COMPUTATIONAL SCIENCE SIMULATION TRACK SOME PRACTICAL OPTIMIZATION METHODS

Geoffrey Fox

Syracuse University
Northeast Parallel Architectures Center
111 College Place
Syracuse, New York 13244-4100
(315) 443-2163
gcf@npac.syr.edu
http://www.npac.syr.edu

• Abstract of Optimization Presentation
• Optimization Examples---I
• Examples -- II
• Examples -- III
• Examples IV -- Linear Programming
• Optimization Examples -- V
• A Collection of Methods for Optimization
• Optimization Example -- V: Analysis of Experimental Data
• Analysis of Experimental Data (cont.)
• Data Analysis Examples---I
• Data Analysis Examples---II
• The Computational and Numerical Issues
• SSC Scenario---I
• SSC Scenario II
• Uncertainties in SSC Data Analysis
• SSC Data Analysis Problem Statement
• Maximum Likelihood Principle---Example
• Rod Quivering in an Earthquake--II
• Bayes Formula
• Interpretation of Bayes Relation -- I
• Interpretation of Bayes Relation -- II
• Basic Likelihood Formula
• Pictorial View of Maximum Likelihood
• General Maximum Likelihood Method
• Lifetime Example for Maximum Likelihood---I
• Lifetime Example for Maximum Likelihood -- II
• Multiplication of Experiments
• General Maximum Likelihood
• Method
• Method Derived from Likelihood
• Standard Deviation
• Scattering Experiment Example
• Individual Data Points
• Histogrammed Data
• Scattering Experiment--- Minimization
• Formulae
• Errors in
• Example II -- Regression Analysis
• Example III -- Nuclear Decay
• Maximum Likelihood and for Experimental Data Analysis
• When Should You Use and When Maximum Likelihood?
• Least Squares
• Nonlinear Minimization
• Validity of Linearization When Does It Work?
• Nonlinear Minimization That Works!
• Linear Programming
• Convex Regions and Linear Programming
• Matrix Formulation of Linear Programming
• Computational Issues in and Maximum Likelihood
• Matrices in Maximum Likelihood
• Basic Software Structure for Derivative Calculation
• Computational Complexity
• Histograms
• Histogram Formalism I
• Histogram Formalism II
• Errors of Histograms -- I
• Errors of Histograms -- II
• Histograms as Robust Data Exploration
• General Histogram
• Scatterplots
• Possible Projects I---Maximum Likelihood
• Possible Projects II
• Possible Projects II (cont.)
• More Possible Maximum Likelihood Projects
• Projects---Data Exploration
• More Data Exploration Projects