Front Matter

• Notices
• Programming Interface Information
• Trademarks and Service Marks
• About this Book
• How to Use This Book
• General Information about This Book
• Finding a Subroutine Description
• Finding the Names of Related Publications
• Looking Up a Reference
• Understanding the Terminology
• Interpreting the Abbreviated Names
• Interpreting the Fonts
• Interpreting the Special Characters, Symbols, and Expressions
• Interpreting the Subroutine Descriptions

Guide Information

• Introducing the Optimization Library
• What Is the Optimization Library?
• A Range of Operating Environments
• Support for Several Areas of Mathematical Programming
• Before Designing Your Application
• Compatibility
• Product Requirements
• Storage
• Processing Your Program
• Thread-Safety
• Compiling, Linking, and Executing your Application with the Optimization Library
• Associating File Names with FORTRAN Unit Numbers
• Handling Problems

Application Design Principles

• OSL Terms and Concepts
• Mathematical Programming and OSL
• Linear Programming
• Mixed-Integer Programming
• Quadratic Programming
• Quadratic Programming: Parametrics
• Performance Tuning
• Applications versus Models
• OSL Data Structures
• Problem Matrix
• Sparse Matrices   Storage of:  by:  Indices,   Columns,  or  Rows
• Matrix Blocks  and  Vector Blocks
• Passing Models to OSL
• Controlling OSL
• Control Variables | Bit Masks | Getting and Setting Values
• Customizing Messages
• User Exit Subroutines
• Storage Allocation
• What Is DSPACE?
• How DSPACE Is Allocated
• Selection Lists
• Diagrams of Sample Application Programs
• Strategies for Optimization Problems
• Linear Programming
• Simplex (EKKSSLV)
• Interior-Point Barrier (EKKBSLV)
• Network Programming (EKKNSLV)
• Mixed-Integer Programming (EKKMPRE and EKKMSLV)
• Branch-and-Bound
• Preprocessing the Problem with EKKMPRE
• Implementing the Data Structures
• Choosing a Node
• Branching
• Supernode Processing
• Related Control Variables
• Quadratic Programming (EKKQSLV and EKKQPAR)
• Related Control Variables
• Post Solution Analysis of LP Problems
• LP Sensitivity Analysis
• Sensitivity to the Objective Function (EKKSOBJ)
• Sensitivity to Bounds (EKKSBND)
• LP Parametrics (EKKSPAR)
• Infeasibility Analysis (EKKNFES)
• Performance Considerations
• Crash (EKKCRSH)
• Presolve and Postsolve (EKKPRSL and EKKPSSL)
• Scale (EKKSCAL)
• Linear Programming Decomposition (EKKLPDC)
• Using EKKLPDC
• General Performance Considerations
• Passing Your Model Using Library Data Structures
• Linear Programming Model Data (EKKLMDL)
• A Sample Problem
• A Sample Problem Involving Basis Data
• Mixed-Integer Programming Data (EKKIMDL)
• Simplex Parametric Programming Data (EKKPMDL)
• Network Programming Data (EKKNMDL)
• Quadratic Programming Data (EKKQMDL)
• Defining an "Empty" Linear Programming Model (EKKEMDL)
• Passing Your Model Using Mathematical Programming System (MPS) Format
• Using MPS Format
• Types of Records
• Order of Records
• Fixed Format Input
• Free Format Input
• NAME and ENDATA Records
• NAME Indicator Record Format
• ENDATA Indicator Record Format
