SAS/OR(R) 9.2 User's Guide: Mathematical Programming
Acknowledgments- What's New in SAS/OR 9.2
- Using This Book
- Purpose
- Organization
- Typographical Conventions
- Conventions for Examples
- Accessing the SAS/OR Sample Library
- Online Help System and Updates
- Additional Documentation for SAS/OR Software
- Introduction to Optimization
- Overview
- Linear Programming Problems
- Network Problems
- Mixed Integer Linear Problems
- Quadratic Programming Problems
- Nonlinear Problems
- Model Building
- Matrix Generation
- Exploiting Model Structure
- Report Writing
- References
- The INTPOINT Procedure
- Overview: INTPOINT Procedure
- Mathematical Description of NPSC
- Mathematical Description of LP
- The Interior Point Algorithm
- Network Models
- Introduction
- Syntax: INTPOINT Procedure
- Functional Summary
- Dictionary of Options
- PROC INTPOINT Statement
- CAPACITY Statement
- COEF Statement
- COLUMN Statement
- COST Statement
- DEMAND Statement
- HEADNODE Statement
- ID Statement
- LO Statement
- NAME Statement
- NODE Statement
- QUIT Statement
- RHS Statement
- ROW Statement
- RUN Statement
- SUPDEM Statement
- SUPPLY Statement
- TAILNODE Statement
- TYPE Statement
- VAR Statement
- Details: INTPOINT Procedure
- Input Data Sets
- Output Data Sets
- Converting Any PROC INTPOINT Format to an MPS-Format SAS Data Set
- Case Sensitivity
- Loop Arcs
- Multiple Arcs
- Flow and Value Bounds
- Tightening Bounds and Side Constraints
- Reasons for Infeasibility
- Missing S Supply and Missing D Demand Values
- Balancing Total Supply and Total Demand
- How to Make the Data Read of PROC INTPOINT More Efficient
- Stopping Criteria
- Macro Variable _ORINTPO
- Memory Limit
- Examples: INTPOINT Procedure
- Example 2.1: Production, Inventory, Distribution Problem
- Example 2.2: Altering Arc Data
- Example 2.3: Adding Side Constraints
- Example 2.4: Using Constraints and More Alteration to Arc Data
- Example 2.5: Nonarc Variables in the Side Constraints
- Example 2.6: Solving an LP Problem with Data in MPS Format
- Example 2.7: Converting to an MPS-Format SAS Data Set
- References
- The LP Procedure
- Overview: LP Procedure
- Getting Started: LP Procedure
- An Introductory Example
- An Integer Programming Example
- An MPS Format to Sparse Format Conversion Example
- Syntax: LP Procedure
- Functional Summary
- Dictionary of Options
- PROC LP Statement
- COEF Statement
- COL Statement
- ID Statement
- IPIVOT Statement
- PIVOT Statement
- PRINT Statement
- QUIT Statement
- RANGE Statement
- RESET Statement
- RHS Statement
- RHSSEN Statement
- ROW Statement
- RUN Statement
- SHOW Statement
- TYPE Statement
- VAR Statement
- Details: LP Procedure
- Missing Values
- Dense Data Input Format
- Sparse Data Input Format
- Converting Any PROC LP Format to an MPS-Format SAS Data Set
- Converting Standard MPS Format to Sparse Format
- The Reduced Costs, Dual Activities, and Current Tableau
- Macro Variable _ORLP_
- Pricing
- Scaling
- Preprocessing
- Integer Programming
- Sensitivity Analysis
- Range Analysis
- Parametric Programming
- Interactive Facilities
- Memory Management
- Output Data Sets
- Input Data Sets
- Displayed Output
- ODS Table and Variable Names
- Memory Limit
- Examples: LP Procedure
- Example 3.1: An Oil Blending Problem
- Example 3.2: A Sparse View of the Oil Blending Problem
- Example 3.3: Sensitivity Analysis: Changes in Objective Coefficients
- Example 3.4: Additional Sensitivity Analysis
- Example 3.5: Price Parametric Programming for the Oil Blending Problem
- Example 3.6: Special Ordered Sets and the Oil Blending Problem
- Example 3.7: Goal-Programming a Product Mix Problem
- Example 3.8: A Simple Integer Program
- Example 3.9: An Infeasible Problem
- Example 3.10: Restarting an Integer Program
- Example 3.11: Alternative Search of the Branch-and-Bound Tree
- Example 3.12: An Assignment Problem
- Example 3.13: A Scheduling Problem
- Example 3.14: A Multicommodity Transshipment Problem with Fixed Charges
- Example 3.15: Converting to an MPS-Format SAS Data Set
- References
- The NLP Procedure
- Overview: NLP Procedure
- Getting Started: NLP Procedure
