357,0.6357)^𝑇
27	(0.0078,1.0000)^𝑇	1.0𝑒−004∗(0.6053,0.6053)^𝑇
28	(0.0076,1.0000)^𝑇	1.0𝑒−004∗(0.5777,0.5777)^𝑇
29	(0.0074,1.0000)^𝑇	1.0𝑒−004∗(0.5525,0.5525)^𝑇
30	(0.0073,1.0000)^𝑇	1.0𝑒−004∗(0.5293,0.5293)^𝑇
31	(0.0071,1.0000)^𝑇	1.0𝑒−004∗(0.5080,0.5080)^𝑇
32	(0.00699,1.0000)^𝑇	1.0𝑒−004∗(0.4884,0.4884)^𝑇
33	(0.0069,1.0000)^𝑇	1.0𝑒−004∗(0.4702,0.4702)^𝑇
34	(0.0067,1.0000)^𝑇	1.0𝑒−004∗(0.4533,0.4533)^𝑇
35	(0.0066,1.0000)^𝑇	1.0𝑒−004∗(0.4376,0.4376)^𝑇
36	(0.0065,1.0000)^𝑇	1.0𝑒−004∗(0.4229,0.4229)^𝑇
37	(0.0064,1.0000)^𝑇	1.0𝑒−004∗(0.4092,0.4092)^𝑇
38	(0.0063,1.0000)^𝑇	1.0𝑒−004∗(0.3963,0.3963)^𝑇
39	(0.0062,1.0000)^𝑇	1.0𝑒−004∗(0.3842,0.3842)^𝑇