Optimization with Disjunctive Constraints

I: Introduction -- 1.1 Basic Concepts -- 1.2 Special Cases of Disjunctive Programs and Their Applications -- 1.3 Notes and References -- II: Basic Concepts and Principles -- 2.1 Introduction -- 2.2 Surrogate Constraints -- 2.3 Pointwise-Supremal Cuts -- 2.4 Basic Disjunctive Cut Principle -- 2.5 Notes and References -- III: Generation of Deep Cuts Using the Fundamental Disjunctive Inequality -- 3.1 Introduction -- 3.2 Defining Suitable Criteria for Evaluating the Depth of a Cut -- 3.3 Deriving Deep Cuts for DC1 -- 3.4 Deriving Deep Cuts for DC2 -- 3.5 Other Criteria for Obtaining Deep Cuts -- 3.6 Some Standard Choices of Surrogate Constraint Multipliers -- 3.7 Notes and References -- IV: Effect of Disjunctive Statement Formulation on Depth of Cut and Polyhedral Annexation Techniques -- 4.1 Introduction -- 4.2 Illustration of the Tradeoff Between Effort for Cut Generation and the Depth of Cut -- 4.3 Some General Comments with Applications to the Generalized Lattice Point and the Linear Complementarity Problem -- 4.4 Sequential Polyhedral Annexation -- 4.5 A Supporting Hyperplane Scheme for Improving Edge Extensions -- 4.6 Illustrative Example -- 4.7 Notes and References -- V: Generation of Facets of the Closure of the Convex Hull of Feasible Points -- 5.1 Introduction -- 5.2 A Linear Programming Equivalent of the Disjunctive Program -- 5.3 Alternative Characterization of the Closure of the Convex Hull of Feasible Points -- 5.4 Generation of Facets of the Closure of the Convex Hull of Feasible Points -- 5.5 Illustrative Example -- 5.6 Facial Disjunctive Programs -- 5.7 Notes and References -- VI: Derivation and Improvement of Some Existing Cuts Through Disjunctive Principles -- 6.1 Introduction -- 6.2 Gomory’s Mixed Integer Cuts -- 6.3 Convexity or Intersection Cuts with Positive Edge Extensions -- 6.4 Reverse Outer Polar Cuts for Zero-One Programming -- 6.5 Notes and References -- VII: Finitely Convergent Algorithms for Facial Disjunctive Programs with Applications to the Linear Complementarity Problem -- 7.1 Introduction -- 7.2 Principal Aspects of Facial Disjunctive Programs -- 7.3 Stepwise Approximation of the Convex Hull of Feasible Points -- 7.4 Approximation of the Convex Hull of Feasible Points Through an Extreme Point Characterization -- 7.5 Specializations of the Extreme Point Method for the Linear Complementarity Problem -- 7.6 Notes and References -- VIII: Some Specific Applications of Disjunctive Programming Problems -- 8.1 Introduction -- 8.2 Some Examples of Bi-Quasiconcave Problems -- 8.3 Load Balancing Problem -- 8.4 The Segregated Storage Problem -- 8.5 Production Scheduling on N-Identical Machines -- 8.6 Fixed Charge Problem -- 8.7 Project Selection/Portfolio Allocation/Goal Programming -- 8.8 Other Applications -- 8.9 Notes and References -- Selected References.