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Highlights • A new variational model for image retinex is proposed. • The existence of minimizer for the variational model is proved. • An efficient algorithm is derived to solve the model by adding auxiliary variables. • The convergence of the numerical algorithm is proved under some assumptions. • The proposed method can be extended to other regularization and fidelity terms. Abstract In this paper, we propose a detail preserving variational model for Retinex to simultaneously estimate the illumination and the reflectance from an observed image. Most previous models use the log-transform as pretreatment which results in loss of details in reflectance. From this observation, a detail preserving variational method is proposed for better decomposition. Different from the log-transform based models, the proposed model performs the decomposition directly in the image domain. Mathematically, we prove the existence of a solution for the proposed model. Numerically, we derive an efficient iterative algorithm by utilizing alternating direction method of multipliers (ADMM) method. Experimental results demonstrate the effectiveness of the proposed method. Compared with other closely related Retinex methods, the proposed method achieves competitive results on both subjective and objective assessments. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a new second-order accurate central scheme for the numerical solution of the two-dimensional system of shallow water equations (SWE) featuring wet and dry states over variable waterbeds. The proposed central scheme follows a classical Riemann-free finite volume method and evolves the numerical solution of systems of hyperbolic balance laws on a single Cartesian grid. Furthermore, the proposed well-balanced scheme preserves the lake at rest constraint thanks to a careful well-balanced discretization of the SWE system, and allows a proper interaction between wet and dry states whenever water run-ups/drains arise. For verification purposes, classical SWE problems appearing in the recent literature are successfully solved. [ABSTRACT FROM AUTHOR]

This paper addresses a nonconvex optimization problem with the cost function and inequality constraints given by d.c. functions. The original problem is reduced to a problem without inequality constraints by the exact penalization procedure. A special local search method for the penalized problem is developed, which is based, first, on the linearization procedure with respect to the basic nonconvexity and, second, on the consecutive solutions of linearized convex problems. Convergence properties of the method are investigated. In particular, it is shown that a limit point of the sequence produced by the method is considerably stronger than the usual KKT-vector. In addition, the relations between an approximate solution of linearized convex problem and the KKT-vector of the original problem are established, and the various stopping criteria are substantiated. Besides, we established the relations among the Lagrange multipliers of the original problem, those ones of the linearized problem, and the value of the penalty parameter. Finally, a preliminary computational testing of the LSM developed has been carried out on several test problems taken from literature. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, He’s homotopy perturbation method (HPM) is applied for solving linear programming (LP) problems. This paper shows that some recent findings about this topic cannot be applied for all cases. Furthermore, we provide the correct application of HPM for LP problems. The proposed method has a simple and graceful structure. Finally, a numerical example is displayed to illustrate the proposed method. [Copyright &y& Elsevier]

Abstract: TOPSIS (technique for order preference by similarity to ideal solution) is a multiple criteria method to identify solutions from a finite set of alternatives based upon simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. This paper proposes a fuzzy TOPSIS algorithm to solve bi-level multi-objective decision-making (BL-MODM) problems, and in which the objective function at each level are non-linear functions which are to be maximized. The proposed model for getting the satisfactory solution of the BL-MODM problems includes the membership functions for the upper level decision variables vector with possible tolerances, the membership function of the distance function from the positive ideal solution (PIS) and the membership function of the distance function from the negative ideal solution (NIS). A numerical illustrative example is given to clarify the proposed TOPSIS approach of this paper. [Copyright &y& Elsevier]

The two-dimensional Helmholtz differential equation governs vibrational problems for a thin membrane and is therefore well studied. Analytical solutions are limited to particular domain shapes, so that in general numerical methods are used when an arbitrary domain is considered. In this paper, a quasi-analytical solution is proposed, suitable to be applied to an arbitrary domain shape. Concretely, the Helmholtz equation is transformed to account for a conformal map between the shape of the physical domain and the unit disk as canonical domain. This way, the transformed Helmholtz equation is solved exploiting well known analytical solutions for a circular domain and the solution in the physical domain is obtained by applying the conformal map. The quasi-analytical approach is compared to analytical solutions for the case of a circular, elliptic and squared domain. [ABSTRACT FROM AUTHOR]

