فهرست مطالب

  • Volume:9 Issue:2, 2019
  • تاریخ انتشار: 1398/07/13
  • تعداد عناوین: 12
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  • K. Rezaei, F. Rahbarnia*, F. Toutounian Pages 1-16

    We propose a new preconditioned global conjugate gradient (PGL-CG) method for the solution of matrix equation AXB = C, where A and B are sparse Stieltjes matrices. The preconditioner is based on the support graph preconditioners. By using Vaidya’s maximum spanning tree precon ditioner and BFS algorithm, we present a new algorithm for computing the approximate inverse preconditioners for matrices A and B and constructing a preconditioner for the matrix equation AXB = C. This preconditioner does not require solving any linear systems and is highly parallelizable. Numerical experiments are given to show the efficiency of the new algorithm on CPU and GPU for the solution of large sparse matrix equation.

    Keywords: Krylov subspace methods, matrix equation, approximate in-verse preconditioner, global conjugate gradient, support graph precondi-tioner, Vaidya's maximum spanning tree preconditioner
  • M. Eslami*, S.A. Taleghani Pages 17-29

    We expand a new generalization of the two-dimensional differential trans form method. The new generalization is based on the two-dimensional differential transform method, fractional power series expansions, and conformable fractional derivative. We use the new method for solving a nonlinear con formable fractional partial differential equation and a system of conformable fractional partial differential equation. Finally, numerical examples are presented to illustrate the preciseness and effectiveness of the new technique.

    Keywords: Conformable fractional derivative, Differential transform method, two-dimensional differential transform method
  • S. Ahdiaghdam*, S. Shahmorad Pages 31-47

    The aim of the present work is to introduce a method based on the Chebyshev polynomials for numerical solution of a system of Cauchy type singular integral equations of the first kind on a finite segment. Moreover, an estimation error is computed for the approximate solution. Numerical resultsdemonstrate the effectiveness of the proposed method.

    Keywords: System of singular linear integral equations, Orthogonal polynomials, Fourier series, Best approximation
  • F. Mohammadi* Pages 49-75

    An efficient direct and numerical method has been proposed to approximate a solution of time-delay fractional optimal control problems. First, a class of discrete orthogonal polynomials, called Hahn polynomials, has been introduced and their properties are investigated. These properties are employed to derive a general formulation of their operational matrix of fractional integration, in the Riemann–Liouville sense. Then, the fractional derivative of the state function in the dynamic constraint of time-delay fractional optimal control problems is approximated by the Hahn polynomials with unknown coefficients. The operational matrix of fractional integration together with the dynamical constraints is used to approximate the control function directly as a function of the state function. Finally, these approximations were put in the performance index and necessary conditions for optimality transform the under consideration time-delay fractional optimal control prob lems into an algebraic system. Some illustrative examples are given and the obtained numerical results are compared with those previously published in the literature.

    Keywords: Delay fractional optimal control problems, Riemann–Liouville integration, Hahn polynomials, Operational matrix
  • F. Mohammadizadeh*, H. A. Tehrani, M. H. Noori Pages 77-102

    In this study, an indirect method is proposed based on the Chebyshev pseudo-spectral method for solving optimal control problems governed by Burgers’ equation. Pseudo-spectral methods are one of the most accurate methods for solving nonlinear continuous-time problems, specially optimal control problems. By using optimality conditions, the original optimal control problem is first reduced to a system of partial differential equations with boundary conditions. Control and state functions are then approximated by interpolating polynomials. The convergence is analyzed, and some numerical examples are solved to show the efficiency and capability of the method.

    Keywords: Burgers’ equation, Optimal control, Chebyshev-Gauss-Lobatto nodes
  • A. Ebrahimi, G. B. Barid *, M. Sarfraz Pages 103-121

    We design a fast technique for fitting cubic B´ezier curves to the boundary of 2D shapes. The technique is implemented by means of the Nelder–Mead simplex procedure to optimize the control points. The natural attributes of the B´ezier curve are utilized to discover the initial vertex points of the Nelder–Mead procedure. The proposed technique is faster than traditional methods and helps to obtain a better fit with a desirable precision. The comparative analysis of our results describes that the introduced approach has a high compression ratio and a low fitting error.

