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In this paper, we study a kind of conjugate gradient viscosity approximation algorithm for finding a common solution of split generalized equilibrium problem and variational inequality problem. Under mild conditions, we prove that the sequence generated by the proposed iterative algorithm converges strongly to the common solution. The conclusion presented in this paper is the generalization, extension, and supplement of the previously known results in the corresponding references. Some numerical results are illustrated to show the feasibility and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Management of electric equipment has a direct impact on companies’ performance and profitability. Considering the critical role that electric power materials play in supporting maintenance operations and preventing equipment failure, it is essential to maintain an inventory to a reasonable level. However, a majority of these electric power materials exhibit an intermittent demand pattern characterized by random arrivals interspersed with time periods with no demand at all. These characteristics cause additional difficulty for companies in managing these electric power material inventories. In response to the above problem, this paper, based on the electric power material demand data of Shanghai Electric Power Company, develops a new method to determine the optimal order quantity Q⁎ in a cost-oriented periodic review (T,Q) system, whereby unsatisfied demands are backordered and demand follows a compound Erlang distribution. Q⁎corresponds to the value of Q that gives the minimum expected total inventory holding and backordering cost. Subsequently, an empirical investigation is conducted to compare this method with the Newsvendor model. Results verify its superiority in cost savings. Ultimately, considering the complicated calculation and low efficiency of that algorithm, this paper proposes an approximation and a heuristic algorithm which have a higher level of utility in a real industrial context. The approximation algorithm simplifies the calculation process by reducing iterative times while the heuristic algorithm achieves it by generalizing the relationship between the optimal order quantity Q⁎ and mean demand interarrival rate λ. [ABSTRACT FROM AUTHOR]

A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid. The rational interpolant is of the formmotivated by Tan and Fang (2000), which is combined by Newton interpolant and branched continued fractions, with scalar denominator. The matrix quotients are based on the generalized inverse for a matrixwhich is introduced by C. Gu the author of this paper, and it is effective in continued fraction interpolation. The algorithm and some other important conclusions such as divisibility and characterization are given. In the end, two examples are also given to show the effectiveness of the algorithm. The numerical results of the second example show that the algorithm of this paper is better than the method of Thieletype matrix-valued rational interpolant in Gu (1997). [ABSTRACT FROM AUTHOR]

The research on the triangle packing problem has important theoretic significance, which has broad application prospects in material processing, network resource optimization, and so forth. Generally speaking, the orientation of the triangle should be limited in advance, since the triangle packing problem is NP-hard and has continuous properties. For example, the polygon is not allowed to rotate; then, the approximate solution can be obtained by optimization method. This paper studies the triangle packing problem by a new kind of method. Such concepts as angle region, corner-occupying action, corner-occupying strategy, and edge-conjoining strategy are presented in this paper. In addition, an edge-conjoining and corner-occupying algorithm is designed, which is to obtain an approximate solution. It is demonstrated that the proposed algorithm is highly efficient, and by the time complexity analysis and the analogue experiment result is found. [ABSTRACT FROM AUTHOR]

In radial basis function approximation, the shape parameter can be variable. The values of the variable shape parameter strategies are selected from an interval which is usually determined by trial and error. As yet there is not any algorithm for determining an appropriate interval, although there are some recipes for optimal values. In this paper, a novel algorithm for determining an interval is proposed. Different variable shape parameter strategies are examined. The results show that the determined interval significantly improved the accuracy and is suitable enough to count on in variable shape parameter strategies. [ABSTRACT FROM AUTHOR]

The purpose of this paper is using Korpelevich's extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. Under suitable conditions, some existence theorems and approximation solvability theorems are proved. The results presented in the paper improve and extend some recent results. [ABSTRACT FROM AUTHOR]

Retrial queues can only be solved in a closed form in very few and simple cases, so researchers must resort to approximate models. However, most of the papers that propose approximate models assume the convergence of the proposed models to their exact counterparts, without providing a rigorous mathematical proof. In this paper we demonstrate the convergence of finite truncated models with two reattempt orbits. [ABSTRACT FROM AUTHOR]

