| Linear and Nonlinear Programming | |
| Unconstrained Minimization | |
| Linear Programming | |
| Simplex Method | |
| Revised Simplex Method | |
| Duality in Linear Programming | |
| Dual Simplex and Primal-Dual Algorithms | |
| Nonlinear Programming | |
| Convexity | |
| Kuhn-Tucker Conditions | |
| Saddle Points and Sufficiency Conditions | |
| Methods of Nonlinear Programming References | |
| Large Mathematical Programs with Special Structure | |
| Introduction | |
| Activity analysis | |
| Production and Inventory Problem | |
| Dynamic Leontief Model | |
| Angular and Dual-Angular Structures | |
| Linear Programs with Many Rows or Columns | |
| Nonlinear Programs with Coupling Variables | |
| Mixed-Variable Programs and a Location Problem Problems, References | |
| The Dantzig-Wolfe Decomposition Principle | |
| Introduction | |
| A Theorem on Convex Combinations | |
| Column Generation | |
| Development of the Decomposition Principle | |
| Example of the Decomposition Principle | |
| Economic Interpretation of the Decomposition Principle | |
| Lower Bound for the Minimal Cost | |
| Application to Transportation Problems | |
| Generalized Transportation Problems and a Forestry-Cutting Example | |
| Optimal Allocation of Limited Resources | |
| General formulation | |
| Specializing the Model--Lot Sizes and Labor Allocations | |
| Computational Experience | |
| Primal-Dual Approach to the Master Program | |
| Linear Fractional Programming | |
| Application of the Primal-Dual Method to the Master Program | |
| Example of the Primal-Dual Method | |
| Three Algorithms for Solving the Master Program--A comparison Problems, References | |
| Solution of Linear Programs with Many Columns by Column-Generation Procedures | |
| The Cutting-Stock Problem | |
| Column-Generation and Multi-item Scheduling | |
| Generalized Linear Programming | |
| Grid Linearization and Nonlinear Programming | |
| General Development | |
| Nonlinear Version of the Dantzig-Wolfe Decomposition Principle | |
| Design of Multiterminal Flow Networks Problems, References | |
| Partitioning and Relaxation Procedures in Linear Programming | |
| Introduction | |
| Relaxation | |
| Problems with Coupling constraints and Coupling Variables | |
| Rosen's Partitioning Procedure for Angular and Dual-Angular Problems | |
| Development of the Algorithm | |
| Computational Considerations | |
| Computational Experience | |
| Example of Rosen's Partitioning Method Problems, References | |
| Compact Inverse Methods | |
| Introduction | |
| Revised Simplex Method with Inverse in Product Form | |
| Upper Bounding Methods | |
| Generalized Upper Bounding | |
| Development of the Algorithm | |
| Example of the Generalized Upper Bounding Method | |
| Extension to Angular Structures Problems, References | |
| Partitioning Procedures in Nonlinear Programming | |
| Introduction | |
| Rosen's Partitioning Algorithm for Nonlinear Programs | |
| Development of the Algorithm | |
| Use of Partition Programming in Refinery Optimization | |
| Benders' Partitioning Algorithm for Mixed-Variable Programming Problems | |
| Development of the Algorithm | |
| Relation to the Decomposition Principle and Cutting-Plane Algorithms | |
| Application to a Warehouse Location Problem | |
| Numerical Example | |
| Computational Experience Problems, References | |
| Duality and Decomposition in Mathematical Programming | |
| Introduction | |
| Decomposition Using a Pricing Mechanism | |
| Saddle Points of Lagrangian Functions | |
| Basic Theorems | |
| Everetts Theorem | |
| Application to Linear Integer Programs | |
| Minimax Dual Problem | |
| Differentiability of the Dual Objective Function | |
| Computational Methods for Solving the Dual | |
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