On the O(1/n) Convergence Rate of the Auxiliary Problem Principle for Separable Convex Programming and Its Application to the Power Systems Multi-Area Economic Dispatch Problem
Abstract
:1. Introduction
2. The Convergence Analysis of APP
3. The Convergence Rate Analysis of APP
4. Numerical Experiments
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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i | |||||
---|---|---|---|---|---|
1 | 40 | 80 | 0.03073 | 8.336 | 170.44 |
2 | 60 | 120 | 0.02028 | 7.0706 | 309.54 |
3 | 80 | 190 | 0.00942 | 8.1817 | 369.03 |
4 | 24 | 42 | 0.08482 | 6.9467 | 135.48 |
5 | 26 | 42 | 0.09693 | 6.5595 | 135.19 |
6 | 68 | 140 | 0.01142 | 8.0543 | 222.33 |
7 | 110 | 300 | 0.00357 | 8.0323 | 287.71 |
8 | 135 | 300 | 0.00492 | 6.999 | 391.98 |
9 | 135 | 300 | 0.00573 | 6.602 | 455.76 |
10 | 130 | 300 | 0.00605 | 12.908 | 722.82 |
11 | 94 | 375 | 0.00515 | 12.986 | 635.2 |
12 | 94 | 375 | 0.00569 | 12.796 | 654.69 |
13 | 125 | 500 | 0.00421 | 12.501 | 913.4 |
14 | 125 | 500 | 0.00752 | 8.8412 | 1760.4 |
15 | 125 | 500 | 0.00708 | 9.1575 | 1728.3 |
16 | 125 | 500 | 0.00708 | 9.1575 | 1728.3 |
17 | 125 | 500 | 0.00708 | 9.1575 | 1728.3 |
18 | 220 | 500 | 0.00313 | 7.9691 | 647.85 |
19 | 220 | 500 | 0.00313 | 7.955 | 649.69 |
20 | 242 | 550 | 0.00313 | 7.9691 | 647.83 |
21 | 242 | 550 | 0.00313 | 7.9691 | 647.81 |
22 | 254 | 550 | 0.00298 | 6.6313 | 785.96 |
23 | 254 | 550 | 0.00298 | 6.6313 | 785.96 |
24 | 254 | 550 | 0.00298 | 6.6313 | 785.53 |
25 | 254 | 550 | 0.00298 | 6.6313 | 785.53 |
26 | 254 | 550 | 0.00277 | 7.1032 | 801.32 |
27 | 254 | 550 | 0.00277 | 7.1032 | 801.32 |
28 | 10 | 150 | 0.52124 | 3.3353 | 1055.1 |
29 | 10 | 150 | 0.52124 | 3.3353 | 1055.1 |
30 | 10 | 150 | 0.52124 | 3.3353 | 1055.1 |
31 | 20 | 70 | 0.25098 | 13.052 | 1207.8 |
32 | 20 | 70 | 0.16766 | 21.887 | 810.79 |
33 | 20 | 70 | 0.2635 | 10.244 | 1247.7 |
34 | 20 | 70 | 0.30575 | 8.3707 | 1219.2 |
35 | 18 | 60 | 0.18362 | 26.258 | 641.43 |
36 | 18 | 60 | 0.32563 | 9.6956 | 1112.8 |
37 | 20 | 60 | 0.33722 | 7.1633 | 1044.4 |
38 | 25 | 60 | 0.23915 | 16.339 | 832.24 |
39 | 25 | 60 | 0.23915 | 16.339 | 834.24 |
40 | 25 | 60 | 0.23915 | 16.339 | 1035.2 |
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Ren, Y.; Chen, Z. On the O(1/n) Convergence Rate of the Auxiliary Problem Principle for Separable Convex Programming and Its Application to the Power Systems Multi-Area Economic Dispatch Problem. Math. Comput. Appl. 2016, 21, 35. https://doi.org/10.3390/mca21030035
Ren Y, Chen Z. On the O(1/n) Convergence Rate of the Auxiliary Problem Principle for Separable Convex Programming and Its Application to the Power Systems Multi-Area Economic Dispatch Problem. Mathematical and Computational Applications. 2016; 21(3):35. https://doi.org/10.3390/mca21030035
Chicago/Turabian StyleRen, Yaming, and Zhongxian Chen. 2016. "On the O(1/n) Convergence Rate of the Auxiliary Problem Principle for Separable Convex Programming and Its Application to the Power Systems Multi-Area Economic Dispatch Problem" Mathematical and Computational Applications 21, no. 3: 35. https://doi.org/10.3390/mca21030035