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

Table 1

𝑥₀=(1,1)^𝑇𝜆₁=0.01,𝜆₂=1 and computes 𝑑_𝑘 by (3.4).

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	(0.2506,1.0000)^𝑇	(0.0628,0.0628)^𝑇
4	(0.1255,1.0000)^𝑇	(0.0157,0.0157)^𝑇
5	(0.0628,1.0000)^𝑇	(0.0039,0.0039)^𝑇
6	(0.0314,1.0000)^𝑇	1.0𝑒−003∗(0.9888,0.9888)^𝑇
7	(0.0157,1.0000)^𝑇	1.0𝑒−003∗(0.2478,0.2478)^𝑇
8	(0.0079,1.0000)^𝑇	1.0𝑒−004∗(0.6211,0.6211)^𝑇
9	(0.0039,1.0000)^𝑇	1.0𝑒−004∗(0.1557,0.1557)^𝑇
10	(0.0019,1.0000)^𝑇	1.0𝑒−005∗(0.3901,0.3901)^𝑇
11	(0.00098,1.0000)^𝑇	1.0𝑒−006∗(0.97777,0.97777)^𝑇
12	(0.000495,1.0000)^𝑇	1.0𝑒−006∗(0.24505,0.24505)^𝑇
13	(0.00024,1.0000)^𝑇	1.0𝑒−007∗(0.61416,0.61416)^𝑇
14	(0.00012,1.0000)^𝑇	1.0𝑒−007∗(0.15392,0.15392)^𝑇
15	(0.000062,1.0000)^𝑇	1.0𝑒−008∗(0.38577,0.38577)^𝑇