In this paper, d-accretive mappings, which belong to accretive-type mappings but are different from m-accretive mappings, are studied. Some relaxed projection iterative algorithms for an infinite family of d-accretive...
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In this paper, d-accretive mappings, which belong to accretive-type mappings but are different from m-accretive mappings, are studied. Some relaxed projection iterative algorithms for an infinite family of d-accretive mappings are constructed in a real uniformly convex and uniformly smooth Banach space. The iterative sequences are proved to be strongly convergent to a common zero point of the family of d-accretive mappings. Compared to the related work, the construction of the iterative algorithms are simpler and easily realized. Moreover, a kind of generalized (p, q)-Laplacian parabolic systems is exemplified. The example also emphasizes the importance of the study on d-accretive mappings and sets up a relationship between iterative algorithms and nonlinear systems.
A variety of strategies are used to construct algorithms for solving equations. However, higher order derivatives are usually assumed to calculate the convergence order. More importantly, bounds on error and uniquenes...
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A variety of strategies are used to construct algorithms for solving equations. However, higher order derivatives are usually assumed to calculate the convergence order. More importantly, bounds on error and uniqueness regions for the solution are also not derived. Therefore, the benefits of these algorithms are limited. We simply use the first derivative to tackle all these issues and study the ball analysis for two sixth order algorithms under the same set of conditions. In addition, we present a calculable ball comparison between these algorithms. In this manner, we enhance the utility of these algorithms. Our idea is very general. That is why it can also be used to extend other algorithms as well in the same way.
We proposed an algorithm for calculating a DOE forming vortex beams with a preset distribution of minima and maxima. We discussed several versions of this algorithm. We presented the calculation of some configurations...
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We proposed an algorithm for calculating a DOE forming vortex beams with a preset distribution of minima and maxima. We discussed several versions of this algorithm. We presented the calculation of some configurations of traps to capture transparent and non-transparent micro-objects.
In this paper, we investigate model reduction for positive linear time-invariant systems in the H ∞ sense. First, the bounded real lemma is further developed to obtain a new characterization of the H ∞ performance, ...
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In this paper, we investigate model reduction for positive linear time-invariant systems in the H ∞ sense. First, the bounded real lemma is further developed to obtain a new characterization of the H ∞ performance, which does not include any product term between the Lyapunov matrix and the parameter of the reduced-order model. Then a new parameterization of a positive reduced-order model is proposed, and accordingly, an iterative algorithm is constructed, which makes use of the coarse reduced-order models resulting from the (generalized) balanced truncation as the initial value to search for a desired positive one. Both continuous- and discrete-time systems are considered in the same framework. Numerical examples clearly show the effectiveness and advantages of the proposed method.
In this paper, we first introduce a new class of generalized accretive operators named （H,η）-accretive in Banach space. By studying the properties of （H,η）-accretive, we extend the concept of resolvent operators...
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In this paper, we first introduce a new class of generalized accretive operators named （H,η）-accretive in Banach space. By studying the properties of （H,η）-accretive, we extend the concept of resolvent operators associated with m-accretive operators to the new （H,η）-accretive operators. In terms of the new resolvent operator technique, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.
The study of efficient iterative algorithms for addressing nonlinear least-squares (NLS) problems is of great importance. The NLS problems, which belong to a special class of unconstrained optimization problems, are o...
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The study of efficient iterative algorithms for addressing nonlinear least-squares (NLS) problems is of great importance. The NLS problems, which belong to a special class of unconstrained optimization problems, are of particular interest because of the special structure of their gradients and Hessians. In this paper, based on the spectral parameters of Barzillai and Borwein (1998), we propose three structured spectral gradient algorithms for solving NLS problems. Each spectral parameter in the respective algorithms incorporates the structured gradient and the information gained from the structured Hessian approximation. Moreover, we develop a safeguarding technique for the first two structured spectral parameters to avoid negative curvature directions. Moreso, using a nonmonotone line-search strategy, we show that the proposed algorithms are globally convergent under some standard conditions. The comparative computational results on some standard test problems show that the proposed algorithms are efficient.
In this paper, we give a characterization of strong convergence theorem of the Ishikawa iterative sequence with errors for the generalized set-valued variational inclusion problem involving a generalized set-valued qu...
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In this paper, we give a characterization of strong convergence theorem of the Ishikawa iterative sequence with errors for the generalized set-valued variational inclusion problem involving a generalized set-valued quasi-contractive mapping in a real Banach space. First, the existence of the solution of the generalized set-valued variational inclusion problem is proved. Then, using the existence result, the Ishikawa iterative algorithm with errors is constructed and the convergence of the iterative sequences is proved. Finally, numerical experiments are proposed to support the main result. The results improve and extend some known results.
Vehicle routing problem(VRP) is one of important research in the logistics system. Nowadays, there are many researches on the VRP, but their don’t consider the cost of inventory. Thus, the conclusion doesn’t meet re...
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Vehicle routing problem(VRP) is one of important research in the logistics system. Nowadays, there are many researches on the VRP, but their don’t consider the cost of inventory. Thus, the conclusion doesn’t meet reality. This paper studies on the inventory routing problem (IRP)and uses one target function to describe these two conflicting problems, which are very important in the logistics optimization. The paper establishes the model of single client and many clients’ inventory routing problem. An optimizing iterative algorithm is presented to solve the model. According to the model we can confirm the best quantity, efficiency and route of delivery. Finally, an example is given to illustrate the efficiency of model and algorithm.
Based on the funding project "a concrete-filled steel tube truss type half-through arch bridge (CFSTTTHAB) with the span of 220 m," in view of the difference of tension between one pair of suspenders, this p...
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Based on the funding project "a concrete-filled steel tube truss type half-through arch bridge (CFSTTTHAB) with the span of 220 m," in view of the difference of tension between one pair of suspenders, this paper proposed an improved influence matrix method for the tension of a single suspender, which was developed from a conventional influence matrix. A method for adjusting suspender tension at the completed state of construction by using numerical simulation and iterative algorithm was also presented. Finite element numerical model was used to calculate the influence matrix of a single suspender. Moreover, an iterative algorithm was used to solve the adjustment value of suspender tension. Based on the proposed method, by processing several iterations, the difference between the measured and designed suspender tension would be controlled within 6% in the projects of suspender tension adjustment. Finally, the comparison between the measured and designed suspender tension at the completed state of construction proved the feasibility and accuracy satisfaction of the proposed method for engineering requirement.
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