• Examples
• ROWS Section
• Indicator Record
• Data Record
• Indicator Code
• Example
• COLUMNS Section
• Indicator Record
• Data Record
• Examples
• RHS Section
• Indicator Record
• Data Record
• Example
• RANGES Section
• Indicator Record
• Data Record
• Effect of Range Value on the RHS
• Example
• BOUNDS Section
• Indicator Record
• Data Record
• Bound Types
• Default Bounds
• Example
• Integer Data
• Indicator Records
• General Integer Variables
• Special Ordered Set (SOS)
• Examples
• QSECTION Section
• Order of Records
• Indicator Records
• Data Record
• Example
• Optimization Library Compatibility with MPS Format
• EKKBCDO
• EKKMPS
• EKKBASI
• Indicator Code
• EKKBASO
• Optimization Library Extensions to MPS Format
• Optimization Library Restrictions to MPS Format
• Compatibility with MPSX
• Programming Examples
• Linear and Mixed-Integer Programming
• Quadratic Programming
• Related Control Variables
• Passing Your Model to OSL Using Spreadsheet Format
• Formulating Models with Lotus 1-2-3
• Examples
• Linear Programming
• Quadratic Programming
• Mixed-Integer Programming
• Creating and Defining an Optimization Problem with Lotus 1-2-3
• Using Range Sets
• Creating and Defining Adjustable Cells
• Creating and Defining Constraints
• Creating and Defining an Objective Function
• Creating and Defining Special Ordered Sets
• Creating Names for Problem Variables and Constraints
• Using EKKSMDL
• OSL Restrictions to Lotus 1-2-3 Format
• Utilities
• Making Copies of the Matrix for Yourself (EKKCOPY)
• Adding, Replacing, Getting, or Deleting Columns and Rows (EKKCOL and EKKROW)
• Getting and Putting Model Data (EKKGTMD and EKKPTMD)
• Controlling EKKGTMD and EKKPTMD
• Using EKKGTMD and EKKPTMD
• Other Considerations
• Computing a Matrix Vector Product (EKKGEMV)
• Solving a Basic System of Equations (EKKGES)
• Invert: Create the Primal and Dual Solutions Corresponding to a Given Basis (EKKINVT)
• Creating, Changing, or Retrieving Row and Column Names (EKKNAME)
• Control Variables
• Using EKKNAME
• Retrieving Names Directly
• Quadratic Input
• Creating a Basis of All Logical Variables (EKKNLBS)
• Creating a New Copy of a Matrix (EKKNWMT)
• Printing the Solution (EKKPRTS)
• Controlling the Output
• Basic Output
• Advanced Output
• Additional Output from LP Sensitivity Analysis
• Repeat an Existing Matrix Block As a New Block (EKKRPTB)
• Using EKKRPTB
• Control Variables
• Creating or Changing Selection Lists (EKKSEL)
• What Is a Selection List?
• Format of a Selection List
• How EKKSEL Works
• Wildcard and Arbitrary Characters
• Operating on Selection Lists Directly
• Saving Selection Lists
• Storage Management Subroutines
• Saving and Restoring Model Information in Storage (EKKPSHS and EKKPOPS)
• Reserving Some High Storage for Your Program (EKKHIS)
• Finding the Starting Indices of Data in Storage (EKKNGET)
• Getting and Putting Model Information (EKKGTMI and EKKPTMI)
• Debugging Your Program
• Using EKKSMAP for Debugging
• Using EKKSTAT for Debugging
• Explanation of EKKSTAT Output
• Modifying Your Message Options
• What Can You Do with the Message-Handling Subroutines?
