Synopses & Reviews
This book is a collection of papers presented at the Large Scale Optimization Conference held at the Center for Applied Optimization, University of Florida, Gainesville, in February, 1993. Accurate modelling of scientific problems often leads to the formulation of large-scale optimization problems involving thousands of continuous and/or discrete variables. As a consequence of new algorithmic developments and of the increased power of computers, large-scale optimization has seen a dramatic increase in activities in the past decade. Topics include large-scale linear, nonlinear and stochastic programming, network optimization, decomposition methods, methods for optimal control, nonsmooth equations, integer programming, and software development. In addition, applications are included in location theory, structural mechanics, molecular configuration, transportation, multitarget tracking, and database design. The book is a valuable source of information for faculty students and researchers in mathematical programming and related fields.
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
Preface. Restarting Strategies for the DQA Algorithm; A.J. Berger, J.M. Mulvey, A. Ruszczynski. Mathematical Equivalence of the Auction Algorithm for Assignment and the epsilon-Relaxation (Preflow-Push) Method for Min Cost Flow; D.P. Bertsekas. Preliminary Computational Experience with Modified Log-Barrier Functions for Large-Scale Nonlinear Programming; M.G. Breitfeld, D.F. Shanno. A New Stochastic/Perturbation Method for Large-Scale Global Optimization and its Application to Water Cluster Problems; R.H. Byrd, T. Derby, E. Eskow, K.P.B. Oldenkamp, R.B. Schnabel. Improving the Decomposition of Partially Separable Functions in the Context of Large-Scale Optimization: a First Approach; A.R. Conn, N. Gould, P.L. Toint. Gradient-Related Constrained Minimization Algorithms in Function Spaces: Convergence Properties and Computational Implications; J.C. Dunn. Some Reformulations and Applications of the Alternating Direction Method of Multipliers; J. Eckstein, M. Fukushima. Experience with a Primal Presolve Algorithm; R. Fourer, D.M. Gay. A Trust Region Method for Constrained Nonsmooth Equations; S.A. Gabriel, Jong-Shi Pang. On the Complexity of a Column Generation Algorithm for Convex or Quasiconvex Feasibility Problems; J.-L. Goffin, Zhi-Quan Luo, Yinyu Ye. Identificiation of the Support of Nonsmoothness; C.T. Kelley. On Very Large Scale Assignment Problems; Y. Lee, J.B. Orlin. Numerical Solution of Parabolic State Constrained Control Problems Using SQP and Interior-Point-Methods; F. Leibfritz, E.W. Sachs. A Global Optimization Method for Weber's Problem with Attraction and Repulsion; C.D. Maranas, C.A. Floudas. Large-Scale Diversity Minimization via Parallel Genetic Algorithms; R.R. Meyer, J. Yackel. A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization; S.G. Nash, R. Polyak, A. Sofer. A Numerical Study of Some Data Association Problems Arising in Multitarget Tracking; A.B. Poore, N. Rijavec. Identifying the Optimal Face of a Network Linear Program with a Globally Convergent Interior Point Method; M.G.C. Resende, T. Tsuchiya, G. Veiga. Solution of Large Scale Stochastic Programs with Stochastic Decomposition Algorithms; S. Sen, J.Mai, J.L. Higle. A Simple, Quadratically Convergent Interior Point Algorithm for Linear Programming and Convex Quadratic Programming; A.L. Tits, J.L. Zhou. On Two Algorithms for Nonconvex Nonsmooth Optimization Problems in Structural Mechanics; M.Ap. Tzaferopoulos, E.S. Mistakidis, C.D. Bisbos, P.D. Panagiotopoulos.