Evaluating the reliability of a transportation network often involves an intensive simulation exercise to randomly generate and evaluate different possible network states. This paper proposes an algorithm to approximate the network reliability which minimizes the use of such simulation procedure. The algorithm will dissect and classify the network states into reliable, unreliable, and un-determined partitions. By postulating the monotone property of the reliability function, each reliable and/or unreliable state can be used to determine a number of other reliable and/or unreliable states without evaluating all of them with an equilibrium assignment procedure. The paper also proposes the cause-based failure framework for representing dependent link degradation probabilities. The algorithm and framework proposed are tested with a medium size test network to illustrate the performance of the algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a two-level additive Schwarz preconditioning algorithm for the weak Galerkin approximation of the second-order elliptic equation. In the algorithm, a P1 conforming finite element space is defined on the coarse mesh, and a stable intergrid transfer operator is proposed to exchange the information between the spaces on the coarse mesh and the fine mesh. With the framework of the Schwarz method, it is proved that the condition number of the preconditioned system only depends on the rate of the coarse mesh size and the overlapping size. Some numerical experiments are carried out to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Most calculations in model reduction involve the solutions of a sequence of dual linear systems with multiple right-hand sides. To solve such systems efficiently, a new deflated BiCG method is explored in this paper. The proposed algorithm uses harmonic Ritz vectors to approximate left and right invariant subspaces inexpensively via small descenting direction vectors found by subsequent runs of deflated BiCG and then derives the deflated subspaces for the next pair of dual linear systems. This process leads to faster convergence for the next pair of systems. Numerical examples illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Nodes in underwater wireless sensor networks (UWSNs) keep moving and dispersing due to force of water flow and aquatic creatures touching, and thus some isolated unknown nodes emerge. This type of isolated unknown nodes cannot directly communicate with enough beacons in their neighborhoods, which makes localizations for them disabled or the localization error unbearable. To this end, a multihops fitting localization approach is proposed in this paper. Firstly, some intermediate nodes between beacons and unknown nodes are set as routers to construct paths via a greedy method; then, the multihop paths are approximately fitted into straight lines; finally, the positions of unknown nodes can be estimated by trilateration. The proposed algorithm is analyzed and simulated in terms of localization error and error variance, and the results are proven preferable. [ABSTRACT FROM AUTHOR]

As the first priority of query processing in wireless sensor networks is to save the limited energy of sensor nodes and in many sensing applications a part of skyline result is enough for the user’s requirement, calculating the exact skyline is not energy-efficient relatively. Therefore, a new approximate skyline query, β-approximate skyline query which is limited by a guaranteed error bound, is proposed in this paper. With an objective to reduce the communication cost in evaluating β-approximate skyline queries, we also propose an energy-efficient processing algorithm using mapping and filtering strategies, named Actual Approximate Skyline (AAS). And more than that, an extended algorithm named Hypothetical Approximate Skyline (HAS) which replaces the real tuples with the hypothetical ones is proposed to further reduce the communication cost. Extensive experiments on synthetic data have demonstrated the efficiency and effectiveness of our proposed approaches with various experimental settings. [ABSTRACT FROM AUTHOR]

In this paper, we develop a modified gradient based algorithm for solving matrix equations AXB + CXTD = F. Different from the gradient based method introduced by Xie et al., 2010, the information generated in the first half-iterative step is fully exploited and used to construct the approximate solution. Theoretical analysis shows that the new method converges under certain assumptions. Numerical results are given to verify the efficiency of the new method. [ABSTRACT FROM AUTHOR]

This paper addresses a new performance measure for scheduling problems, entitled "biased tardiness penalty." We study the approximability of minimum biased tardiness on a single machine, provided that all the due dates are equal. Two heuristic algorithms are developed for this problem, and it is shown that one of them has a worst-case ratio bound of 2. Then, we propose a dynamic programming algorithm and use it to design an FPTAS. The FPTAS is generated by cleaning up some states in the dynamic programming algorithm, and it requires O(n3/ε) time. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of an adaptive neural network dynamic surface control (DSC) based on disturbance observer for the wheeled mobile robot with uncertain parameters and unknown disturbances. The nonlinear observer is used to compensate for the external disturbance, and the neural network is employed to approximate the uncertain and nonlinear items of system. Then, the Lyapunov theory is introduced to demonstrate the stabilization of the proposed control algorithm. Finally, the simulation results illustrate that the proposed algorithm not only is superior to conventional DSC in trajectory tracking and external friction disturbance compensation but also has better response, adaptive ability, and robustness. [ABSTRACT FROM AUTHOR]

