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In this article, based on the modified secant equation, we propose a modified Hestenes-Stiefel (HS) conjugate gradient method which has similar form as the CG-DESCENT method proposed by Hager and Zhang (SIAM J Optim 16:170–192, 2005). The presented method can generate sufficient descent directions without any line search. Under some mild conditions, we show that it is globally convergent with Armijo line search. Moreover, the R-linear convergence rate of the modified HS method is established. Preliminary numerical results show that the proposed method is promising, and competitive with the well-known CG-DESCENT method.  相似文献
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Project portfolio selection is one of the most important decision-making problems for most organizations in project management and engineering management. Usually project portfolio decisions are very complicated when project interactions in terms of multiple selection criteria and preference information of decision makers (DMs) in terms of the criteria importance are taken into consideration simultaneously. In order to solve this complex decision-making problem, a multi-criteria project portfolio selection problem considering project interactions in terms of multiple selection criteria and DMs?? preferences is first formulated. Then a genetic algorithm (GA)-based nonlinear integer programming (NIP) approach is used to solve the multi-criteria project portfolio selection problem. Finally, two illustrative examples are presented for demonstration and verification purposes. Experimental results obtained indicate that the GA-based NIP approach can be used as a feasible and effective solution to multi-criteria project portfolio selection problems.  相似文献
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