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The paper discusses a task preference-based bottleneck assignment problem in which there are n tasks that are divided into three phases in order of preference of performance of various tasks. The assignment problem is balanced with an equal number of agents and tasks. An agent can perform only one task and each task can be accomplished by exactly one agent. Tasks belonging to a particular phase cannot be commenced until the tasks of the previous phase have been completed. Given the performance time of each task by each agent, the aim is to find an assignment of agents to the tasks that minimize the total completion time of all tasks. The total completion time here refers to the sum of the overall completion times of three phases. An iterative algorithm for solving such a task preference-based bottleneck assignment problem is proposed in the paper. The proposed algorithm is validated with the help of theoretical results and numerical illustration. The algorithm has been coded in MATLAB and the computational results show that the algorithm performs well in terms of computing time for finding optimal assignments for task preference-based assignment problems of different sizes.

In this paper, we present a new QP-free method without using a penalty function for inequality constrained optimization. It is an infeasible method. At each iteration, three linear equations with the same coefficient matrix are solved. The nearly active set technique is used in the algorithm, which eliminates some inactive constraints and reduces the dimension of coefficient matrix, and thereby reduces the amount of computational work. Moreover, the algorithm reduces the value of objective function or the measure of constraints violation according to the relationship between optimality and feasibility. Under common conditions, we prove that the proposed method has global and superlinear local convergence. Lastly, preliminary numerical results are reported.

We propose a simple numerical procedure to approach the symbol of a self-adjoint linear operator $$\mathcal {A}$$ by using trace estimates of a corresponding discretization matrix A, with numerical data. The Symbol Approximation Method (SAM) is based on an adaptation of the matrix trace estimator to successive distinct numerical spectral bands in order to build a piece-wise constant function as an approximation of the symbol $$\sigma $$ of $$\mathcal {A}$$ . The decomposition of the spectral interval into band of frequencies is proposed with several approaches, from the formal spectral to the multi-grid one. We apply the new method to different operators when discretized in finite differences or in finite elements. The SAM is also proposed as a tool for the modeling of waves equations, and is presented a means to capture an additional linear damping term (hidden operator) in hydrodynamics models such as Korteweig–de Vries or Benjamin Ono equations.

One of the aims of image inpainting is recovering an image some of which Fourier transform coefficients are lost. In this paper, we present a new algorithm for image inpainting in Fourier transform domain. We consider the effect of spectrum and phase angle of the Fourier transform, separately. Hence, two regularization parameters are generated; therefore, we have two degree of freedom. Some numerical examples confirm our proposed method.

Let A be a tridiagonal Toeplitz matrix denoted by $$A = {\text {Tritoep}} (\beta , \alpha , \gamma )$$ . The matrix A is said to be: strictly diagonally dominant if $$|\alpha |>|\beta |+|\gamma |$$ , weakly diagonally dominant if $$|\alpha |\ge |\beta |+|\gamma |$$ , subdiagonally dominant if $$|\beta |\ge |\alpha |+|\gamma |$$ , and superdiagonally dominant if $$|\gamma |\ge |\alpha |+|\beta |$$ . In this paper, we consider the solution of a tridiagonal Toeplitz system $$A\mathbf {x}= \mathbf {b}$$ , where A is subdiagonally dominant, superdiagonally dominant, or weakly diagonally dominant, respectively. We first consider the case of A being subdiagonally dominant. We transform A into a block $$2\times 2$$ matrix by an elementary transformation and then solve such a linear system using the block LU factorization. Compared with the LU factorization method with pivoting, our algorithm takes less flops, and needs less memory storage and data transmission. In particular, our algorithm outperforms the LU factorization method with pivoting in terms of computing efficiency. Then, we deal with superdiagonally dominant and weakly diagonally dominant cases, respectively. Numerical experiments are finally given to illustrate the effectiveness of our algorithms.