Recent developments in compressive sensing (CS) show that it is possible to accurately reconstruct the magnetic resonance (MR) image from under sampled K-space data by solving nonsmooth convex optimization problems, which therefore significantly reduce the scanning time. In this paper, we propose a new MR image reconstruction method based on a compound regularization model associated with the nonlocal total variation (NLTV) and the wavelet approximate sparsity. Nonlocal total variation can restore periodic textures and local geometric information better than total variation. The wavelet approximate sparsity achieves more accurate sparse reconstruction than fixed wavelet l0 and l1 norm. Furthermore, a variable splitting and augmented Lagrangian algorithmis presented to solve the proposed minimization problem. Experimental results on MR image reconstruction demonstrate that the proposed method outperforms many existing MR image reconstruction methods both in quantitative and in visual quality assessment. [ABSTRACT FROM AUTHOR]

We construct a neural network based on smoothing approximation techniques and projected gradient method to solve a kind of sparse reconstruction problems. Neural network can be implemented by circuits and can be seen as an importantmethod for solving optimization problems, especially large scale problems. Smoothing approximation is an efficient technique for solving nonsmooth optimization problems. We combine these two techniques to overcome the difficulties of the choices of the step size in discrete algorithms and the item in the set-valued map of differential inclusion. In theory, the proposed network can converge to the optimal solution set of the given problem. Furthermore, some numerical experiments show the effectiveness of the proposed network in this paper. [ABSTRACT FROM AUTHOR]

Aiming at the phenomenon of slow convergence rate and low accuracy of bat algorithm, a novel bat algorithm based on differential operator and Lévy lights trajectory is proposed. In this paper, a differential operator is introduced to accelerate the convergence speed of proposed algorithm, which is similar to mutation strategy "DE/best/2" in differential algorithm. Lévy lights trajectory can ensure the diversity of the population against premature convergence and make the algorithm effectively jump out of local minima. 14 typical benchmark functions and an instance of nonlinear equations are tested; the simulation results not only show that the proposed algorithm is feasible and effective, but also demonstrate that this proposed algorithm has superior approximation capabilities in high-dimensional space. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of the minimum length link scheduling (MLLS) in multiuser MIMO (MU-MIMO) networks. Generally, in the networks with MU-MIMO capability, the number of concurrent transmissions can be as large as that of antenna elements at the receiver. As a result, link interference is no longer binary but demonstrates a strong correlation among multiple links, which cannot be captured by the conventional conflict graph interference model. Hence, we propose a novel hypergraph interference model, which can accurately and efficiently characterize the relationship of multiple interferences induced by concurrent transmissions, and provide a tractable formalization of the minimumlength link scheduling in MU-MIMO networks (MU-MIMO MLLS). Afterwards, we prove that the MU-MIMO MLLS problem is NP-hard and introduce two approximation algorithms to find the near-optimal feasible schedule. Finally, extensive simulation experiments are presented. [ABSTRACT FROM AUTHOR]

This paper proposes some diagonal matrices that approximate the (inverse) Hessian by parts using the variational principle that is analogous to the one employed in constructing quasi-Newton updates. The way we derive our approximations is inspired by the least change secant updating approach, in which we let the diagonal approximation be the sum of two diagonal matrices where the first diagonal matrix carries information of the local Hessian, while the second diagonal matrix is chosen so as to induce positive definiteness of the diagonal approximation at a whole. Some numerical results are also presented to illustrate the effectiveness of our approximating matrices when incorporated within the L-BFGS algorithm. [ABSTRACT FROM AUTHOR]

