Modified LQP Method with a New Search Direction for Nonlinear Complimentarity Problems

An improvement LQP method for nonlinear complementarity problems

“…We test the problems (4.1) with different dimensions and q ∈ (−500, 500) in Table 1, and q ∈ (−500, 0) in Table 2. We compare the proposed method with those in [7,27]. In all tests, we take η = 0.9, γ + δ k = 3.35.…”

“…The method in [7] The method in [27] Tables 1-2 show the high efficiency and robustness of the proposed method. Numerical results indicate that the proposed method can be save about 51 ∼ 101 percent of the number of iterations and about 57 ∼ 107 of the amount of computing the value of function F for that in [7] and about 132 ∼ 212 percent of the number of iterations and about 150 ∼ 231 of the amount of computing the value of function F for that in [27]. Example 4.2.…”

“…where The test results for problems (4.2) for different ε are reported in Table 3, k is the number of iterations and l denotes the number of evaluations of mapping F. The stopping criterion is min{x, F(x)} ∞ min{x 0 , F(x 0 )} ∞ ≤ ε. Table 3 reports the comparison between the methods of [7,27] and the proposed method. The number of iterations and the amount of computing the value of function F have great advantages.…”

“…Many practical problems show that often one of subproblem (1.8) is expensive to solve. Driven by the fact of eliminating this drawback, various iterative algorithms for approximating solutions have been proposed by numerous researchers, see, e.g., [4,6,5,7,17,20,26,27]. Based on the work of [1], Bnouhachem [4] proposed that the predictor is obtained via solving the following system…”