This paper considers a two-warehouse inventory problem for deteriorating items with a constant demand rate over a finite time horizon. A modified first-in-first-out dispatching policy is first proposed, and a new two-warehouse inventory model based on this dispatching policy is developed. The results of this model are then compared with those of other models based on classical dispatching policies, such as the last-in-first-out, modified last-in-first-out and first-in-first-out dispatching policies. We also prove the existence and uniqueness of the optimal solutions for the models considered. Finally, a numerical example is presented to illustrate the results, and several key conditions are derived for comparing the general cases of these four models. [ABSTRACT FROM AUTHOR]

Abstract: Computing traffic equilibria with a general nonadditive route cost disutility function is considered in this paper. Following the user equilibrium (UE) condition, that is, no driver can unilaterally change route to achieve less travel costs, the traffic equilibrium problem (TEP) can be formulated as a nonlinear complementary problem (NCP). In this paper, we propose a semismooth Newton method with a penalized Fischer–Burmeister (PFB) NCP function to solve the NCP formulation of the TEP, and also, we investigate the properties of the proposed method. Numerical results are provided and compared with the classical TEP with additive route cost functions. The results show the algorithm can achieved substantially better performance than the existing approaches. A sensitivity analysis is also conducted to examine the parameter of the proposed nonadditive route cost function. [Copyright &y& Elsevier]

Abstract: This paper proposes a sequential approach to determine the unknown parameters for inverse heat conduction problems which have multiple time-dependent heat sources. There are two main aims in this study, one is to derive an inverse algorithm that can estimate the unknown conditions effectively, and the other is to bring up a theoretical sensitivity analysis to discuss what causes the growth of errors. This paper has three major achievements with regard to the literature on IHCPs, as follows: (1) proposing an efficient sequential inverse algorithm that can simultaneously determine several unknown time-dependent parameters; (2) exploring why the sequential function specification method can provide a stable but inaccurate estimation when tackling problems with larger measurement errors; and (3) discussing the sensitivity problem and analyzing what factors cause the growth in error sensitivity. Three examples are applied to demonstrate the performance of the proposed method, and the numerical results show that the accurate estimations can be obtained by alleviating the error sensitivity when the measurement error is considered. [Copyright &y& Elsevier]

Abstract: The VIKOR method was developed for multi-criteria optimization of complex systems. It determines the compromise ranking list and the compromise solution obtained with the initial (given) weights. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. It introduces the multi-criteria ranking index based on the particular measure of “closeness” to the “ideal” solution. The aim of this paper is to extend the VIKOR method for decision making problems with interval number. The extended VIKOR method’s ranking is obtained through comparison of interval numbers and for doing the comparisons between intervals, we introduce α as optimism level of decision maker. Finally, a numerical example illustrates and clarifies the main results developed in this paper. [Copyright &y& Elsevier]

This paper is concerned with the numerical solutions of the generalized time fractional burgers equation. We propose a linear implicit finite difference scheme for solving the equation. Iterative methods become dispensable. As a result, the computational cost can be significantly reduced compare to the usual implicit finite difference schemes. Meanwhile, the finite difference method is proved to be unconditional globally stable and convergent. Numerical examples are shown to demonstrate the accuracy and stability of the method. [ABSTRACT FROM AUTHOR]

In this paper we study an asymptotic-numerical solver for first-order ordinary differential equations with extrinsic oscillation. First we derive bounds on the terms of the asymptotic-numerical solver and estimate global errors of the method for a linear system. A numerical experiment is carried out to demonstrate the efficiency and robustness of this method for a linear system. Then the bounds on the terms of the asymptotic-numerical solver are also discussed for a nonlinear system and two numerical experiments are presented for that case. [ABSTRACT FROM AUTHOR]

This paper investigates uncertain maximum flow problem. To obtain the uncertainty distribution of the maximum flow, an α -maximum flow model is formulated under uncertainty theory framework. It is proved that there exists an equivalence relationship between the α -maximum flow model and the classic deterministic maximum flow model. Furthermore, some important properties of α -maximum flow model are analyzed, based on which a polynomial algorithm is proposed. Finally, a numerical example is presented to illustrate the model and the algorithm. [ABSTRACT FROM AUTHOR]

