Portfolio theory deals with the question of how to allocate resources among several competing alternatives (stocks, bonds), many of which have an unknown outcome. In this paper we provide an overview of different port...
详细信息
Portfolio theory deals with the question of how to allocate resources among several competing alternatives (stocks, bonds), many of which have an unknown outcome. In this paper we provide an overview of different portfolio models with emphasis on the corresponding optimization problems. For the classical Markowitz mean-variance model we present computational results, applying a dual algorithm for constrained optimization.
In this paper, we study a nonlinear multigrid method for solving a general image denoising model with two L (1)-regularization terms. Different from the previous studies, we give a simpler derivation of the dual formu...
详细信息
In this paper, we study a nonlinear multigrid method for solving a general image denoising model with two L (1)-regularization terms. Different from the previous studies, we give a simpler derivation of the dual formulation of the general model by augmented Lagrangian method. In order to improve the convergence rate of the proposed multigrid method, an improved dual iteration is proposed as its smoother. Furthermore, we apply the proposed method to the anisotropic ROF model and the anisotropic LLT model. We also give the local Fourier analysis (LFAs) of the Chambolle's dual iterations and a modified smoother for solving these two models, respectively. Numerical results illustrate the efficiency of the proposed method and indicate that such a multigrid method is more suitable to deal with large-sized images.
The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant fe...
详细信息
The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix. Second the dual algorithm as first described by Adler et al., is the same as the extended primal algorithm applied to the dual.
First, the concepts of fuzzy valuation convex (or concave) function and fuzzy convex-geometric-programming problem are based on a fuzzy valuation set in this paper. Secondly, fuzzy posynomial geometric programming and...
详细信息
First, the concepts of fuzzy valuation convex (or concave) function and fuzzy convex-geometric-programming problem are based on a fuzzy valuation set in this paper. Secondly, fuzzy posynomial geometric programming and its dual-form properties concerned are discussed by means of a fuzzy geometric inequality and of a fuzzy dual theory. Lastly, direct and dual algorithms of fuzzy posynomial geometric programming are respectively deduced by the aid of a fuzzy fixed-point theorem and the notion of α, β-cut.
The iterative methods by Ben-Israel and others for computing the Moore-Penrose inverse of a matrix are examined. Ill conditioned test matrices are inverted by the methods and some difficulties are found out. The itera...
详细信息
The iterative methods by Ben-Israel and others for computing the Moore-Penrose inverse of a matrix are examined. Ill conditioned test matrices are inverted by the methods and some difficulties are found out. The iterative methods do not seem superior to direct ones.
This paper focuses on the study of rescaling Lagrangians for solving nonconvex semidefinite programming problems. The rescaling nonlinear Lagrangians are generated by Lowner operators associated with convex real-value...
详细信息
This paper focuses on the study of rescaling Lagrangians for solving nonconvex semidefinite programming problems. The rescaling nonlinear Lagrangians are generated by Lowner operators associated with convex real-valued functions. A set of conditions on the convex real-valued functions is proposed to guarantee the convergence of nonlinear rescaling Lagrangian algorithms. These conditions are satisfied by well-known nonlinear Lagrangians appeared in the literature. The convergence theorem shows that, under the second-order sufficient conditions with sigma-term and the strict constraint nondegeneracy condition, the nonlinear rescaling Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter. Compared to the analysis in the nonlinear rescaling Lagrangian method for nonlinear programming, we have to deal with the sigma term in the convergence analysis.
A critical challenge in image restoration is the presence of various types of noise. Meanwhile, noise detection is a crucial step in mixed noise removal. This paper tackles the challenge of restoring images corrupted ...
详细信息
A critical challenge in image restoration is the presence of various types of noise. Meanwhile, noise detection is a crucial step in mixed noise removal. This paper tackles the challenge of restoring images corrupted by a mixture of additive Gaussian and multiplicative Gamma noise. In the proposed method, we integrate the noise detection process into a variational model using a dual formulation of a maximum a posteriori (MAP) estimator. The variational model consists of a novel adaptive fidelity term and a plugin-and-play regularization term. The fidelity term contains an adaptive weight that can automatically detect the noise types, levels, and pollution ways for each pixel. There is flexibility in choosing a plugin-and-play regularization term. For example, we can use a model-based regularizer or a deep learning-based regularizer. In addition, we present a splitting algorithm to minimize the proposed cost functional. This splitting technique enables us to transfer a mixed noise removing problem to several subproblems, including noise removal and detection. The noise detection process can be iteratively estimated by the proposed algorithm itself. Therefore, in the numerical experiments, the proposed model outperforms the existing Rudin-Osher-Fatemi (ROF), Aubert-Aujol (AA), BM3D, and deep learning-based single type denoiser. Experimental results show that the proposed model can remove noise more efficiently and better preserve details in images. Compared to the existing best-performing single type denoiser, on average, the improvements of PSNR values range from 0.33 dB to 0.81 dB under noise mixture ratios alpha = 0.4, 0.6.
This paper explores a model for the operation of an ad hoc mobile network. The model incorporates incentives for users to act as transit nodes on multi-hop paths and to be rewarded with their own ability to send traff...
详细信息
This paper explores a model for the operation of an ad hoc mobile network. The model incorporates incentives for users to act as transit nodes on multi-hop paths and to be rewarded with their own ability to send traffic. The paper explores consequences of the model by means of fluid-level simulations of a network and illustrates the way in which network resources are allocated to users according to their geographical position. (C) 2004 Elsevier B.V. All rights reserved.
In this paper, we extend Householder's [4] generalization of an algorithm of Sebastião e Silva [11] by adding a new elimination rule for defining the sequences which converge to the factors of the given polyn...
详细信息
This paper explores a model for the operation of an ad hoc mobile network. The model incorporates incentives for users to act as transit nodes on multi-hop paths and to be rewarded with their own ability to send traff...
详细信息
This paper explores a model for the operation of an ad hoc mobile network. The model incorporates incentives for users to act as transit nodes on multi-hop paths and to be rewarded with their own ability to send traffic. The paper explores consequences of the model by means of fluid-level simulations of a network and illustrates the way in which network resources are allocated to users according to their geographical position. (C) 2004 Elsevier B.V. All rights reserved.
暂无评论