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In this paper, we consider a nonsmooth vector optimization problem involving locally Lipschitz generalized approximate convex functions and find some relations between approximate convexity and generalized approximate convexity. We establish relationships between vector variational inequalities and nonsmooth vector optimization problem using the generalized approximate convexity as a tool. [ABSTRACT FROM AUTHOR]

We consider the initial boundary value problem of the long-short wave equations on the whole line. A fully discrete spectral approximation scheme is developed based on Chebyshev rational functions in space and central difference in time. A priori estimates are derived which are crucial to study numerical stability and convergence of the fully discrete scheme. Then, unconditional numerical stability is proved. Convergence of the fully discrete scheme is shown by the method of error estimates. Finally, numerical experiments are presented to demonstrate the efficiency and accuracy of the convergence results. [ABSTRACT FROM PUBLISHER]

This article presents an elementary informal technique for deriving the convergence of known distributions to limiting normal or non-normal distributions. The presentation should be of interest to teachers and students of first year graduate level courses in probability and statistics. [ABSTRACT FROM PUBLISHER]

In this paper, we consider two time-harmonic inverse scattering problems of reconstructing penetrable inhomogeneous obstacles from near field measurements. First, we appeal to the Born approximation for reconstructing small isotropic scatterers via the MUSIC algorithm. Some numerical reconstructions using the MUSIC algorithm are provided for reconstructing the scatterer and piecewise constant refractive index using a Bayesian method. We then consider the reconstruction of an anisotropic extended scatterer by a modified linear sampling method and the factorization method applied to the near field operator. This provides a rigorous characterization of the support of the anisotropic obstacle in terms of a range test derived from the measured data. Under appropriate assumptions on the material parameters, the derived factorization can be used to determine the support of the medium without a priori knowledge of the material properties. [ABSTRACT FROM PUBLISHER]

This paper is concerned with theH∞model reduction for negative imaginary (NI) systems. For a given linear time-invariant system that is stable and NI, our goal is to find a stable reduced-order NI system satisfying a pre-specifiedH∞approximation error bound. Sufficient conditions in terms of matrix inequalities are derived for the existence and construction of anH∞reduced-order NI system. Iterative algorithms are provided to solve the matrix inequalities and to minimise theH∞approximation error. Finally, a numerical example is used to demonstrate the effectiveness of the proposed model reduction method. [ABSTRACT FROM PUBLISHER]

The smoothed particle hydrodynamics (SPH) method is a meshless numerical modeling technique. It has been applied in many different research fields in coastal engineering. Due to the drawback of its kernel approximation, however, the accuracy of SPH simulation results still needs to be improved in the prediction of violent wave impact. This paper compares several different forms of correction on the first-order derivative of ISPH formulation aiming to find one optimum kernel approximation. Based on four benchmark case analysis, we explored different kernel corrections and compared their accuracies. Furthermore, we applied them to one solitary wave and two dam-break flows with violent wave impact. The recommended method has been found to achieve much more promising results as compared with experimental data and other numerical approaches. [ABSTRACT FROM AUTHOR]

This paper studies maintenance policies for multi-component systems in which failure interactions and opportunistic maintenance (OM) involve. This maintenance problem can be formulated as a Markov decision process (MDP). However, since an action set and state space in MDP exponentially expand as the number of components increase, traditional approaches are computationally intractable. To deal with curse of dimensionality, we decompose such a multi-component system into mutually influential single-component systems. Each single-component system is formulated as an MDP with the objective of minimising its long-run average maintenance cost. Under some reasonable assumptions, we prove the existence of the optimal (n,N) type policy for a single-component system. An algorithm to obtain the optimal (n,N) type policy is also proposed. Based on the proposed algorithm, we develop an iterative approximation algorithm to obtain an acceptable maintenance policy for a multi-component system. Numerical examples find that failure interactions and OM pose significant effects on a maintenance policy. [ABSTRACT FROM AUTHOR]

This article addresses the flow shop scheduling problem to minimize the sum of the completion times. On the basis of the properties in job sequencing, the triangular shortest processing time (TSPT) first and dynamic triangular shortest processing time first heuristics are designed to solve the static and dynamic versions of this problem, respectively. Moreover, an improvement scheme is provided for these heuristics to enhance the quality of the original solutions. For further numerical evaluation of the heuristics, two new lower bounds with performance guarantees are presented for the two versions of the problem. At the end of the article, a series of numerical experiments is conducted to demonstrate the effectiveness of the algorithms. [ABSTRACT FROM AUTHOR]