• Fragment 1, restricting log output
• Fragment 2, suppressing message numbers
• Fragment 3, suppressing ALL output
• Understanding User Exit Subroutines
• Overview
• Informational User Exit Subroutines
• Iteration User Exit Subroutine (EKKITRU)
• Message User Exit Subroutine (EKKMSGU)
• Using Mixed-Integer User Exit Subroutines
• Branch-and-Bound User Exit Subroutines (EKKBRNU, EKKCHNU, EKKEVNU, EKKSLVU, and EKKNODU)
• Sample EKKMSLV Program for Use with EKKBRNU, EKKCHNU, and EKKEVNU
• Branch User Exit Subroutine (EKKBRNU)
• Choose Node User Exit Subroutine (EKKCHNU)
• Evaluate a Node User Exit Subroutine (EKKEVNU)
• Solve Node User Exit Subroutine (EKKSLVU)
• Save Node Information User Exit Subroutine (EKKNODU)
• Supernode User Exit Subroutines (EKKCUTU and EKKHEUU)
• Add Cuts User Exit Subroutine (EKKCUTU)
• Use Heuristics User Exit Subroutine (EKKHEUU)
• Row Ordering User Exit Subroutine (EKKORDU)
• Advanced Topics
• Helpful Hints
• Declaring the Size of Your DSPACE Array
• Execution Timing
• Setting Control Variables
• Specifying the Problem Name in Your Quadratic Input File
• Default Column Bounds
• Indexing into DSPACE and MSPACE
• Resuming EKKMSLV
• Suppressing Message Numbers
• Severe Error Messages
• Iteration Counts and EKKQSLV
• Accessing Linear Programming Dual Variables
• Special Topics related to MIP Problems
• Adding Integer Variables
• Resuming EKKMSLV
• Defining MIP Problems and Special Ordered Sets with EKKIMDL
• Identifying Special Ordered Sets of Types 1 and 3 with EKKSOS
• Transforming General Integer MIP Problems into 0/1 MIP Problems
• Writing Branch User Exits for EKKMSLV
• Using EKKLPDC to Solve Block Structured Problems
• Block Structured Problems
• Getting Started with EKKLPDC
• Solving Staircase Problems
• Solving Dantzig-Wolfe Problems
• Solving Completely Separable Problems
• Other Useful Library Routines
• Summary
• Combining Input Data from Multiple Sources
• Using Lotus 1-2-3 Workfiles

Reference

• Optimization Library Subroutines
• EKKBASI - Read a Basis in MPS Format from a File
• EKKBASO - Write the Current Basis to a File in MPS Fixed Format
• EKKBCDO - Write a Model in MPS Fixed Format to a File
• EKKBMPR - Transform a General MIP Problem into a 0/1 MIP Problem
• EKKBMPS - Map the 0/1 Solution Back to Original General Integer Variables
• EKKBSLV - Solve a Linear Programming Problem Using an Interior-Point Method
• EKKCGET - Request Current Values of Character Control Variables
• EKKCLCB - Clear all Callback Functions
• EKKCOL - Add, Replace, Get, or Delete a Column in the Problem Matrix
• EKKCOPY - Copy the Problem Matrix Stored by Columns or by Rows
• EKKCRSH - Crash: Produce a Starting Basis
• EKKCSET - Set Character Control Variables
• EKKDSCA - Describe a Mathematical Programming Application
• EKKDSCB - Describe One Block of the Problem Matrix for a Model
• EKKDSCM - Describe a Mathematical Programming Model
• EKKEMDL - Specify an Empty Model
• EKKFCLS - Close and Disconnect FORTRAN I/O Units
• EKKFOPN - Open and Connect Files to FORTRAN I/O Units
• EKKFREW - Rewind Files Associated with FORTRAN I/O Unit numbers
• EKKGEMV - Compute a Matrix Vector Product
• EKKGES - Solve a Basic System of Equations
• EKKGTMD - Get a Model from a File
• EKKGTMI - Get Model Information
• EKKHIS - Reserve Permanent Space for the User
• EKKIGET - Request Current Values of Integer Control Variables
• EKKIMDL - Specify the Integer Parts of a Model