The Forward Least-Squares Approximation (FLSA) SVM is a newly-emerged Least-Square SVM (LS-SVM) whose solution is extremely sparse. The algorithm uses the number of support vectors as the regularization parameter and ensures the linear independency of the support vectors which span the solution. This paper proposed a variant of the FLSA-SVM, namely, Reduced FLSA-SVM which is of reduced computational complexity and memory requirements. The strategy of "contexts inheritance" is introduced to improve the efficiency of tuning the regularization parameter for both the FLSA-SVM and the RFLSA-SVM algorithms. Experimental results on benchmark datasets showed that, compared to the SVM and a number of its variants, the RFLSA-SVM solutions contain a reduced number of support vectors, while maintaining competitive generalization abilities. With respect to the time cost for tuning of the regularize parameter, the RFLSA-SVM algorithm was empirically demonstrated fastest compared to FLSA-SVM, the LS-SVM, and the SVM algorithms. [ABSTRACT FROM AUTHOR]

To achieve behavior and structure optimization for a type of software program whose data exchange processes are represented by nonlinear polynomial systems, this paper establishes a novel formal description called a nonlinear polynomial transition system to represent the behavior and structure of the software program. Then, the notion of bisimulation for software programs is proposed based on the equivalence relation of corresponding nonlinear polynomial systems in their nonlinear polynomial transition systems. However, the exact equivalence is too strict in application. To enhance the flexibility of the relation among the different software systems, the notion of approximate bisimulation within a controllable error range and the calculation algorithm of approximate bisimulation based on symbolic-numeric computation are given. In this calculation, an approximate relation is represented as a MAX function that is resolved with the full filled method. At the same time, the actual error is calculable. An example on a multithreading program indicates that the approximate bisimulation relation is feasible and effective in behavior and structure optimization. [ABSTRACT FROM AUTHOR]

This paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the information of the local Hessian. The new parameterization of the interpolating curve in variable space is obtained by utilizing accumulative approach via a norm weighting defined by two positive definite weighting matrices. We also note that the storage needed for all computation of the proposed method is just On. Numerical results show that the proposed algorithm is efficient and superior by comparison with some other gradient-type methods. [ABSTRACT FROM AUTHOR]

The present paper describes a parallel preconditioned algorithm for the solution of partial eigenvalue problems for large sparse symmetric matrices, on parallel computers. Namely, we consider the Deflation-Accelerated Conjugate Gradient (DACG) algorithm accelerated by factorized-sparse- approximate-inverse- (FSAI-) type preconditioners. We present an enhanced parallel implementation of the FSAI preconditioner and make use of the recently developed Block FSAI-IC preconditioner, which combines the FSAI and the Block Jacobi-IC preconditioners. Results onto matrices of large size arising from finite element discretization of geomechanical models reveal that DACG accelerated by these type of preconditioners is competitive with respect to the available public parallel hypre package, especially in the computation of a few of the leftmost eigenpairs. The parallel DACG code accelerated by FSAI is written in MPI-Fortran 90 language and exhibits good scalability up to one thousand processors. [ABSTRACT FROM AUTHOR]

This paper deals with an inverse problem for identifying multiparameters in 1D space fractional advection dispersion equation (FADE) on a finite domain with final observations. The parameters to be identified are the fractional order, the diffusion coefficient, and the average velocity in the FADE. The forward problem is solved by a finite difference scheme, and then an optimal perturbation regularization algorithm is introduced to determine the three parameters simultaneously. Numerical inversions are performed both with the accurate data and noisy data, and several factors having influences on realization of the algorithm are discussed. The inversion solutions are in good approximations to the exact solutions demonstrating the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Under the condition that the values of mapping F are evaluated approximately, we propose a proximal analytic center cutting plane algorithm for solving variational inequalities. It can be considered as an approximation of the earlier cutting plane method, and the conditions we impose on the corresponding mappings are more relaxed. The convergence analysis for the proposed algorithm is also given at the end of this paper. [ABSTRACT FROM AUTHOR]

