Intro; Preface; Contents; 1 Disjunctive Programming and Its Relation to Integer Programming; 1.1 Introduction; 1.2 Intersection Cuts; 1.3 Inequality Systems with Logical Connectives; 1.4 Valid Inequalities for Disjunctive Sets; 1.5 Duality for Disjunctive Programs; 2 The Convex Hull of a Disjunctive Set; 2.1 The Convex Hull Via Lifting and Projection; 2.1.1 Tightness of the Lifted Representation; 2.1.2 From the Convex Hull to the Union Itself; 2.2 Some Facts About Projecting Polyhedra; 2.2.1 Well Known Special Cases; 2.2.2 Dimensional Aspects of Projection

2.2.3 When Is the Projection of a Facet a Facet of the Projection?2.3 Projection with a Minimal System of Inequalities; 2.4 The Convex Hull Via Polarity; 3 Sequential Convexification of Disjunctive Sets; 3.1 Faciality as a Sufficient Condition; 3.2 A Necessary Condition for Sequential Convexifiability; 4 Moving Between Conjunctive and Disjunctive Normal Forms; 4.1 The Regular Form and Basic Steps; 4.2 The Hull Relaxation and the Associated Hierarchy; 4.3 When to Convexify a Subset; 4.4 Parsimonious MIP Representation of Disjunctive Sets

4.5 An Illustration: Machine Sequencing Via Disjunctive Graphs4.5.1 A Disjunctive Programming Formulation; 4.5.2 A Tighter Disjunctive Programming Formulation; 4.6 Disjunctive Programs with Trigger Variables; 5 Disjunctive Programming and Extended Formulations; 5.1 Comparing the Strength of Different Formulations; 5.1.1 The Traveling Salesman Problem; 5.1.2 The Set Covering Problem; 5.1.3 Nonlinear 0-1 Programming; 5.2 Proving the Integrality of Polyhedra; 5.2.1 Perfectly Matchable Subgraphs of a Bipartite Graph; 5.2.2 Assignable Subgraphs of a Digraph

5.2.3 Path Decomposable Subgraphs of an Acyclic Digraph5.2.4 Perfectly Matchable Subgraphs of an Arbitrary Graph; 6 Lift-and-Project Cuts for Mixed 0-1 Programs; 6.1 Disjunctive Rank; 6.2 Fractionality of Intermediate Points; 6.3 Generating Cuts; 6.4 Cut Lifting; 6.5 Cut Strengthening; 6.6 Impact on the State of the Art in Integer Programming; 7 Nonlinear Higher-Dimensional Representations; 7.1 Another Derivation of Lift-and-Project Cuts; 7.2 The Lovász-Schrijver Construction; 7.3 The Sherali-Adams Construction; 7.4 Lasserre's Construction; 7.5 The Bienstock-Zuckerberg Lift Operator

8 The Correspondence Between Lift-and-Project Cuts and Simple Disjunctive Cuts8.1 Feasible Bases of the CGLP Versus (Feasible or Infeasible) Bases of the LP; 8.2 The Correspondence Between the Strengthened Cuts; 8.3 Bounds on the Number of Essential Cuts; 8.4 The Rank of P with Respect to Different Cuts; 9 Solving (CGLP)k on the LP Simplex Tableau; 9.1 Computing Reduced Costs of (CGLP)k Columns for the LP Rows; 9.2 Computing Evaluation Functions for the LP Columns; 9.3 Generating Lift-and-Project Cuts by Pivoting in the LP Tableau