Can Linear Superiorization Be Useful for Linear Optimization Problems

作者: Yair Censor

DOI: 10.1088/1361-6420/33/4/044006

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摘要: Linear superiorization considers linear programming problems but instead of attempting to solve them with optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers toward reduced (not necessarily minimal) target function values. The two questions that we set out explore experimentally are (i) Does provide a feasible point whose value is lower than obtained by running the same algorithm without under identical conditions? (ii) How does fare in comparison Simplex method for solving problems? Based on our computational experiments presented here, answers these are: "yes" "very well", respectively.

参考文章(33)
Yair Censor, Tommy Elfving, Gabor T. Herman, Touraj Nikazad, On Diagonally Relaxed Orthogonal Projection Methods SIAM Journal on Scientific Computing. ,vol. 30, pp. 473- 504 ,(2007) , 10.1137/050639399
Dan Gordon, Rachel Gordon, Component-Averaged Row Projections: A Robust, Block-Parallel Scheme for Sparse Linear Systems SIAM Journal on Scientific Computing. ,vol. 27, pp. 1092- 1117 ,(2005) , 10.1137/040609458
Wenma Jin, Yair Censor, Ming Jiang, A Heuristic Superiorization-Like Approach to Bioluminescence Tomography Springer, Berlin, Heidelberg. pp. 1026- 1029 ,(2013) , 10.1007/978-3-642-29305-4_269
T. S. Motzkin, I. J. Schoenberg, The Relaxation Method for Linear Inequalities Canadian Journal of Mathematics. ,vol. 6, pp. 393- 404 ,(1954) , 10.4153/CJM-1954-038-X
Shmuel Agmon, The Relaxation Method for Linear Inequalities Canadian Journal of Mathematics. ,vol. 6, pp. 382- 392 ,(1954) , 10.4153/CJM-1954-037-2
Yair Censor, Weak and Strong Superiorization: Between Feasibility-Seeking and Minimization Analele Universitatii "Ovidius" Constanta - Seria Matematica. ,vol. 23, pp. 41- 54 ,(2015) , 10.1515/AUOM-2015-0046
Shousheng Luo, Tie Zhou, Superiorization of EM algorithm and its application in Single-Photon Emission Computed Tomography(SPECT) Inverse Problems and Imaging. ,vol. 8, pp. 223- 246 ,(2014) , 10.3934/IPI.2014.8.223
Y Censor, R Davidi, G T Herman, Perturbation resilience and superiorization of iterative algorithms Inverse Problems. ,vol. 26, pp. 65008- 65008 ,(2010) , 10.1088/0266-5611/26/6/065008