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A Simple New algorithm for Quadratic Programming with Applications in Statistics

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2013年第5期42卷 1126-1139页

作者： Meyer, Mary C. Colorado State Univ Dept Stat Ft Collins CO 80523 USA

Problems involving estimation and inference under linear inequality constraints arise often in statistical modeling. In this article, we propose an algorithm to solve the quadratic programming problem of minimizing for positive definite Q, where is constrained to be in a closed polyhedral convex cone , and the m x n matrix is not necessarily full row rank. The three-step algorithm is intuitive and easy to code. Code is provided in the R programming language.

关键词： Cone projection Constrained parameter estimation dual algorithm Inequality constraints Polar cone Primal-dual methods Restricted least squares Shape-restricted regression

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Nonlinear multigrid method for solving the anisotropic image denoising models

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NUMERICAL algorithmS 2013年第2期63卷 291-315页

作者： Zhang, Jun Yang, Yu-Fei Hunan Univ Coll Math & Econometr Changsha 410082 Hunan Peoples R China Changsha Univ Dept Informat & Comp Sci Changsha 410003 Hunan Peoples R China

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.

关键词： Image denoising dual algorithm Anisotropic ROF model Anisotropic LLT model Local Fourier analysis Nonlinear multigrid method

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An improved region-based model with local statistical features for image segmentation

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PATTERN RECOGNITION 2012年第4期45卷 1578-1590页

作者： Ge, Qi Xiao, Liang Zhang, Jun Wei, Zhi Hui Nanjing Univ Sci & Technol Sch Comp Nanjing 210094 Jiangsu Peoples R China Nanjing Univ Sci & Technol Sch Sci Nanjing 210094 Jiangsu Peoples R China

In this paper, we propose a new region-based active contour model (ACM) for image segmentation. In particular, this model utilizes an improved region fitting term to partition the regions of interests in images depending on the local statistics regarding the intensity and the magnitude of gradient in the neighborhood of a contour. By this improved region fitting term, images with noise, intensity non-uniformity, and low-contrast boundaries can be well segmented. Integrated with the duality theory and the anisotropic diffusion process based on structure tensor, a new regularization term is defined through the duality formulation to penalize the length of active contour. By this new regularization term, the structural information of images is utilized to improve the ability of capturing the geometric features such as corners and cusps. From a numerical point of view, we minimize the energy function of our model by an efficient dual algorithm, which avoids the instability and the non-differentiability of traditional numerical solutions, e.g. the gradient descent method. Experiments on medical and natural images demonstrate the advantages of the proposed model over other segmentation models in terms of both efficiency and accuracy. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Active contour model Image segmentation Improved regularization term Structure tensor Local statistics dual algorithm

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Joint Power Allocation for DF MIMO Relay Links with Hybrid Power Constraints

Joint Power Allocation for DF MIMO Relay Links with Hybrid P...

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8th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM)

作者： Lu, Feng Liu, Chen Fu, Youhua Zhao, Hua-An Southeast Univ Sch Informat Sci & Engn Nanjing 210096 Jiangsu Peoples R China Nanjing Univ Posts & Telecommunicat Sch Elect Sci & Engn Nanjing Peoples R China Kumamoto Univ Dept Comp Sci & Elect Engn Kumamoto 8608555 Japan

ISBN: (纸本)9781612846835;9781612846828

This paper deals with joint power allocation (PA) for decode-and-forward (DF) two-hop MIMO relay links with hybrid power constraints. In order to maximize the instantaneous information rate of each hop, we propose an optimal PA scheme via a primal-dual algorithm. Then, we jointly allocate the power between the source and the relay to improve the power efficiency further. The simulations will validate the proposed scheme and show that, compared with the traditional uniform PA, our scheme outperforms the counterpart.

关键词： relay decode-and-forward power allocation hybrid power constraints dual algorithm

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A Hierarchical Matrix Inversion algorithm for Vectorless Power Grid Verification

A Hierarchical Matrix Inversion Algorithm for Vectorless Pow...

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IEEE and ACM International Conference on Computer-Aided Design

作者： Xiong, Xuanxing Wang, Jia IIT Dept Elect & Comp Engn Chicago IL 60616 USA

ISBN: (纸本)9781424481927

Vectorless power grid verification is a powerful technique to validate the robustness of the on-chip power distribution network for all possible current waveforms. Formulated and solved as linear programming problems, vectorless power grid verification demands intensive computational power due to the large number of nodes in modern power grids. Previous work showed that the performance bottleneck of this powerful technique is within the sub-problem of power grid analysis, which essentially computes the inverse of the sparse but large power grid matrix. In this paper, we propose a hierarchical matrix inversion algorithm to compute the rows of the inverse efficiently by exploiting the structure of the power grid. The proposed algorithm is integrated with a previous dual algorithm addressing an orthogonal sub-problem for vectorless power grid verification. Results show that the proposed hierarchical algorithm accelerates the matrix inversion significantly, and thus makes the overall vectorless power grid verification efficient.

