Multiscale optimization methods and applications - Hager, William W. (Nonconvex Optimization and Its Applications, 2006)
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. Multiscale Optimization in VLSI Physical Design Automation -- A Distributed Method for Solving Semidefinite Programs Arising from Ad Hoc Wireless Sensor Network Localization -- Optimization Algorithms for Sparse Representations and Applications -- A Unified Framework for Modeling and Solving Combinatorial Optimization Problems: A Tutorial -- Global Convergence of a Non-monotone Trust-Region Filter Algorithm for Nonlinear Programming -- Factors Affecting the Performance of Optimization-based Multigrid Methods -- A Local Relaxation Method for Nonlinear Facility Location Problems -- Fluence Map Optimization in IMRT Cancer Treatment Planning and A Geometric Approach -- Panoramic Image Processing using Non-Commutative Harmonic Analysis Part I: Investigation -- Generating Geometric Models through Self-Organizing Maps -- Self-similar Solution of Unsteady Mixed Convection Flow on a Rotating Cone in a Rotating Fluid -- Homogenization of a Nonlinear Elliptic Boundary Value Problem Modelling Galvanic Interactions on a Heterogeneous Surface -- A Simple Mathematical Approach for Determining Intersection of Quadratic Surfaces -- Applications of Shape-Distance Metric to Clustering Shape-Databases -- Accurately Computing the Shape of Sandpiles -- Shape Optimization of Transfer Functions -- Achieving Wide Field of View Using Double-Mirror Catadioptric Sensors -- Darcy Flow, Multigrid, and Upscaling -- Iterated Adaptive Regularization for the Operator Equations of the First Kind -- Recover Multi-tensor Structure from HARD MRI Under Bi-Gaussian Assumption -- PACBB: A Projected Adaptive Cyclic Barzilai-Borwein Method for Box Constrained Optimization -- Nonrigid Correspondence and Classification of Curves Based on More Desirable Properties.