A Computer-Assisted Analysis System for Mathematical Programming Models and Solutions - H J Greenberg

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Résumé :
Welcome to ANALYZE, designed to provide computer assistance for analyzing linear programs and their solutions. Chapter 1 gives an overview of ANALYZE and how to install it. It also describes how to get started and how to obtain further documentation and help on-line. Chapter 2 reviews the forms of linear programming models and describes the syntax of a model. One of the routine, but important, functions of ANALYZE is to enable convenient access to rows and columns in the matrix by conditional delineation. Chapter 3 illustrates simple queries, like DISPLAY, LIST, and PICTURE. This chapter also introduces the SUBMAT command level to define any submatrix by an arbitrary sequence of additions, deletions and reversals. Syntactic explanations and a schema view are also illustrated. Chapter 4 goes through some elementary exercises to demonstrate computer? assisted analysis and introduce additional conventions of the ANALYZE language. Besides simple queries, it demonstrates the INTERPRT command, which automates the analysis process and gives English explanations of results. The last 2 exercises are diagnoses of elementary infeasible instances of a particular model. Chapter 5 progresses to some advanced uses of ANALYZE. The first is blocking to obtain macro views of the model and for finding embedded substructures, like a netform. The second is showing rates of substitution described by the basic equations. Then, the use of the REDUCE and BASIS commands are illustrated for a variety of applications, including solution analysis, infeasibility diagnosis, and redundancy detection.

Sommaire:
1 Overview, Installation, and Help.- 1.1 What you have and how to begin.- 1.2 Modular design.- 1.3 Quick install for DOS environment.- 1.4 Some interactive language conventions.- 1.5 On-line documentation.- 2 Anatomy of a Linear Program.- 2.1 Algebraic form.- 2.2 Model Syntax.- 2.3 Conditional delineation of rows and columns.- 3 Simple Queries.- 3.1 The sign-on and interactive conventions.- 3.2 Basic query commands.- 3.3 Syntax-based explanations.- 3.4 Schema view.- 4 Examples of Analysis.- 4.1 Price interpretation for the LP expert.- 4.2 Automatic interpretation.- 4.3 A case of infeasibility.- 4.4 A case of unboundedness.- 5 Further Examples.- 5.1 Blocking.- 5.2 Rates of substitution.- 5.3 Using the basis.- 5.4 The REDUCE command.- 5.5 The AGGREGAT command.- 6 File Interfaces.- 6.1 Environment controls.- 6.2 Dictionaries, documents, help and keyword files.- 6.3 Execution files.- 6.4 Matrix and packed files.- 6.5 Solution files.- 6.6 Syntax files.- 6.7 Rule files.- 6.8 Submatrix, block, schema and graph files.- 6.9 Setting up an environment for analysis.- 7 Advanced Exercises.- 7.1 A forestry model.- 7.2 A REDUCE anomaly.- 7.3 Assisting model management.- 8 Utilities.- 8.1 HPAGER.- 8.2 LPRENAME.- 8.3 FORTREF.- 9 Algorithms and Heuristics.- 9.1 Discourse formation.- 9.2 Path tracing.- 9.3 Basis rearrangement.- 9.4 Rates of substitution.- 9.5 Redundancy test.- 9.6 Successive bound reduction.- 9.7 Logical implication tests.- 10 More Views.- 10.1 Block plots.- 10.2 Step plots.- 10.3 Table formations and displays.- 10.4 Graphs of linear programs.- 10.5 Schema equations.- 11 Rulebase Development.- 11.1 Basic concepts and tools.- 11.2 Rule file commands.- 11.3 Simple examples.- 11.4 Price interpretation.- 11.5 Testing new rule files.- 12 Using the Modules.- 12.1 Setup for an alternative computing environment.- 12.2 FLIP.- 12.3 GETMAT.- 12.4 VIEWS.- Appendix A: Error Messages.- Appendix B: The ANALYZE Library.