Titlebook: Disjunctive Programming; Egon Balas Book 2018 Springer Nature Switzerland AG 2018 optimization.integer programming.nonconvex programming.l

干涉

Nonlinear Higher-Dimensional Representations,Apart from the extended formulations discussed in Chap. 5, a number of authors have proposed nonlinear higher dimensional constructions that provide tighter relaxations of conv...

供过于求

The Correspondence Between Lift-and-Project Cuts and Simple Disjunctive Cuts,From the fact that the constraint set (6.3) of (CGLP). defines the convex hull of . ∩{. : .. ∈{0, 1}}, and that conv.., the integer hull, can be derived by imposing the disjunctions .. ≤ 0 ∨ .. ≥ 1 sequentially, it follows that any valid cut for a mixed 0-1 program can be represented as a lift-and-project cut.

Definitive

Solving (CGLP), on the LP Simplex Tableau,The major practical consequence of the correspondence established in Theorems 8.4A/8.4B is that the cut generating linear program (CGLP). need not be formulated and solved explicitly; instead, the procedure for solving it can be mimicked on the linear programming relaxation (LP) of the original mixed 0-1 problem.

palliative-care

Implementation and Testing of Variants,The discovery of the possibility of generating L&P cuts through pivoting in the LP tableau, without recourse to the higher-dimensional (CGLP), has opened the door to the introduction of this class of cuts into commercial optimizers

内向者

Cuts from General Disjunctions,In the early years of the twenty-first century the topic of cutting planes from split disjunctions seemed to have been exhausted, and attention turned to cuts from more general (non-split) disjunctions.

anthesis

Disjunctive Cuts from the , -Polyhedral Representation,Given a disjunctive set in disjunctive normal form, i.e. as a union of polyhedra.

莎草

ethnology

Introvert

Egon BalasThe first and so far only book on this important subject.Written in a style accessible to all mathematically literate readers.The author is a famous expert in mathematical optimisation

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