关键词： current waveforms dual algorithm hierarchical matrix inversion algorithm integrated circuit design linear programming linear programming problems on-chip power distribution network orthogonal sub-problem power grid analysis power grid matrix power grids power supply circuits vectorless power grid verification

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The dual algorithm based on a class of nonlinear Lagrangians for nonlinear programming

The dual algorithm based on a class of nonlinear Lagrangians...

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6th World Congress on Intelligent Control and Automation

作者： Ren, Yong-Hong Zhang, Li-Wei Dalian Univ Technol Dept Appl Math Dalian Liaoning Provin Peoples R China

ISBN: (纸本)1424403316

This paper studies the properties of a class of nonlinear Lagrangians for nonlinear programming with inequality constraints. It's shown that under a set of conditions this class of Lagrange algorithm is locally convergent when the penalty parameter is larger than a threshold. An error bound estimate of the solution, depending on the penalty, is also established. The paper also discusses the properties of the dual function associated with the proposed nonlinear Lagrangians. Finally, the dual algorithm corresponding to the proposed nonlinear Lagrangians is developed and used to solve some numerical examples by using the nonlinear Lagrangians in the literature. Numerical results suggest that the dual algorithm is effective for solving nonlinear programming.

关键词： nonlinear programming nonlinear Lagrangian dual function dual algorithm

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Log-Sigmoid nonlinear Lagrange method for nonlinear optimization problems over second-order cones

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2009年第1期229卷 129-144页

作者： Gu, Jian Zhang, Liwei Xiao, Xiantao Dalian Univ Technol Dept Appl Math Dalian 116024 Peoples R China

This paper analyzes the rate of local convergence of the Log-Sigmoid nonlinear Lagrange method for nonconvex nonlinear second-order cone programming. Under the componentwise strict complementarity condition, the constraint nondegeneracy condition and the second-order sufficient condition, we show that the sequence of iteration points generated by the proposed method locally converges to a local solution when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter. Finally, we report numerical results to show the efficiency of the method. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Log-Sigmoid function Nonlinear Lagrangian method Nonlinear second-order cone programming dual algorithm Rate of convergence

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A dual algorithm FOR MINIMAX PROBLEMS

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2005年第1-2期17卷 401-418页

作者： He, Suxiang Wuhan Univ Technol Sch Sci Wuhan 430070 Peoples R China

In this paper, a dual algorithm, based on a smoothing function of Bertsekas (1982), is established for solving unconstrained minimax problems. It is proven that a sequence of points, generated by solving a sequence of unconstrained minimizers of the smoothing function with changing parameter t, converges with Q-superlinear rate to a Kuhn-Tucker point locally under some mild conditions. The relationship between the condition number of the Hessian matrix of the smoothing function and the parameter is studied, which also validates the convergence theory. Finally the numerical results are reported to show the effectiveness of this algorithm.

关键词： Minimax problem smoothing function dual algorithm condition number Q-superlinear rate

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A class of nonlinear Lagrangians: Theory and algorithm

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2008年第3期25卷 327-371页

作者： Zhang, Li-Wei Ren, Yong-Hong Wu, Yue Xiao, Xian-Tao Dalian Univ Technol Dept Appl Math Dalian 116024 Peoples R China Liaoning Normal Univ Sch Math Dalian 116029 Peoples R China Univ Southampton Sch Management Southampton SO17 1BJ Hants England

This paper establishes a theory framework of a class of nonlinear Lagrangians for solving nonlinear programming problems with inequality constraints. A set of conditions are proposed to guarantee the convergence of nonlinear Lagrangian algorithms, to analyze condition numbers of nonlinear Lagrangian Hessians as well as to develop the dual approaches. These conditions are satisfied by well-known nonlinear Lagrangians appearing in literature. The convergence theorem shows that the dual algorithm based on any nonlinear Lagrangian in the class is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions and the error bound solution, depending on the penalty parameter, is also established. The paper also develops the dual problems based on the proposed nonlinear Lagrangians, and the related duality theorem and saddle point theorem are demonstrated. Furthermore, it is shown that the condition numbers of Lagrangian Hessians at optimal solutions are proportional to the controlling penalty parameters. We report some numerical results obtained by using nonlinear Lagrangians.

关键词： nonconvex optimization nonlinear Lagrangian dual algorithm condition number dual function

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Average Behavior of Greedy algorithms for the Minimization Knapsack Problem: General Coefficient Distributions

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2008年第9期48卷 1521-1535页

作者： Diubin, G. N. Korbut, A. A. Russian Acad Sci St Petersburg Inst Econ & Math St Petersburg 191187 Russia

For the minimization knapsack problem with Boolean variables, primal and dual greedy algorithms are formally described. Their relations to the corresponding algorithms for the maximization knapsack problem are shown. The average behavior of primal and dual algorithms for the minimization problem is analyzed. It is assumed that the coefficients of the objective function and the constraint are independent identically distributed random variables on [ 0, 1] with an arbitrary distribution having a density and that the right-hand side d is deterministic and proportional to the number of variables (i.e., d = mu n). A condition on mu is found under which the primal and dual greedy algorithms have an asymptotic error of t

关键词： knapsack problem greedy algorithms dual algorithm average behavior arbitrary coefficient distributions

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