- Syntax: NLP Procedure
- Functional Summary
- Dictionary of Options
- PROC NLP Statement
- ARRAY Statement
- BOUNDS Statement
- BY Statement
- CRPJAC Statement
- DECVAR Statement
- GRADIENT Statement
- HESSIAN Statement
- INCLUDE Statement
- JACNLC Statement
- JACOBIAN Statement
- LABEL Statement
- LINCON Statement
- MATRIX Statement
- MIN, MAX, and LSQ Statements
- MINQUAD and MAXQUAD Statements
- NLINCON Statement
- PROFILE Statement
- Program Statements
- Details: NLP Procedure
- Criteria for Optimality
- Optimization Algorithms
- Finite-Difference Approximations of Derivatives
- Hessian and CRP Jacobian Scaling
- Testing the Gradient Specification
- Termination Criteria
- Active Set Methods
- Feasible Starting Point
- Line-Search Methods
- Restricting the Step Length
- Computational Problems
- Covariance Matrix
- Input and Output Data Sets
- Displayed Output
- Missing Values
- Computational Resources
- Memory Limit
- Examples: NLP Procedure
- Example 4.1: Using the DATA= Option
- Example 4.2: Using the INQUAD= Option
- Example 4.3: Using the INEST=Option
- Example 4.4: Restarting an Optimization
- Example 4.5: Approximate Standard Errors
- Example 4.6: Maximum Likelihood Weibull Estimation
- Example 4.7: Simple Pooling Problem
- Example 4.8: Chemical Equilibrium
- Example 4.9: Minimize Total Delay in a Network
- References
- The NETFLOW Procedure
- Overview: NETFLOW Procedure
- Introduction
- Network Models
- Side Constraints
- Advantages of Network Models over LP Models
- Mathematical Description of NPSC
- Flow Conservation Constraints
- Nonarc Variables
- Warm Starts
- Getting Started: NETFLOW Procedure
- Syntax: NETFLOW Procedure
- Functional Summary
- Dictionary of Options
- Interactivity
- PROC NETFLOW Statement
- CAPACITY Statement
- COEF Statement
- COLUMN Statement
- CONOPT Statement
- COST Statement
- DEMAND Statement
- HEADNODE Statement
- ID Statement
- LO Statement
- MULT Statement
- NAME Statement
- NODE Statement
- PIVOT Statement
- PRINT Statement
- QUIT Statement
- RESET Statement
- RHS Statement
- ROW Statement
- RUN Statement
- SAVE Statement
- SHOW Statement
- SUPDEM Statement
- SUPPLY Statement
- TAILNODE Statement
- TYPE Statement
- VAR Statement
- Details: NETFLOW Procedure
- Input Data Sets
- Output Data Sets
- Converting Any PROC NETFLOW Format to an MPS-Format SAS Data Set
- Case Sensitivity
- Loop Arcs
- Multiple Arcs
- Pricing Strategies
- Dual Variables, Reduced Costs, and Status
- The Working Basis Matrix
- Flow and Value Bounds
- Tightening Bounds and Side Constraints
- Reasons for Infeasibility
- Missing S Supply and Missing D Demand Values
- Balancing Total Supply and Total Demand
- Warm Starts
- How to Make the Data Read of PROC NETFLOW More Efficient
- Macro Variable _ORNETFL
- Memory Limit
- The Interior Point Algorithm: NETFLOW Procedure
- Introduction
- Network Models: Interior Point Algorithm
- Linear Programming Models: Interior Point Algorithm
- Generalized Networks: NETFLOW Procedure
- Using the New EXCESS= Option in Pure Networks: NETFLOW Procedure
- Handling Excess Supply or Demand
- Handling Missing Supply and Demand Simultaneously
- Maximum Flow Problems
- Handling Supply and Demand Ranges
- Using the New EXCESS= Option in Generalized Networks: NETFLOW Procedure
- Total Supply and Total Demand: How Generalized Networks Differ from Pure Networks
- The EXCESS=SUPPLY Option
- The EXCESS=DEMAND Option
- Examples: NETFLOW Procedure
- Example 5.1: Shortest Path Problem
- Example 5.2: Minimum Cost Flow Problem
- Example 5.3: Using a Warm Start
- Example 5.4: Production, Inventory, Distribution Problem
- Example 5.5: Using an Unconstrained Solution Warm Start
- Example 5.6: Adding Side Constraints, Using a Warm Start
- Example 5.7: Using a Constrained Solution Warm Start
- Example 5.8: Nonarc Variables in the Side Constraints
- Example 5.9: Pure Networks: Using the EXCESS= Option
- Example 5.10: Maximum Flow Problem
- Example 5.11: Generalized Networks: Using the EXCESS= Option
- Example 5.12: Generalized Networks: Maximum Flow Problem
- Example 5.13: Machine Loading Problem