• EKKINIT - Initialize OSL
• EKKINVT - Invert: Create the Primal and Dual Solutions Corresponding to a Given Basis
• EKKISET - Set Integer Control Variables
• EKKLMDL - Specify the Linear Part of a Model
• EKKLPDC - Perform Specialized Decomposition
• EKKMPRE - Preprocess the MIP Branch-and-Bound Tree to Take Advantage of Structures
• EKKMPS - Input a Model in MPS Format from a File
• EKKMSAV - Save the Option Settings for a Message
• EKKMSET - Set New Option Settings for a Message
• EKKMSLV - Solve a Mixed-Integer Programming Problem
• EKKMSTR - Restore the Saved Option Settings for a Message
• EKKNAME - Specify or Retrieve Names for Rows and Columns in a Model
• EKKNFES - Analyze an Infeasible Linear Programming Problem
• EKKNGET - Request Current Start Indices of OSL Information
• EKKNLBS - Create a Basis of All Logical Variables
• EKKNMDL - Specify a Network Model
• EKKNSLV - Solve a Network Flow Problem
• EKKNWMT - Create a New Copy of the Problem Matrix
• EKKPMDL - Specify a Parametric Model
• EKKPOPS - Pop Storage: Restore Storage Pointers
• EKKPRSL - Presolve: Reduce the Problem Size
• EKKPRTS - Print the Problem Solution
• EKKPSHS - Push Storage: Save Current Storage Pointers
• EKKPSSL - Postsolve: Map the Solution Back to Original Variables
• EKKPTMD - Put a Model into a File
• EKKPTMI - Put Current Model Information
• EKKQMDL - Specify the Quadratic Parts of a Model
• EKKQMPS - Specify the Quadratic Parts of a Model in MPS Format from a File
• EKKQPAR - Parametrically Analyze a Quadratic Programming Problem
• EKKQRMD - Query Model Number
• EKKQSLV - Solve a Quadratic Programming Problem
• EKKRGCB - Register a Callback Function
• EKKRGET - Request Current Values of Real Control Variables
• EKKROW - Add, Replace, Get, or Delete a Row in the Problem Matrix
• EKKRPTB - Repeat an Existing Matrix Block As a New Block in the Current Problem Matrix
• EKKRSET - Set Real Control Variables
• EKKSBND - Analyze the Sensitivity of a Solution to Row and Column Bounds
• EKKSCAL - Scale the Coefficient Matrix
• EKKSEL - Modify Selection Lists
• EKKSMAP - Print the Storage Map
• EKKSMDL - Specify a Model in Spreadsheet Format
• EKKSOBJ - Analyze the Sensitivity of a Solution to Objective Function
• EKKSOS - Identify Special Ordered Sets of Types 1 and 3
• EKKSPAR - Parametrically Analyze a Linear Programming Problem
• EKKSSLV - Solve a Linear Programming Problem Using the Simplex Method
• EKKSTAT - Print Problem Statistics
• Informational User Exit Subroutines and EKKORDU
• EKKITRU - Iteration User Exit Subroutine
• EKKMSGU - Message User Exit Subroutine
• EKKORDU - Row Ordering User Exit Subroutine
• The MIP User Exit Subroutines
• EKKBRNU - Branch User Exit Subroutine
• EKKCHNU - Choose Node User Exit Subroutine
• EKKCUTU - Cut Generation User Exit Subroutine
• EKKEVNU - Evaluate a Node User Exit Subroutine
• EKKHEUU - Heuristic Fixing User Exit Subroutine
• EKKNODU - Node User Exit Subroutine
• EKKSLVU - Branch User Exit Subroutine
• Appendix A. Optimization Library Messages
• Message Conventionsand Return Codes
• Message Option Table
• List of OSL Messages
• Appendix B. Sample Application Programs, in C and FORTRAN, Sample

     Include Files and User Exit Subroutines in C  and  FORTRAN,  and 
     Sample Data Sets
• Sample C Application Programs
• Sample C Program EXBMPR
• Sample C Program EXMPS
• Sample C Program EXNAME
• Sample C Program EXPRSL
