primal-dual algorithm

A new hybrid variational model is presented for image denoising, which in-corporates the merits of Shannon interpolation, total generalized variation (TGV) regularization, and a symmetrized derivative regularization term based on l1-norm. In this model, the regularization term is a combination of a TGV functional and the symmetrized derivative regularization term, while the data fidelity term is characterized by the l2-norm. Unlike most variational models that are discretized using a finite-difference scheme, our approach in structure is based on Shannon interpolation. Quantitative and qualitative assessments of the new model indicate its effectiveness in restoration accuracy and staircase effect suppression. Numerical experi-ments are carried out using the primal-dual algorithm. Numerous real- world examples are conducted to confirm that the newly proposed method outperforms several current state-of-the-art numerical methods in terms of the peak signal to noise ratio and the structural similarity (SSIM) index.

We apply a primal-dual simplex algorithm for solving the biobjective min imum cost-time network flow problem such that the total shipping cost and the total shipping fixed time are considered as the first and second objective functions, respectively. To convert the proposed model into a single-objective parametric one, the weighted sum scalarization technique is commonly used. This problem is a mixed-integer programming, which the decision variables are directly dependent together. Generally, the previous works have consid ered the linear biobjective problem with the traditional network flow con straints, while in this paper, corresponding to each flow variable, a binary variable is defined. These zero-one variables are utilized to describe a fixed shipping time for positive flows. The proposed method is successful in finding all supported efficient solutions of a real numerical example.