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.