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ABSTRACT: In this paper, a new trust-region subproblem combining with the BFGS update is proposed for solving nonlinear equations, where
the trust region radius is defined by a new way. The global convergence without the nondegeneracy assumption and the quadratic
convergence are obtained under suitable conditions. Numerical results show that this method is more effective than the norm
method.
KeywordsTrust region method–BFGS update–Global convergence–Nonlinear equations
Computing 05/2012; 92(4):317-333. · 0.70 Impact Factor
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Annals OR. 01/2011; 191:97-113.
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ABSTRACT: This paper studies the preemptive stochastic online scheduling problem, which is a simple combination of online and stochastic scheduling. The processing times of jobs are assumed to be subject to independent probability distributions, and we assume that jobs arrive overtime, which means there is no knowledge about the jobs that arrive in the future. We particularly consider the preemptive setting where a job is allowed to be interrupted during its processing. The weight (holding cost ratio) associated with each job may change during its processing, and the objective is to minimize the expected value of total holding cost for all jobs. For the single and m identical machine problems, we propose scheduling policies, SPGS [semi-preemptive Gittins Index Priority Policy (GIPP) on single machine] and SPGI (semi-preemptive GIPP on identical machines), respectively, both of which are proved to be constant-factor approximation. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pacific Journal of Chemical Engineering 08/2009; 5(4):681 - 689. · 0.76 Impact Factor
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Annals OR. 01/2009; 166:73-90.
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J. Computational Applied Mathematics. 01/2009; 233:519-530.
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Computers & Mathematics with Applications. 01/2008; 55:116-129.
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ABSTRACT: In this paper, an active set limited BFGS algorithm is proposed for bound constrained optimization. The global convergence will be established under some suitable conditions. Numerical results show that the given method is effective.
Applied Mathematical Modelling 35(7):3561-3573. · 1.58 Impact Factor
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ABSTRACT: This paper addresses a stochastic online scheduling problem in which a set of independent jobs are to be processed by two uniform machines whose speeds are 1 and s(s⩾1). Each job has a processing time, which is a random variable with an arbitrary distribution, and all the jobs are arriving overtime, which means that no information of the job is known in advance before its arrival. During the processing, jobs are allowed to be preempted and resumed later. The objective is to minimize the sum of expected weighted completion times. In this paper, the optimal policy, named SMPR, is designed for the single-machine preemptive stochastic scheduling problem where jobs have a common arriving time. Based on SMPR, the online approximative policy-UMPR, is devised for the preemptive stochastic online scheduling on two uniform machines. Then, UMPR is proved to have an approximation factor of 2. Furthermore, it is concluded that UMPR could not have a smaller approximation factor than 2, which means 2 is the approximation ratio of UMPR for the two-uniform-machine scheduling problem.
Information Processing Letters.
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ABSTRACT: In this paper, we propose a BFGS trust-region method for solving symmetric nonlinear equations. The global convergence and the superlinear convergence of the presented method will be established under favorable conditions. Numerical results show that the new algorithm is effective.
Journal of Computational and Applied Mathematics.