In this article, we present a primal-dual 3-approximation algorithm for the stochastic priority facility location problem. Combined with greedy augmentation procedure, such performance factor is further improved to 1.8526. [ABSTRACT FROM PUBLISHER]

Variational image restoration models for both additive and multiplicative noise (MN) removal are rarely encountered in the literature. This paper proposes a new variational model and a fast algorithm for its numerical approximation to remove independent additive and MN from digital images. Two previous works by L. Rudin, S. Osher, and E. Fatemi [Nonlinear total variation based noise removal algorithms, Phys. D 60 (1992), pp. 259–268] and Z. Jin and X. Yang [Analysis of a new variational model for multiplicative noise removal, J. Math. Anal. Appl. 362 (2010), pp. 415–426] are used to develop the new model. As a result, developing a fast numerical algorithm is difficult because the associated Euler–Lagrange equation is highly nonlinear and standard unilevel iterative methods are not appropriate. To this end, we develop an efficient nonlinear multigrid approach via a robust fixed-point smoother. Numerical tests using both synthetic and realistic images not only confirm that our new model delivers quality results but also that the proposed numerical algorithm allows a very fast numerical realization of the model. [ABSTRACT FROM PUBLISHER]

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach. [ABSTRACT FROM PUBLISHER]

This article deals with multicriteria optimization models and algorithms of movement scheduling for many objects to synchronize their movement (2CMSS problem). The model consists of two parts: (1) node–disjoint path planning visiting specified nodes for K objects with a given vector of intermediate nodes for each one (NDSP problem); (2) movement synchronization in some intermediate nodes (MS problem). For synchronous movement, two categories of criteria are defined: time of movement and ‘distance’ of K-moved objects from the movement pattern. We defined the problem as a discrete-continuous, non-linear, two-criteria mathematical programming problem. We proposed to use a two-stage algorithm to solve the 2CMSS problem (as lexicographic solution): At first we have to find the vector of node–disjoint shortest paths for K objects visiting intermediate nodes to set optimal paths under the assumption that we use maximal possible velocities on each arc belonging to a path for each object (solution of the NDSP problem), and next we try to decrease the values of velocities to optimize the second criterion (synchronization, solution of the MS problem). Experimental analyses of effectiveness and complexity of the algorithms are presented. [ABSTRACT FROM AUTHOR]

This article models a multi-vehicle material handling system as a closed-loop queueing network with finite buffers and general service times, where the vehicles represent the jobs in the network. This type of network differs from other queueing systems, because the vehicles' residence times on track segments (servers) depend on the number of jobs (vehicles) in circulation. A new iterative approximation algorithm is presented that estimates throughput capacity and decomposes the network consisting of S servers into S separate G/G/1 systems. Each subsystem is analyzed separately to estimate the work-in-process via a population constraint to ensure that the summation of the average buffer sizes across all servers equals the total number of vehicles. Numerical results show that the methodology proposed is accurate in a wide range of operating scenarios. [ABSTRACT FROM AUTHOR]

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional parabolic inverse Cauchy-Stefan problem, where boundary data and the initial condition are to be determined from the Cauchy data prescribed on a given moving interface. In [B.T. Johansson, D. Lesnic, and T. Reeve, A method of fundamental solutions for the one-dimensional inverse Stefan Problem, Appl. Math Model. 35 (2011), pp. 4367-4378], the inverse Stefan problem was considered, where only the boundary data is to be reconstructed on the fixed boundary. We extend the MFS proposed in Johansson et al. (2011) and show that the initial condition can also be simultaneously recovered, i.e. the MFS is appropriate for the inverse Cauchy-Stefan problem. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be efficiently obtained with small computational cost. [ABSTRACT FROM AUTHOR]

We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. [ABSTRACT FROM AUTHOR]

The article offers information on the value function of perpetual American put option pricing for level dependent volatility models. It mentions that the sequential representation of value function was useful in the analysis of value function behavior and yields good numerical schemes. It says that the value function was classical solution for the corresponding quasi-variational inequality. Moreover, the approximation techniques were used to estimate optimal stopping problems for diffusions.

In this article, we propose a family of second derivative Adams-type methods (SDAMs) of order up to 2k + 2 (k is the step number) for initial value problems. The methods are constructed through a continuous approximation of the SDAM which is obtained by multistep collocation. The continuous approximation is used to obtain initial value methods, which are simultaneously applied to generate all approximations on the entire interval. The order and the linear stability properties of the methods are discussed. Numerical experiments are performed and the results are compared with those of existing methods in the literature. [ABSTRACT FROM AUTHOR]