Very recently, Ahmad and Yao 2009( introduced and considered a system of generalized resolvent equationswith corresponding system of variational inclusions in uniformly smooth Banach spaces. In this paper we introduce and study a general system of generalized resolvent equations with corresponding general system of variational inclusions in uniformly smooth Banach spaces. We establish an equivalence relation between general system of generalized resolvent equations and general system of variational inclusions. The iterative algorithms for finding the approximate solutions of general system of generalized resolvent equations are proposed. The convergence criteria of approximate solutions of general system of generalized resolvent equations obtained by the proposed iterative algorithm are also presented. Our results represent the generalization, improvement, supplement, and development of Ahmad and Yao corresponding ones. [ABSTRACT FROM AUTHOR]

Very recently, Moudafi (2011) introduced an algorithm with weak convergence for the split common fixed-point problem. In this paper, we will continue to consider the split common fixedpoint problem. We discuss the strong convergence of the viscosity approximation method for solving the split common fixed-point problem for the class of quasi-nonexpansive mappings in Hilbert spaces. Our results improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

The object of investigation of the paper is a special type of functional differential equations containing the maximum value of the unknown function over a past time interval. An improved algorithm of the monotone-iterative technique is suggested to nonlinear differential equations with "maxima." The case when upper and lower solutions of the given problem are known at different initial time is studied. Additionally, all initial value problems for successive approximations have both initial time and initial functions different. It allows us to construct sequences of successive approximations as well as sequences of initial functions, which are convergent to the solution and to the initial function of the given initial value problem, respectively. The suggested algorithm is realized as a computer program, and it is applied to several examples, illustrating the advantages of the suggested scheme. [ABSTRACT FROM AUTHOR]

The goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis. By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix degradative enzymes, degrade extracellular matrix, and invade due to diffusion and haptotactic migration. For the numerical simulations of the interactions between the tumour cells and the surrounding tissue, we apply numerical approximations, which are spectrally accurate and based on small amounts of grid-points. Our numerical experiments illustrate the metastatic ability of tumour cells. [ABSTRACT FROM AUTHOR]

Convex multiobjective programming problems and multiplicative programming problems have important applications in areas such as finance, economics, bond portfolio optimization, engineering, and other fields. This paper presents a quite easy algorithm for generating a number of efficient outcome solutions for convex multiobjective programming problems. As an application, we propose an outer approximation algorithm in the outcome space for solving the multiplicative convex program. The computational results are provided on several test problems. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a nonlinear stationary Stokes problem with mixed boundary conditions that describes the ice velocity and pressure fields of grounded glaciers under Glen's flow law. Using convex analysis arguments, we prove the existence and the uniqueness of a weak solution. A finite element method is applied with approximation spaces that satisfy the inf-sup condition, and a priori error estimates are established by using a quasinorm technique. Several algorithms including Newton's method are proposed to solve the nonlinearity of the Stokes problem and are proved to be convergent. Our results are supported by numerical convergence studies. [ABSTRACT FROM AUTHOR]

The minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms. When the number of variables is large, one of the most widely used strategies is to project the original problem into a small dimensional subspace. In this paper, we introduce an algorithm for solving nonlinear least squares problems. This algorithm is based on constructing a basis for the Krylov subspace in conjunction with a model trust region technique to choose the step. The computational step on the small dimensional subspace lies inside the trust region. The Krylov subspace is terminated such that the termination condition allows the gradient to be decreased on it. A convergence theory of this algorithm is presented. It is shown that this algorithm is globally convergent. [ABSTRACT FROM AUTHOR]

The approximate inverse (AINV) and the factored approximate inverse (FAPINV) are two known algorithms in the field of preconditioning of linear systems of equations. Both of these algorithms compute a sparse approximate inverse of matrix A in the factored form and are based on computing two sets of vectors which are A-biconjugate. The AINV algorithm computes the inverse factors W and Z of a matrix independently of each other, as opposed to the AINV algorithm, where the computations of the inverse factors are done independently. In this paper, we show that, without any dropping, removing the dependence of the computations of the inverse factors in the FAPINV algorithm results in the AINV algorithm. [ABSTRACT FROM AUTHOR]

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT. [ABSTRACT FROM AUTHOR]

Sevimlican suggested an effective algorithm for space and time fractional telegraph equations by the variational iteration method. This paper shows that algorithm can be updated by either variational iteration algorithm-II or the fractional variational iteration method. [ABSTRACT FROM AUTHOR]