Adding weight restrictions on multiplier DEA models to incorporate value judgments is equivalent to accepting trade-offs between inputs and outputs in envelopment forms. To obtain the corresponding DEA model with the trade-off axiom, the production possibility set (PPS) is changed which has led to the introduction of the three-stage model. Although the efficiency of DMUs and efficient targets can be determined by the three-stage model, the result might be unacceptable because of locating the PPS in the negative area; clarification for which has been provided by means of a numerical example. An improved PPS and its corresponding model will be presented in this paper. The structure of the modified PPS preserves its non-negativity and efficient targets can be achieved through solving merely one max-slack model. [ABSTRACT FROM AUTHOR]

In this paper, a new adaptive mesh strategy has been developed for solving convection dominated, convection–diffusion singularly perturbed problems (SPP) using second order central difference schemes. Our strategy uses a novel, entropy-like variable as the adaptation parameter for convection diffusion SPP. Further, unlike the popular layer adapted meshes mainly by Bakhvalov (B-type) and Shishkin (S-type), no pre-knowledge of the location and width of the layers (boundary as well as interior) is needed. The method is completely free of arbitrary perturbation parameters ∊ (robust) and results in oscillation free solutions to a range of convection–diffusion SPP. Numerical results for various test problems: linear (boundary layers with and without turning points), nonlinear and systems of coupled equations are presented. This method is expected to aid in robust computations of convection dominated SPP. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, periodized Shannon wavelets are applied as basis functions in solution of the high-order ordinary differential equations and eigenvalue problem. The first periodized Shannon wavelets are defined. The second the connection coefficients of periodized Shannon wavelets are related by a simple variable transformation to the Cattani connection coefficients. Finally, collocation method is used for solving the high-order ordinary differential equations and eigenvalue problem. Some equations are solved in order to find out advantage of such choice of the basis functions. [Copyright &y& Elsevier]

Abstract: In this paper a numerical approach combining the least squares method and the genetic algorithm (sequential and multi-core parallelization approach) is proposed for the determination of temperature in an inverse heat conduction problem (IHCP). Some numerical experiments confirm the utility of this algorithm as the results are in good agreement with the exact data. Results show that an excellent estimation can be obtained by implementation sequential genetic algorithm within a CPU with clock speed 2.7GHz, and parallel genetic algorithm within a 16-core CPU with clock speed 2.7GHz for each core. [Copyright &y& Elsevier]

Abstract: In this paper, we propose and analyze a fully discrete local discontinuous Galerkin (LDG) finite element method for time-fractional fourth-order problems. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. Stability is ensured by a careful choice of interface numerical fluxes. We prove that our scheme is unconditional stable and convergent. Numerical examples are shown to illustrate the efficiency and accuracy of our scheme. [Copyright &y& Elsevier]

Abstract: This paper proposes a new mathematical model to solve the cell formation, operator assignment and inter-cell layout problems, simultaneously. The objectives of proposed model are minimization of inter–intra cell part trips, machine relocation cost and operator related issues. Since the objective function of the proposed model consists of none commensurable statements, the preferred solution is obtained by the LP-metric approach. In order to validate the proposed model, some numerical examples are generated randomly and solved by branch and bound technique. Moreover; a real case study is illustrated in order to verify its applicability in an automobile producer company. Moreover the sensitivity analysis of proposed model shows that considering the operator assignment problem has significant impact on the overall system efficiency. [Copyright &y& Elsevier]

Abstract: In multi-objective geometric programming problem there are more than one objective functions. There is no single optimal solution which simultaneously optimizes all the objective functions. Under these conditions the decision makers always search for the most “preferred” solution, in contrast to the optimal solution. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper -constraint method has been applied to find the non-inferior solution. A brief solution procedure of -constraint method has been presented to find the non-inferior solution of the multi-objective programming problems. Further, the multi-objective programming problems is solved by the fuzzy programming technique to find the optimal compromise solution. Finally, two numerical examples are solved by both the methods and compared with their obtained solutions. [Copyright &y& Elsevier]

Abstract: In this paper, we provide a new modification of the variational iteration method (MVIM) for solving van der Pol equations. The modification couples the classical variational iteration method with He’s polynomials, where the He’s polynomials are applied to the approximate solution and the initial condition to eliminate secular terms. For the large ɛ, the numerical results demonstrate that the modification method get an accurate approximate period than the other presented methods. [Copyright &y& Elsevier]

