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32nd Annual International Conference of the IEEE Engineering-in-Medicine-and-Biology-Society (EMBC 10)

作者： Yu, Yeyang Hong, Mingjian Liu, Feng Wang, Hua Crozier, Stuart Univ Queensland Sch Informat Technol & Elect Engn Brisbane Qld Australia Chongqing Univ Sch Software Engn Chongqing 630044 Peoples R China

ISBN: (纸本)9781424441242

Compressed sensing (CS) theory has been recently applied in Magnetic Resonance Imaging (MRI) to accelerate the overall imaging process. In the CS implementation, various algorithms have been used to solve the nonlinear equation system for better image quality and reconstruction speed. However, there are no explicit criteria for an optimal CS algorithm selection in the practical MRI application. A systematic and comparative study of those commonly used algorithms is therefore essential for the implementation of CS in MRI. In this work, three typical algorithms, namely, the Gradient Projection For Sparse Reconstruction (GPSR) algorithm, interior-point algorithm (l(1)_ls), and the Stagewise Orthogonal Matching Pursuit (StOMP) algorithm are compared and investigated in three different imaging scenarios, brain, angiogram and phantom imaging. The algorithms' performances are characterized in terms of image quality and reconstruction speed. The theoretical results show that the performance of the CS algorithms is case sensitive;overall, the StOMP algorithm offers the best solution in imaging quality, while the GPSR algorithm is the most efficient one among the three methods. In the next step, the algorithm performances and characteristics will be experimentally explored. It is hoped that this research will further support the applications of CS in MRI.

关键词： GPSR algorithm StOMP algorithm biomedical MRI biomedical MRI compressed sensing implementation data compression gradient projection for sparse reconstruction image quality image reconstruction image reconstruction speed interior-point algorithm iterative methods magnetic resonance imaging medical image processing nonlinear algorithms nonlinear equation system nonlinear equations stagewise orthogonal matching pursuit

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An interior-point trust-region polynomial algorithm for convex quadratic minimization subject to general convex constraints

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OPTIMIZATION METHODS & SOFTWARE 2008年第2期23卷 251-258页

作者： Lu, Ye Yuan, Ya-Xiang MIT Ctr Operat Res Cambridge MA 02139 USA Chinese Acad Sci Acad Math & Syst Sci Inst Math LSECICMSEC Beijing 100080 Peoples R China

An interior-point trust-region algorithm is proposed for minimization of a convex quadratic objective function over a general convex set. The algorithm uses a trust-region model to ensure descent on a suitable merit f... 详细信息

关键词： interior-point algorithm self-concordant barrier trust-region subproblem

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A High-Order Dikin-Type algorithm for P＊（k）-LCPs in a Wide Neighborhood of the Central Path

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Journal of Mathematical Research and Exposition 2009年第1期29卷 76-84页

作者： GONG Xiao Yu ZHANG Ming Wang College of Science Maoming University Guangdong 525000 China College of Science Three Gorges University Hubei 443002 China

Based on the idea of Dikin-type primal-dual affine scaling method for linear program-ming,we describe a high-order Dikin-type algorithm for P_*(κ)-matrix linear complementarity problem in a wide neighborhood of the central path,and its polynomial-time complexity bound is ***,two numerical experiments are provided to show the effectiveness of the proposed algorithms.

关键词： complementarity problem high-order affine scaling polynomial-time complexity interior-point algorithm P＊（κ）-matrix.

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A note on the local convergence of a predictor-corrector interior-point algorithm for the semidefinite linear complementarity problem based on the Alizadeh-Haeberly-Overton search direction

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SIAM JOURNAL ON OPTIMIZATION 2005年第4期15卷 1147-1154页

作者： Lu, ZS Monteiro, RDC Georgia Tech Sch ISyE Atlanta GA 30332 USA

This note points out an error in the local quadratic convergence proof of the predictor-corrector interior-point algorithm for solving the semidefinite linear complementarity problem based on the Alizadeh-Haeberly-Overton search direction presented in [M. Kojima, M. Shida, and S. Shindoh, SIAM J. Optim., 9 (1999), pp. 444-465]. Their algorithm is slightly modified and the local quadratic convergence of the resulting method is established.

关键词： semidefinite linear complementarity problem semidefinite programming interior-point algorithm predictor-corrector algorithm local quadratic convergence

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求解P*（κ）阵线性互补问题的宽邻域Dikin型高阶内点算法（英文）

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Journal of Mathematical Research with Applications 2009年第1期 76-84页

作者：龚小玉张名望 College of Science Maoming University College of Science Three Gorges University

Based on the idea of Dikin-type primal-dual affine scaling method for linear program-ming,we describe a high-order Dikin-type algorithm for P（κ）-matrix linear complementarity problem in a wide neighborhood of the central path,and its polynomial-time complexity bound is ***,two numerical experiments are provided to show the effectiveness of the proposed algorithms.

