Multiscale Optimization Methods and Applications

Multiscale Optimization in VLSI Physical Design Automation

Tony F. Chan, Jason Cong, Joseph R. Shinnerl, Kenton Sze, Min Xie,

Yan Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

A Distributed Method for Solving Semidefinite Programs

Arising from Ad Hoc Wireless Sensor Network Localization

Pratik Biswas, Yinyu Ye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Optimization Algorithms for Sparse Representations and

Applications

Pando G. Georgiev, Fabian Theis, Andrzej Cichocki . . . . . . . . . . . . . . . . . . 85

A Unified Framework for Modeling and Solving Combinatorial

Optimization Problems: A Tutorial

Gary A. Kochenberger, Fred Glover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Global Convergence of a Non-monotone Trust-Region Filter

Algorithm for Nonlinear Programming

Nicholas I. M. Gould, Philippe L. Toint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Factors Affecting the Performance of Optimization-based

Multigrid Methods

Robert Michael Lewis, Stephen G. Nash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

A Local Relaxation Method for Nonlinear Facility Location

Problems

Walter Murray, Uday V. Shanbhag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Fluence Map Optimization in IMRT Cancer Treatment

Planning and A Geometric Approach

Yin Zhang, Michael Merritt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

ii Contents

Panoramic Image Processing using Non-Commutative

Harmonic Analysis Part I: Investigation

Amal Aafif, Robert Boyer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

Generating Geometric Models through Self-Organizing Maps

Jung-ha An, Yunmei Chen, Myron N. Chang, David Wilson, Edward

Geiser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

Self-similar Solution of Unsteady Mixed Convection Flow on

a Rotating Cone in a Rotating Fluid

Devarapu Anilkumar, Satyajit Roy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

Homogenization of a Nonlinear Elliptic Boundary Value

Problem Modelling Galvanic Interactions on a Heterogeneous

Surface

Y.S. Bhat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

A Simple Mathematical Approach for Determining

Intersection of Quadratic Surfaces

Ken Chan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

Applications of Shape-Distance Metric to Clustering

Shape-Databases

Shantanu H. Joshi, Anuj Srivastava . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

Accurately Computing the Shape of Sandpiles

Christopher M. Kuster, Pierre A. Gremaud . . . . . . . . . . . . . . . . . . . . . . . . . 305

Shape Optimization of Transfer Functions

Jiawang Nie, James W. Demmel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

Achieving Wide Field of View Using Double-Mirror

Catadioptric Sensors

Ronald Perline, Emek K¨ose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

Darcy Flow, Multigrid, and Upscaling

James M. Rath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

Iterated Adaptive Regularization for the Operator Equations

of the First Kind

Yanfei Wang, Qinghua Ma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

Recover Multi-tensor Structure from HARD MRI Under

Bi-Gaussian Assumption

Qingguo Zeng, Yunmei Chen, Weihong Guo, Yijun Liu . . . . . . . . . . . . . . . 379

PACBB: A Projected Adaptive Cyclic Barzilai-Borwein

Method for Box Constrained Optimization

Hongchao Zhang, William W. Hager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

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Nonrigid Correspondence and Classification of Curves Based

on More Desirable Properties

Xiqiang Zheng, Yunmei Chen, David Groisser, David Wilson . . . . . . . . . . 393