- Example 5.14: Generalized Networks: Distribution Problem
- Example 5.15: Converting to an MPS-Format SAS Data Set
- References
- The OPTMODEL Procedure
- Overview: OPTMODEL Procedure
- Getting Started: OPTMODEL Procedure
- OPTMODEL Modeling Language: Basic Concepts
- Named Parameters
- Indexing
- Types
- Names
- Parameters
- Expressions
- Identifier Expressions
- Function Expressions
- Index Sets
- Syntax: OPTMODEL Procedure
- Functional Summary
- PROC OPTMODEL Statement
- Declaration Statements
- CONSTRAINT Declaration
- MAX and MIN Objective Declarations
- NUMBER, STRING, and SET Parameter Declarations
- VAR Declaration
- Programming Statements
- Assignment Statement
- CALL Statement
- CLOSEFILE Statement
- CONTINUE Statement
- CREATE DATA Statement
- DO Statement
- DO Statement, Iterative
- DO UNTIL Statement
- DO WHILE Statement
- DROP Statement
- EXPAND Statement
- FILE Statement
- FIX Statement
- FOR Statement
- IF Statement
- LEAVE Statement
- Null Statement
- PRINT Statement
- PUT Statement
- READ DATA Statement
- RESET OPTIONS Statement
- RESTORE Statement
- SAVE MPS Statement
- SAVE QPS Statement
- SOLVE Statement
- STOP Statement
- UNFIX Statement
- Macro Variable _OROPTMODEL_
- OPTMODEL Expression Extensions
- AND Aggregation Expression
- CARD Function
- CROSS Expression
- DIFF Expression
- IF-THEN/ELSE Expression
- IN Expression
- Index Set Expression
- INTER Expression
- INTER Aggregation Expression
- MAX Aggregation Expression
- MIN Aggregation Expression
- OR Aggregation Expression
- PROD Aggregation Expression
- Range Expression
- Set Constructor Expression
- Set Literal Expression
- SETOF Aggregation Expression
- SLICE Expression
- SUM Aggregation Expression
- SYMDIFF Expression
- Tuple Expression
- UNION Expression
- UNION Aggregation Expression
- WITHIN Expression
- Details: OPTMODEL Procedure
- Conditions of Optimality
- Data Set Input/Output
- Control Flow
- Formatted Output
- ODS Table and Variable Names
- Constraints
- Suffixes
- Integer Variable Suffixes
- Dual Values
- Reduced Costs
- Presolver
- Model Update
- OPTMODEL Options
- Automatic Differentiation
- Conversions
- More on Index Sets
- Memory Limit
- Examples: OPTMODEL Procedure
- Example 6.1: Matrix Square Root
- Example 6.2: Reading from and Creating a Data Set
- Example 6.3: Model Construction
- Example 6.4: Set Manipulation
- Rewriting NLP Models for PROC OPTMODEL
- References
- The Interior Point Nonlinear Programming Solver -- Experimental
- Overview
- Getting Started
- Syntax
- Details
- Basic Definitions and Notation
- Overview of Constrained Optimization
- Overview of Interior Point Methods
- Solver Termination Criterion
- Solver Termination Messages
- Macro Variable _OROPTMODEL_
- Examples
- Example 7.1: Solving Highly Nonlinear Optimization Problems
- Example 7.2: Solving Unconstrained Optimization Problems
- Example 7.3: Solving NLP Problems with Range Constraints
- References
- The Linear Programming Solver
- Overview
- Getting Started
- Syntax
- Details
- Presolve
- Pricing Strategies for the Primal Simplex Solver
- The Interior Point Algorithm: Overview
- Macro Variable _OROPTMODEL_
- Iteration Log for the Simplex Solvers
- Iteration Log for the Interior Point Solver
- Problem Statistics
- Data Magnitude and Variable Bounds
- Variable and Constraint Status
- Irreducible Infeasible Set
- Examples
- Example 8.1: Diet Problem
- Example 8.2: Reoptimizing the Diet Problem Using BASIS=WARMSTART
- Example 8.3: Two-Person Zero-Sum Game
- Example 8.4: Finding an Irreducible Infeasible Set
- References
- The Mixed Integer Linear Programming Solver
- Overview
- Getting Started
- Syntax
- Details
- The Branch-and-Bound Algorithm
- Controlling the Branch-and-Bound Algorithm
- Presolve and Probing
- Cutting Planes
- Primal Heuristics
- Node Log
- Problem Statistics
- Data Magnitude and Variable Bounds
- Macro Variable _OROPTMODEL_
- Examples
- Example 9.1: Scheduling
- Example 9.2: Multicommodity Transshipment Problem with Fixed Charges
- Example 9.3: Facility Location
- Example 9.4: Traveling Salesman Problem
- References
- The NLPC Nonlinear Optimization Solver