关键词： complementarity problem high-order affine scaling polynomial-time complexity interior-point algorithm P*(κ)-matrix

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On the probabilistic complexity of finding an approximate solution for linear programming

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JOURNAL OF COMPLEXITY 2008年第2期24卷 214-227页

作者： Ji, Jun Potra, Florian A. Univ Maryland Dept Math & Stat Baltimore MD 21250 USA Kennesaw State Univ Dept Math Kennesaw GA 30144 USA

We consider the problem of finding an c-optimal solution of a standard linear program with real data, i.e., of finding a feasible point at which the objective function value differs by at most epsilon from the optimal value. In the worst-case scenario the best complexity result to date guarantees that such a point is obtained in at most O(root n vertical bar ln epsilon vertical bar) steps of an interior-point method. We show that the expected value of the number of steps required to obtain an epsilon-optimal solution for a probabilistic linear programming model is at most O(min {n(1.5), m root n ln(n)}) + log(2)(vertical bar ln epsilon vertical bar). (C) 2007 Elsevier Inc. All rights reserved.

关键词： linear programming interior-point algorithm average complexity approximate solution

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Corrector-predictor methods for monotone linear complementarity problems in a wide neighborhood of the central path

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MATHEMATICAL PROGRAMMING 2008年第1-2期111卷 243-272页

作者： Potra, Florian A. Univ Maryland Baltimore Cty Dept Math & Stat Baltimore MD 21250 USA

Two corrector - predictor interior point algorithms are proposed for solving monotone linear complementarity problems. The algorithms produce a sequence of iterates in the N-infinity(-) neighborhood of the central path. The first algorithm uses line search schemes requiring the solution of higher order polynomial equations in one variable, while the line search procedures of the second algorithm can be implemented in O(m n(1+alpha)) arithmetic operations, where n is the dimension of the problems, alpha is an element of (0, 1] is a constant, and m is the maximum order of the predictor and the corrector. If m = Omega(log n) then both algorithms have O(root nL) iteration complexity. They are superlinearly convergent even for degenerate problems.

关键词： linear complementarity problem interior-point algorithm large neighborhood superlinear convergence

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Corrector-predictor methods for monotone linear complementarity problems in a wide neighborhood of the central path

Corrector-predictor methods for monotone linear complementar...

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5th Brazilian Workshop on Continuous Optimization

作者： Potra, Florian A. Univ Maryland Baltimore Cty Dept Math & Stat Baltimore MD 21250 USA

关键词： linear complementarity problem interior-point algorithm large neighborhood superlinear convergence

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Mesh shape-quality optimization using the inverse mean-ratio metric

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MATHEMATICAL PROGRAMMING 2007年第3期110卷 561-590页

作者： Munson, Todd Argonne Natl Lab Div Math & Comp Sci Argonne IL 60439 USA

Meshes containing elements with bad quality can result in poorly conditioned systems of equations that must be solved when using a discretization method, such as the finite-element method, for solving a partial differential equation. Moreover, such meshes can lead to poor accuracy in the approximate solution computed. In this paper, we present a nonlinear fractional program that relocates the vertex coordinates of a given mesh to optimize the average element shape quality as measured by the inverse mean-ratio metric. To solve the resulting large-scale optimization problems, we apply an efficient implementation of an inexact Newton algorithm that uses the conjugate gradient method with a block Jacobi preconditioner to compute the direction. We show that the block Jacobi preconditioner is positive definite by proving a general theorem concerning the convexity of fractional functions, applying this result to components of the inverse mean-ratio metric, and showing that each block in the preconditioner is invertible. Numerical results obtained with this special-purpose code on several test meshes are presented and used to quantify the impact on solution time and memory requirements of using a modeling language and general-purpose algorithm to solve these problems.

关键词： interior-point algorithm CONDITION NUMBER JACOBIAN MATRIX IMPROVEMENT QUANTITIES FRAMEWORK NORM condition number Positive definite modelling languages Inverse Meshes memory requirements Frameworks Medical Subject Headings Mesh Metric conjugate gradient methods

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A superlinearly convergent predictor-corrector method for degenerate LCP in a wide neighborhood of the central path with O(√nL)-iteration complexity (vol 100, pg 317, 2004)

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MATHEMATICAL PROGRAMMING 2007年第2期110卷 443-444页

作者： Potra, Florian A. Univ Maryland Baltimore Cty Baltimore MD 21228 USA

We correct an error in algorithm 2 from [1].

关键词： linear complementarity problem interior-point algorithm large neighborhood superlinear convergence

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