Large Scale Optimization: State of the Art

✍ Scribed by Adam J. Berger, John M. Mulvey, Andrzej Ruszczyński (auth.), W. W. Hager, D. W. Hearn, P. M. Pardalos (eds.)

• Publisher: Springer US
• Year: 1994
• Tongue: English
• Leaves: 470
• Edition: 1
• Category: Library

✦ Synopsis

On February 15-17, 1993, a conference on Large Scale Optimization, hosted by the Center for Applied Optimization, was held at the University of Florida. The con­ ference was supported by the National Science Foundation, the U. S. Army Research Office, and the University of Florida, with endorsements from SIAM, MPS, ORSA and IMACS. Forty one invited speakers presented papers on mathematical program­ ming and optimal control topics with an emphasis on algorithm development, real world applications and numerical results. Participants from Canada, Japan, Sweden, The Netherlands, Germany, Belgium, Greece, and Denmark gave the meeting an important international component. At­ tendees also included representatives from IBM, American Airlines, US Air, United Parcel Serice, AT & T Bell Labs, Thinking Machines, Army High Performance Com­ puting Research Center, and Argonne National Laboratory. In addition, the NSF sponsored attendance of thirteen graduate students from universities in the United States and abroad. Accurate modeling of scientific problems often leads to the formulation of large­ scale optimization problems involving thousands of continuous and/or discrete vari­ ables. Large scale optimization has seen a dramatic increase in activities in the past decade. This has been a natural consequence of new algorithmic developments and of the increased power of computers. For example, decomposition ideas proposed by G. Dantzig and P. Wolfe in the 1960's, are now implement able in distributed process­ ing systems, and today many optimization codes have been implemented on parallel machines.

✦ Table of Contents

Front Matter....Pages i-xiv
Restarting Strategies for the DQA Algorithm....Pages 1-25
Mathematical Equivalence of the Auction Algorithm for Assignment and the ∊-Relaxation (Preflow-Push) Method for Min Cost Flow....Pages 26-44
Preliminary Computational Experience with Modified Log-Barrier Functions for Large-Scale Nonlinear Programming....Pages 45-67
A New Stochastic/Perturbation Method for Large-Scale Global Optimization and its Application to Water Cluster Problems....Pages 68-81
Improving the Decomposition of Partially Separable Functions in the Context of Large-Scale Optimization: a First Approach....Pages 82-94
Gradient-Related Constrained Minimization Algorithms in Function Spaces: Convergence Properties and Computational Implications....Pages 95-114
Some Reformulations and Applications of the Alternating Direction Method of Multipliers....Pages 115-134
Experience with a Primal Presolve Algorithm....Pages 135-154
A Trust Region Method for Constrained Nonsmooth Equations....Pages 155-181
On the Complexity of a Column Generation Algorithm for Convex or Quasiconvex Feasibility Problems....Pages 182-191
Identification of the Support of Nonsmoothness....Pages 192-205
On Very Large Scale Assignment Problems....Pages 206-244
Numerical Solution of Parabolic State Constrained Control Problems Using SQP- and Interior-Point-Methods....Pages 245-258
A Global Optimization Method For Weber’s Problem With Attraction And Repulsion....Pages 259-285
Large-Scale Diversity Minimization via Parallel Genetic Algorithms....Pages 294-311
A Numerical Comparison of Barrier and Modified Barrier Methods For Large-Scale Bound-Constrained Optimization....Pages 319-338
A Numerical Study of Some Data Association Problems Arising in Multitarget Tracking....Pages 339-361
Identifying the Optimal Face of a Network Linear Program with a Globally Convergent Interior Point Method....Pages 362-387
Solution of Large Scale Stochastic Programs with Stochastic Decomposition Algorithms....Pages 388-410
A Simple, Quadratically Convergent Interior Point Algorithm for Linear Programming and Convex Quadratic Programming....Pages 411-427
On Two Algorithms for Nonconvex Nonsmooth Optimization Problems in Structural Mechanics....Pages 428-456

✦ Subjects

Real Functions; Mathematical Modeling and Industrial Mathematics; Geometry; Computational Mathematics and Numerical Analysis