• 대한수학회지
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• 제47권1호
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• pp.63-70
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• 2010

In this paper, we develop a nonmonotone spectral memory gradient method for unconstrained optimization, where the spectral stepsize and a class of memory gradient direction are combined efficiently. The global convergence is obtained by using a nonmonotone line search strategy and the numerical tests are also given to show the efficiency of the proposed algorithm.

• 대한수학회지
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• 제47권4호
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• pp.767-788
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• 2010

In this paper, we propose two limited memory BFGS algorithms with a nonmonotone line search technique for unconstrained optimization problems. The global convergence of the given methods will be established under suitable conditions. Numerical results show that the presented algorithms are more competitive than the normal BFGS method.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.971-980
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• 2012

In this paper, a method associating with one new form of nonmonotone linesearch technique is proposed, which can be regarded as a generalization of the Perry-Shanno memoryless quasi-Newton type method. Under some reasonable conditions, the global convergence of the proposed method is proven. Numerical tests show its efficiency.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.843-856
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• 2022

In this article, we analyze the first order delay dynamic equations with several nonmonotone arguments. Also, we present new oscillation conditions involving lim sup and lim inf for the solutions of these equations. Finally, we give an example to demonstrate the results.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.573-585
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• 2011

SQP method is one of the most important methods for solving nonlinear programming. But it may fail if the quadratic subproblem is inconsistent. In this paper, we propose a modified nonmonotone filter trust region method in which the QP subproblem is consistent. By means of nonmonotone filter, this method has no demand on the penalty parameter which is difficult to obtain. Moreover, the restoration phase is not needed any more. Under reasonable conditions, we obtain the global convergence of the algorithm. Some numerical results are presented.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.981-1000
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• 2009

This paper considers asset liability management problems when their deterministic equivalent formulations are general nonlinear optimization problems. The presented approach uses a nonmonotone trust region strategy for solving a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penalty-barrier function that involves both primal and dual variables. Each subproblem is solved approximately. The algorithm does not restrict a monotonic decrease of the objective function value at each iteration. If a trial step is not accepted, the algorithm performs a non monotone line search to find a new acceptable point instead of resolving the subproblem. We prove that the algorithm globally converges to a point satisfying the second-order necessary optimality conditions.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.123-136
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• 2004

In this paper, a combining trust region and line search algorithm for equality constrained optimization is proposed. At each iteration, we only need to solve the trust region subproblem once, when the trust region trial step can not be accepted, we switch to line search to obtain the next iteration. Hence, the difficulty of repeated solving trust region subproblem in an iterate is avoided. In order to allow the direction of negative curvature, we add second correction step in trust region step and employ nonmonotone technique in line search. The global convergence and local superlinearly rate are established under certain assumptions. Some numerical examples are given to illustrate the efficiency of the proposed algorithm.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.779-793
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• 2009

This paper deals with a delayed SEIRS epidemic model with pulse vaccination and crowded incidence rate. Moreover, the case of vertical and horizontal transmission is considered. By using the discrete dynamical system determined by the stroboscopic map, the exact infection-free periodic solution of the SEIRS model is obtained. Further, by employing the comparison arguments, we prove that under the condition that $R_*$ < 1 the infection-free periodic solution is globally attractive, and that under the condition that $R^*$ > 1 the disease is uniformly persistent, which means that after some period of time the disease will become endemic.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.285-295
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• 2014

In the setting of semidenite linear complementarity problems on $S^n$, we focus on the Stein Transformation $S_A(X)\;:=X-AXA^T$, and show that $S_A$ is (strictly) monotone if and only if ${\nu}_r(UAU^T{\circ}\;UAU^T)$(<)${\leq}1$, for all orthogonal matrices U where ${\circ}$ is the Hadamard product and ${\nu}_r$ is the real numerical radius. In particular, we show that if ${\rho}(A)$ < 1 and ${\nu}_r(UAU^T{\circ}\;UAU^T){\leq}1$, then SDLCP($S_A$, Q) has a unique solution for all $Q{\in}S^n$. In an attempt to characterize the GUS-property of a nonmonotone $S_A$, we give an instance of a nonnormal $2{\times}2$ matrix A such that SDLCP($S_A$, Q) has a unique solution for Q either a diagonal or a symmetric positive or negative semidenite matrix. We show that this particular $S_A$ has the $P^{\prime}_2$-property.