- Overview
- Getting Started
- Syntax
- Details
- Optimization Algorithms
- Conditions of Optimality
- Optimality Control
- Infeasibility
- Feasible Starting Point
- Line-Search Method
- Computational Problems
- Iteration Log
- Macro Variable _OROPTMODEL_
- Examples
- Example 10.1: Least-Squares Problem
- Example 10.2: Maximum Likelihood Weibull Model
- Example 10.3: Simple Pooling Problem
- References
- The Unconstrained Nonlinear Programming Solver
- Overview
- Getting Started
- Syntax
- Details
- Conditions of Optimality
- Line-Search Algorithm
- Broyden-Fletcher-Goldfarb-Shanno (BFGS) Algorithm
- Macro Variable _OROPTMODEL_
- Examples
- Example 11.1: Solving a Highly Nonlinear Problem
- Example 11.2: Solving the Accumulated Rosenbrock Function
- References
- The Quadratic Programming Solver -- Experimental
- Overview
- Getting Started
- Syntax
- Details
- Examples
- Example 12.1: Linear Least-Squares Problem
- Example 12.2: Portfolio Optimization
- Example 12.3: Portfolio Selection with Transactions
- References
- The Sequential Quadratic Programming Solver
- Overview
- Getting Started
- Syntax
- Details
- Examples
- Example 13.1: Solving a Highly Nonlinear Problem
- Example 13.2: Using the HESCHECK Option
- Example 13.3: Choosing a Good Starting Point
- Example 13.4: Using the PENALTY= Option
- Example 13.5: Unconstrained NLP Optimization
- Example 13.6: Solving Large-Scale NLP Problems
- References
- The MPS-Format SAS Data Set
- Overview
- Sections Format
- NAME Section
- ROWS Section
- COLUMNS Section
- RHS Section (Optional)
- RANGES Section (Optional)
- BOUNDS Section (Optional)
- BRANCH Section (Optional)
- QSECTION Section
- ENDATA Section
- Details
- Examples
- Example 14.1: MPS-Format Data Set for a Product Mix Problem
- Example 14.2: Fixed-MPS-Format File
- Example 14.3: Free-MPS-Format File
- Example 14.4: Using the %MPS2SASD Macro
- References
- The OPTLP Procedure
- Overview: OPTLP Procedure
- Getting Started: OPTLP Procedure
- Syntax: OPTLP Procedure
- Details: OPTLP Procedure
- Data Input and Output
- Presolve
- Pricing Strategies for the Simplex Solvers
- Warm Start for the Simplex Solvers
- The Interior Point Algorithm: Overview
- Iteration Log for the Simplex Solvers
- Iteration Log for the Interior Point Solver
- ODS Tables
- Irreducible Infeasible Set
- Memory Limit
- Examples: OPTLP Procedure
- Example 15.1: Oil Refinery Problem
- Example 15.2: Using the Interior Point Solver
- Example 15.3: The Diet Problem
- Example 15.4: Reoptimizing after Modifying the Objective Function
- Example 15.5: Reoptimizing after Modifying the Right-Hand Side
- Example 15.6: Reoptimizing after Adding a New Constraint
- Example 15.7: Finding an Irreducible Infeasible Set
- References
- The OPTMILP Procedure
- Overview: OPTMILP Procedure
- Getting Started: OPTMILP Procedure
- Syntax: OPTMILP Procedure
- Details: OPTMILP Procedure
- Data Input and Output
- Warm Start
- The Branch-and-Bound Algorithm
- Controlling the Branch-and-Bound Algorithm
- Presolve and Probing
- Cutting Planes
- Primal Heuristics
- Node Log
- ODS Tables
- Memory Limit
- Examples: OPTMILP Procedure
- Example 16.1: Simple Integer Linear Program
- Example 16.2: MIPLIB Benchmark Instance
- Example 16.3: Facility Location
- References
- The OPTQP Procedure
- Overview: OPTQP Procedure
- Getting Started: OPTQP Procedure
- Syntax: OPTQP Procedure
- Details: OPTQP Procedure
- Output Data Sets
- Interior Point Algorithm: Overview
- Iteration Log for the OPTQP Procedure
- ODS Tables
- Memory Limit
- Examples: OPTQP Procedure
- Example 17.1: Linear Least-Squares Problem
- Example 17.2: Portfolio Optimization
- Example 17.3: Portfolio Selection with Transactions
- References
Index here
| Product | Release |
|---|---|
| SAS/OR | 9.2 |
- Type
- Usage and Reference
- Copyright Date
- March 2008
- Last Updated
- 24Feb2009
| Using This Book |
Conventions for Examples
Most of the output shown in this book is produced with the following SAS System options:
options linesize=80 pagesize=60 nonumber nodate;
Copyright © 2008 by SAS Institute Inc., Cary, NC, USA. All rights reserved.