• Sample C Program EXROW
• Sample C Program EXSELNAM
• Sample C Program EXIMDL6
• Sample FORTRAN Application Programs
• Sample FORTRAN Program EXBASI
• Sample FORTRAN Program EXBASO
• Sample FORTRAN Program EXBSLV
• Sample FORTRAN Program EXCOPY
• Sample FORTRAN Program EXDANWOL
• Sample FORTRAN Program EXDSCB
• Sample FORTRAN Program EXDSCM2
• Sample FORTRAN Program EXDUAL
• Sample FORTRAN Program EXFRONT
• Sample FORTRAN Program EXGES
• Sample FORTRAN Program EXIMDL
• Sample FORTRAN Program EXIMDL2
• Sample FORTRAN Program EXIMDL3
• Sample FORTRAN Program EXIMDL4
• Sample FORTRAN Program EXIMDL5
• Sample FORTRAN Program EXINIT
• Sample FORTRAN Program EXISET
• Sample FORTRAN Program EXLMDL
• Sample FORTRAN Program EXLPDC
• Sample FORTRAN Program EXLPDC2
• Sample FORTRAN Program EXMPRSL
• Sample FORTRAN Program EXMPS
• Sample FORTRAN Program EXMSAV
• Sample FORTRAN Program EXMSLV
• Sample FORTRAN Program EXMSLV2
• Sample FORTRAN Program EXMSLV3
• Sample FORTRAN Program EXNAME
• Sample FORTRAN Program EXNAME2
• Sample FORTRAN Program EXNFES
• Sample FORTRAN Program EXNCRSH
• Sample FORTRAN Program EXNGET
• Sample FORTRAN Program EXNMDL
• Sample FORTRAN Program EXNSLV
• Sample FORTRAN Program EXOSLBAS
• Sample FORTRAN Program EXPARA1
• Sample FORTRAN Program EXPARA2
• Sample FORTRAN Program EXPRSL
• Sample FORTRAN Program EXPTMD
• Sample FORTRAN Program EXQMDL
• Sample FORTRAN Program EXQPAR
• Sample FORTRAN Program EXQSLV
• Sample FORTRAN Program EXROW
• Sample FORTRAN Program EXRPTB
• Sample FORTRAN Program EXRVIS
• Sample FORTRAN Program EXSELNAM
• Sample FORTRAN Program EXSELNM2
• Sample FORTRAN Program EXSENS1
• Sample FORTRAN Program EXSENS2
• Sample FORTRAN Program EXSMDL
• Sample FORTRAN Program EXSOS
• Sample FORTRAN Application Program EXTOMPSX
• C Include Files
• Character Control Variable Mnemonics #include oslc.h
• Integer Control Variable Mnemonics #include osli.h
• Index Control Variable Mnemonics #include osln.h
• Real Control Variable Mnemonics #include oslr.h
• FORTRAN INCLUDE Files
• Character Control Variable Mnemonics INCLUDE (OSLC)
• Integer Control Variable Mnemonics INCLUDE (OSLI)
• Index Control Variable Mnemonics INCLUDE (OSLN)
• Real Control Variable Mnemonics INCLUDE (OSLR)
• Sample Informational User Exits in C  and  FORTRAN
• A Sample EKKITRU in C  and  FORTRAN
• A Sample EKKITRU for parametric analysis in FORTRAN
• A Sample EKKMSGU in C  and  FORTRAN
• Sample Mixed-Integer User Exit Subroutines in C  and  FORTRAN
• A Sample EKKBRNU in C  and  FORTRAN
• A Second EKKBRNU in FORTRAN
• A Sample EKKCHNU in C  and  FORTRAN
• A Sample EKKCUTU in C  and  FORTRAN
• A Sample EKKEVNU in C  and  FORTRAN
• A Sample EKKHEUU in C  and  FORTRAN
• A Sample EKKNODU in C  and  FORTRAN
• A Sample EKKSLVU in C  and  FORTRAN
• A Sample EKKORDU (Row Ordering User Exit) in C  and  FORTRAN
• Sample MPS Input Files
• Sample Basis Data
• Sample LP Model Data 1
• Sample LP Model Data 2
• Sample LP Model Data 3
• Sample LP Model Data 4
• Sample LP Model Data 5
• Sample LP Model Data 6
• Sample LP Model Data 7
• Sample LP Model Data 8
• Sample LP Model Data 9
• Sample MIP Model Data 1
• Sample MI Model Data 2
• Sample QP Model Data 1
• Sample QP Model Data 2
• Sample Spreadsheet Worksheet File 1
• Appendix C. Control Variables
• Integer Control Variables
• Real Control Variables
• Index Control Variables
• Character Control Variables
• Glossary
• Bibliography