Multiscale Optimization Methods and Applications

Tony F. Chan, Jason Cong, Joseph R. Shinnerl (auth.), William W. Hager, Shu-Jen Huang, Panos M. Pardalos, Oleg A. Prokopyev (eds.)0-387-29549-6, 0-387-29550-X, 978-0387-29549-7

As optimization researchers tackle larger and larger problems, scale interactions play an increasingly important role. One general strategy for dealing with a large or difficult problem is to partition it into smaller ones, which are hopefully much easier to solve, and then work backwards towards the solution of original problem, using a solution from a previous level as a starting guess at the next level. This volume contains 22 chapters highlighting some recent research. The topics of the chapters selected for this volume are focused on the development of new solution methodologies, including general multilevel solution techniques, for tackling difficult, large-scale optimization problems that arise in science and industry. Applications presented in the book include but are not limited to the circuit placement problem in VLSI design, a wireless sensor location problem, optimal dosages in the treatment of cancer by radiation therapy, and facility location.

Audience:
Multiscale Optimization Methods and Applications is intended for graduate students and researchers in optimization, computer science, and engineering.

Table of contents :
Multiscale Optimization in VLSI Physical Design Automation….Pages 1-67
A Distributed Method for Solving Semidefinite Programs Arising from Ad Hoc Wireless Sensor Network Localization….Pages 69-84
Optimization Algorithms for Sparse Representations and Applications….Pages 85-99
A Unified Framework for Modeling and Solving Combinatorial Optimization Problems: A Tutorial….Pages 101-124
Global Convergence of a Non-monotone Trust-Region Filter Algorithm for Nonlinear Programming….Pages 125-150
Factors Affecting the Performance of Optimization-based Multigrid Methods….Pages 151-172
A Local Relaxation Method for Nonlinear Facility Location Problems….Pages 173-204
Fluence Map Optimization in IMRT Cancer Treatment Planning and A Geometric Approach….Pages 205-227
Panoramic Image Processing using Non-Commutative Harmonic Analysis Part I: Investigation….Pages 229-239
Generating Geometric Models through Self-Organizing Maps….Pages 241-250
Self-similar Solution of Unsteady Mixed Convection Flow on a Rotating Cone in a Rotating Fluid….Pages 251-261
Homogenization of a Nonlinear Elliptic Boundary Value Problem Modelling Galvanic Interactions on a Heterogeneous Surface….Pages 263-270
A Simple Mathematical Approach for Determining Intersection of Quadratic Surfaces….Pages 271-298
Applications of Shape-Distance Metric to Clustering Shape-Databases….Pages 299-304
Accurately Computing the Shape of Sandpiles….Pages 305-312
Shape Optimization of Transfer Functions….Pages 313-326
Achieving Wide Field of View Using Double-Mirror Catadioptric Sensors….Pages 327-335
Darcy Flow, Multigrid, and Upscaling….Pages 337-366
Iterated Adaptive Regularization for the Operator Equations of the First Kind….Pages 367-377
Recover Multi-tensor Structure from HARD MRI Under Bi-Gaussian Assumption….Pages 379-386
PACBB: A Projected Adaptive Cyclic Barzilai-Borwein Method for Box Constrained Optimization….Pages 387-392
Nonrigid Correspondence and Classification of Curves Based on More Desirable Properties….Pages 393-407