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

Table 2

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

Step	(𝑥1,𝑥2)^𝑇	𝐹(𝑥)
1	(1.0000,1.0000)^𝑇	(1.0000,1.0000)^𝑇
2	(0.5006,1.0000)^𝑇	(0.2506,0.2506)^𝑇
3	(0.2516,1.0000)^𝑇	(0.0633,0.0633)^𝑇
4	(0.1282,1.0000)^𝑇	(0.0164,0.0164)^𝑇
5	(0.0686,1.0000)^𝑇	(0.0047,0.0047)^𝑇
6	(0.0415,1.0000)^𝑇	(0.0017,0.0017)^𝑇
7	(0.0295,1.0000)^𝑇	1.0𝑒−003∗(0.8693,0.8693)^𝑇
8	(0.0234,1.0000)^𝑇	1.0𝑒−003∗(0.5493,0.5493)^𝑇
9	(0.0199,1.0000)^𝑇	1.0𝑒−003∗(0.3944,0.3944)^𝑇
10	(0.0175,1.0000)^𝑇	1.0𝑒−003∗(0.3055,0.3055)^𝑇
11	(0.0158,1.0000)^𝑇	1.0𝑒−003∗(0.2484,0.2484)^𝑇
12	(0.0145,1.0000)^𝑇	1.0𝑒−003∗(0.2089,0.2089)^𝑇
13	(0.0134,1.0000)^𝑇	1.0𝑒−003∗(0.1801,0.1801)^𝑇
14	(0.0126,1.0000)^𝑇	1.0𝑒−003∗(0.1581,0.1581)^𝑇
15	(0.0119,1.0000)^𝑇	1.0𝑒−003∗(0.1409,0.1409)^𝑇
16	(0.0112,1.0000)^𝑇	1.0𝑒−003∗(0.12696,0.12696)^𝑇
17	(0.0107,1.0000)^𝑇	1.0𝑒−003∗(0.1155,0.1155)^𝑇
18	(0.0103,1.0000)^𝑇	1.0𝑒−003∗(0.10596,0.10596)^𝑇