    Keywords: Interpolation, Splines, Curve fitting, Nelder–Mead simplex method, Computer aided design, Computer graphics
  • Z. Akbari* Pages 123-139

    We present a method to minimize locally Lipschitz functions. At first, a local quadratic model is developed to approximate a locally Lipschitz function. This model is constructed by using the ϵ-subdifferential. We minimize this local model and compute a search direction. It is shown that this direction is descent. We generalize the Wolfe conditions for finding an adequate step length along this direction. Next, the method is equipped with a quasi Newton approach to update the local model and its globally convergence is proposed. Finally, the proposed algorithm is implemented in MATLAB environment on some standard nonsmooth optimization test problems and compared with some algorithms in the literature.

    Keywords: Quasi-Newton method, Quadratic model, Line search algorithm, Locally Lipschitz functions
  • E. Tavakkol, S.M. Hosseini*, A.R. Hosseini Pages 141-163

    Variational models are one of the most efficient techniques for image denoising problems. A variational method refers to the technique of optimizing a functional in order to restore appropriate solutions from observed data that best fit the original image. This paper proposes to revisit the discrete total generalized variation (TGV ) image denoising problem by redefining the operations via the inclusion of a diagonal term to reduce the staircasing effect, which is the patchy artifacts usually observed in slanted regions of the image. We propose to add an oblique scheme in discretization operators, which we claim is aware of the alleviation of the staircasing effect superior to the con ventional TGV method. Numerical experiments are carried out by using the primal-dual algorithm, and numerous real-world examples are conducted to confirm that the new proposed method achieves higher quality in terms of rel ative error and the peak signal to noise ratio compared with the conventional TGV method.

    Keywords: Image denoising, Total variation, Staircasing effect, Total generalized variation, Peak signal to noise ratio
  • S.M. Mirhosseini, Alizamini* Pages 165-183

    We apply the Adomian decomposition method (ADM) to obtain a subop timal control for linear time-varying systems with multiple state and control delays and with quadratic cost functional. In fact, the nonlinear two-point boundary value problem, derived from Pontryagin’s maximum principle, is solved by ADM. For the first time, we present here a convergence proof for ADM. In order to use the proposed method, a control design algorithm with low computational complexity is presented. Through the finite iterations of algorithm, a suboptimal control law is obtained for the linear time-varying multi-delay systems. Some illustrative examples are employed to demonstrate the accuracy and efficiency of the proposed methods.

    Keywords: Multiple time-delay systems, Pontryagin’s maximum principle, Adomian decomposition method
  • B. Mohammadi* Pages 185-191

    We introduce Ciri´c-generalized quasicontractive fuzzy mappings and pro vide the necessary and sufficient conditions of having a unique endpoint for such mappings. Then we introduce β-ψ-quasicontractive fuzzy mappings, es tablishing an endpoint result for them. Finally, we provide some results as an application.

    Keywords: Fuzzy endpoint, Ciri´c-generalized, Quasicontractivefuzzymappings, Fuzzy approximate endpoint property
  • J.W. Yougbare* Pages 193-205

    We exploit the relationship between multiobjective integer linear problem (MOILP) and data envelopment analysis (DEA) to develop an approach to a resource reallocation problem. The general purpose of the mathematical formulation of this multicriteria allocation model based on DEA is to enable decision-makers to take into account the efficiency of units under control to allocate additional resources for a new period of operation. We develop a formal approach based on DEA and MOILP to find the most preferred allocation plan taken account additional resources. The mathematical model is given, and we illustrate it with a numerical example.

    Keywords: Multicriteria decision aiding, Data envelopment analysis, Multiobjective integer linear programming, Additional resource allocation, Efficient frontier
  • M. Allahdadi, A. Batamiz* Pages 207-230

    Many real-world problems occur under uncertainty. In this paper, we consider interval linear programming (ILP) which can be used to tackle un certainties. Several methods have been proposed by researchers, such as the best and worst cases, Two-step method (TSM), improved TSM, ILP, improved ILP, three-step method, and robust two-step method. First, we define feasibility and optimality conditions in ILP models and review some solving methods shortly, and then show that some solutions of the TSM method are not feasible. Therefore, we propose an updated TSM method (namely, UTSM) by considering the feasibility and optimality conditions. In this paper, the UTSM method was applied to identify the reduction of aerosols by using two controllers with a minimized cost to demonstrate its application under uncertainty. Compared with other methods, the solutions obtained through ILP were presented as interval, which can provide intervals for the decision variables, objective function, and decision-makers. Therefore, the decision-makers can make the best decision based on the obtained solutionsthrough ILP, and then identify desired plans for aerosol-emission control under uncertainty.

    Keywords: Interval linear programming, TSM, Uncertainty, Aerosol