Linear-Cutting - blog*spot

In this dissertation, a finitely convergent disjunctive programming procedure, the Convex Hull Tree CHT) algorithm, is proposed to obtain the convex hull of a general mixed-integer linear program with bounded integer variables. The CHT algorithm constructs a linear program that has the same optimal solution as the associated mixed-integer linear program. The standard notion of sequential cutting planes is then combined with ideas underlying the CHT algorithm to help guide the choice of disjunctions to use within a new cutting plane method, the Cutting Plane Tree CPT) algorithm. We show that the CPT algorithm converges to an integer optimal solution of the general mixed-integer linear program with bounded integer variables in finitely many steps. We also enhance the CPT algorithm with several techniques including a “round-of-cuts” approach and an iterative method for solving the cut generation linear program CGLP). Two normalization constraints are discussed in detail for solving the CGLP. For moderately sized instances, our study shows that the CPT algorithm provides significant gap closures with a pure cutting plane method. Key words: Mixed-integer linear program, disjunctive programming, convex hull, cutting plane, finite convergence.