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http://hdl.handle.net/10397/10
2015-10-09T04:06:23ZOn the hierarchical variational inclusion problems in Hilbert spaces
http://hdl.handle.net/10397/7622
Title: On the hierarchical variational inclusion problems in Hilbert spaces
Authors: Chang, Shih-sen; Kim, Jong Kyu; Lee, Heung-wing Joseph; Chun, Chi Kin
Abstract: The purpose of this paper is by using Mainge’s approach to study the existence and approximation problem of solutions for a class of hierarchical variational inclusion problems in the setting of Hilbert spaces. As applications, we solve the convex programming problems and quadratic minimization problems by using the main theorems. Our results extend and improve the corresponding recent results announced by many authors.2013-07-08T00:00:00ZStrong and Δ -convergence for mixed type total asymptotically nonexpansive mappings in CAT(0) spaces
http://hdl.handle.net/10397/7621
Title: Strong and Δ -convergence for mixed type total asymptotically nonexpansive mappings in CAT(0) spaces
Authors: Chang, Shih-sen; Wang, Lin; Lee, Heung-wing Joseph; Chan, Chi-kin
Abstract: It is our purpose in this paper first to introduce the class of total asymptotically nonexpansive nonself mappings and to prove the demiclosed principle for such mappings in CAT(0) spaces. Then, a new mixed Agarwal-O’Regan-Sahu type iterative scheme for approximating a common fixed point of two total asymptotically nonexpansive mappings and two total asymptotically nonexpansive nonself mappings is constructed. Under suitable conditions, some strong convergence theorems and Δ-convergence theorems are proved in a CAT(0) space. Our results improve and extend the corresponding results of Agarwal, O’Regan and Sahu (J. Nonlinear Convex Anal. 8(1):61-79, 2007), Guo et al. (Fixed Point Theory Appl. 2012:224, 2012. doi:10.1186/1687-1812-2012-224), Sahin et al. (Fixed Point Theory Appl. 2013:12, 2013. doi:10.1186/1687-1812-2013-12), Chang et al. (Appl. Math. Comput. 219:2611-2617, 2012), Khan and Abbas (Comput. Math. Appl. 61:109-116, 2011), Khan et al. (Nonlinear Anal. 74:783-791, 2011), Xu (Nonlinear Anal., Theory Methods Appl. 16(12):1139-1146, 1991), Chidume et al. (J. Math. Anal. Appl. 280:364-374, 2003) and others.2013-05-08T00:00:00ZProximal algorithms for a class of mixed equilibrium problems
http://hdl.handle.net/10397/7620
Title: Proximal algorithms for a class of mixed equilibrium problems
Authors: Song, Yisheng; Zhang, Qingnian
Abstract: We present two proximal algorithms for solving the mixed equilibrium problems. Under some simpler framework, the strong and weak convergence of the sequences defined by two general algorithms is respectively obtained. In particular, we deal with several iterative schemes in a united way and apply our algorithms for solving the classical equilibrium problem, the minimization problem, the classical variational inequality problem and the generalized variational inequality problem. Our results properly include some corresponding results in this field as a special case.2012-10-02T00:00:00ZStochastic scheduling with preemptive-repeat machine breakdowns to minimize the expected weighted flow time
http://hdl.handle.net/10397/7619
Title: Stochastic scheduling with preemptive-repeat machine breakdowns to minimize the expected weighted flow time
Authors: Cai, Xiaoqiang; Sun, Xiaoqian; Zhou, Xian
Abstract: We study a stochastic scheduling problem with a single machine subject to random breakdowns. We address the preemptive-repeat model; that is, if a breakdown occurs during the processing of a job, the work done on this job is completely lost and the job has to be processed from the beginning when the machine resumes its work. The objective is to complete all jobs so that the the expected weighted flow time is minimized. Limited results have been published in the literature on this problem, all with the assumption that the machine uptimes are exponentially distributed. This article generalizes the study to allow that (1) the uptimes and downtimes of the machine follow general probability distributions, (2) the breakdown patterns of the machine may be affected by the job being processed and are thus job dependent; (3) the processing times of the jobs are random variables following arbitrary distributions, and (4) after a breakdown, the processing time of a job may either remain a same but unknown amount, or be resampled according to its probability distribution. We derive the necessary and sufficient condition that ensures the problem with the flow-time criterion to be well posed under the preemptive-repeat breakdown model. We then develop an index policy that is optimal for the problem. Several important situations are further considered and their optimal solutions are obtained.2003-10-01T00:00:00Z