Abstract: The available learning and forgetting models do not consider the physical loading that performing a task requires. In some situations, physical loading results in workers’ fatigue on the job that is followed by rest breaks to alleviate it. The aim of this paper is to present the “learning–forgetting–fatigue–recovery model” (LFFRM) that addresses possible issues relating to workers’ capabilities and restrictions in manufacturing environments. Numerical examples are solved to address some research questions regarding the model optimization and its constraints. The main results show that incorporating learning into a production process decreases fatigue and improves the performance of the system. Worker fatigue, on the other hand, increases production time and decreases production output. A recovery break must be of enough length to alleviate some of the accumulated fatigue. However, longer recovery times extend the lead time and deteriorate the production performance due to forgetting. [Copyright &y& Elsevier]

Abstract: To the best of our knowledge, there is no method in literature for solving such fully fuzzy linear programming (FLP) problems in which some or all the parameters are represented by unrestricted L-R flat fuzzy numbers. Also, to propose such a method, there is need to find the product of unrestricted L-R flat fuzzy numbers. However, there is no method in the literature to find the product of unrestricted L-R flat fuzzy numbers. In this paper, firstly the product of unrestricted L-R flat fuzzy numbers is proposed and then with the help of proposed product, a new method (named as Mehar’s method) is proposed for solving fully FLP problems. It is also shown that the fully FLP problems which can be solved by the existing methods can also be solved by the Mehar’s method. However, such fully FLP problems in which some or all the parameters are represented by unrestricted L-R flat fuzzy numbers can be solved by Mehar’s method but can not be solved by any of the existing methods. [Copyright &y& Elsevier]

Abstract: In this paper, we present a two-grid stabilized mixed finite element method for the two-dimensional semilinear elliptic equations. The method combines the two grid scheme with a stabilized mixed finite element method which is based on pressure projection stabilization method by using the lowest equal-order pair for the velocity and pressure. The two-grid method consists of solving a small semilinear system on the coarse mesh and then solving a linear system on the fine mesh. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy . Error estimates are derived for the algorithm of the two-grid method. Finally, we give some numerical experiments to verify the efficiency and the theoretical results of the proposed method. [Copyright &y& Elsevier]

Abstract: The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared. [Copyright &y& Elsevier]

Abstract: This paper deals with multiattribute group decision making (MAGDM) problems with interval-valued 2-tuple linguistic information. First, we introduce some new aggregation operators, such as the interval-valued 2-tuple weighted geometric (IVTWG) operator, the interval-valued 2-tuple ordered weighted geometric (IVTOWG) operator, the generalized interval-valued 2-tuple weighted average (GIVTWA) operator and the generalized interval-valued 2-tuple ordered weighted average (GIVTOWA). Then, we discuss their desired properties and relationships among them. Furthermore, we put forward a new method to determine the weight vector of interval-valued 2-tuple aggregation operator based on the concept of degree of precision. Finally, a numerical example is provided to illustrate the efficiency of the proposed method in dealing with interval-valued 2-tuple linguistic information under multi-granular linguistic contexts. [Copyright &y& Elsevier]

Abstract: In this paper, an improved Legendre collocation method is presented for a class of integro-differential equations which involves a population model. This improvement is made by using the residual function of the operator equation. The error differential equation, gained by residual function, has been solved by the Legendre collocation method (LCM). By summing the approximate solution of the error differential equation with the approximate solution of the problem, a better approximate solution is obtained. We give the illustrative examples to demonstrate the efficiency of the method. Also we compare our results with the results of the known some methods. In addition, an application of the population model is made. [Copyright &y& Elsevier]

Abstract: In this paper, the solution of fuzzy linear system (FLS) is investigated based on a -level expansion. To this end, -level of FLS is solved for calculating the core of fuzzy solution and then its spreads are obtained by solving an optimization problem with a special objective function. Using our proposed method, if the computed solution satisfies the FLS, it can be as exact or approximated solution. Finally, the existence of solution of FLS is proved in details and some numerical examples are solved to illustrate the accuracy and capability of the method. [Copyright &y& Elsevier]

Abstract: This paper focuses on the problem of robust finite-time stabilization for one family of uncertain singular Markovian jump systems. Firstly, the definitions of singular stochastic finite-time boundedness and singular stochastic finite-time boundedness are presented. Secondly, sufficient conditions on singular stochastic finite-time boundedness are obtained for the class of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic finite-time boundedness for the family of singular stochastic systems. Sufficient criteria are provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic finite-time boundedness and singular stochastic finite-time boundedness, which can be reduced to a feasibility problem in the form of linear matrix inequalities with a fixed parameter, respectively. Finally, numerical examples are given to illustrate the validity of the proposed methodology. [Copyright &y& Elsevier]

Abstract: The present paper is devoted to solve the problem of identifying an unknown heat source depending simultaneously on both space and time variables. This problem is transformed into an optimization problem and the uniqueness of minimum element is proved rigorously. Then a variational formulation for solving the optimization problem is given. A conjugate gradient method and a finite difference method are used to solve the variational problem. Some numerical examples are also provided to show the efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: Model updating should be correlated with experimental data to ensure that it models the dynamics of the real structure and the updated model predicts the dynamics of a structure more accurately. Considering that the iterative methods for model updating have aroused little public attention, this paper studies an iterative algorithm for quadratic model updating problems which can incorporate the measured modal data into the finite element model to produce an adjusted finite element model on the mass, gyroscopic and stiffness matrices that closely match the experimental modal data. By this method, the best approximation symmetric and skew-symmetric solutions can be obtained by choosing a convergence factor. Numerical example shows that the introduced iterative algorithm is quite efficient. [Copyright &y& Elsevier]

Abstract: Quadratic knapsack problem has a central role in integer and nonlinear optimization, which has been intensively studied due to its immediate applications in many fields and theoretical reasons. Although quadratic knapsack problem can be solved using traditional nonlinear optimization methods, specialized algorithms are much faster and more reliable than the nonlinear programming solvers. In this paper, we study a mixed linear and quadratic knapsack with a convex separable objective function subject to a single linear constraint and box constraints. We investigate the structural properties of the studied problem, and develop a simple method for solving the continuous version of the problem based on bi-section search, and then we present heuristics for solving the integer version of the problem. Numerical experiments are conducted to show the effectiveness of the proposed solution methods by comparing our methods with some state of the art linear and quadratic convex solvers. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of solving the two-dimensional diffusion equation subject to a non-local condition involving a double integral in a rectangular region is considered. The solution of this type of problems are complicated. Therefore, a simple meshless method using the radial basis functions is constructed for the non-local boundary value problem with Neumann’s boundary conditions. Numerical examples are included to demonstrate the reliability and efficiency of this method. Also N e and root mean square errors are obtained to show the convergence of the method. [Copyright &y& Elsevier]

Abstract: This paper discusses the problem of determining an unknown source which depends only on one variable in two-dimensional Poisson equation from one supplementary temperature measurement at an internal point. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the modified regularization method. For the regularization solution, the Hölder type stability estimate between the regularization solution and the exact solution is given. Numerical results are presented to illustrate the accuracy and efficiency of this method. [Copyright &y& Elsevier]

Abstract: A method based on constrained optimization for updating of an acoustic finite element model using pressure response is proposed in this paper. The constrained optimization problem is solved using sequential quadratic programming algorithm. Updating parameters related to the properties of the sound absorbers and the measurement errors are considered. Effectiveness of the method is demonstrated by numerical studies on a 2D rectangular cavity and a car cavity. It is shown that the constrained formulation, that includes lower and upper bounds on the updating parameters in the form of inequality constraints, is important for obtaining a correct updated model. It is seen that the proposed updating method is not only able to effectively update the model to obtain a close match between the finite element model pressure response and the reference pressure response, but is also able to identify the correction factors to the parameters in error with reasonable accuracy. [Copyright &y& Elsevier]

Abstract: This paper deals with a recently proposed algorithm for obtaining all weak efficient and efficient solutions in a multi objective linear programming (MOLP) problem. The algorithm is based on solving some weighted sum problems, and presents an easy and clear solution structure. We first present an example to show that the algorithm may fail when at least one of these weighted sum problems has not a finite optimal solution. Then, the algorithm is modified to overcome this problem. The modified algorithm determines whether an efficient solution exists for a given MOLP and generates the solution set correctly (if exists) without any change in the complexity. [Copyright &y& Elsevier]