A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems

Hanif D. Sherali, W. P. Adams (Autoren)

Buch | Softcover

518 Seiten

2010 | Softcover reprint of the original 1st ed. 1999
Springer-Verlag New York Inc.
978-1-4419-4808-3 (ISBN)

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This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation.

1 Introduction.- I Discrete Nonconvex Programs.- 2 RLT Hierarchy for Mixed-Integer Zero-One Problems.- 3 Generalized Hierarchy for Exploiting Special Structures in Mixed-Integer Zero-One Problems.- 4 RLT Hierarchy for General Discrete Mixed-Integer Problems.- 5 Generating Valid Inequalities and Facets Using RLT.- 6 Persistency in Discrete Optimization.- II Continuous Nonconvex Programs.- 7 RLT-Based Global Optimization Algorithms for Nonconvex Polynomial Programming Problems.- 8 Reformulation-Convexification Technique for Quadratic Programs and Some Convex Envelope Characterizations.- 9 Reformulation-Convexification Technique for Polynomial Programs: Design and Implementation.- III Special Applications to Discrete and Continuous Nonconvex Programs.- 10 Applications to Discrete Problems.- 11 Applications to Continuous Problems.- References.

Erscheint lt. Verlag	2.12.2010
Reihe/Serie	Nonconvex Optimization and Its Applications ; 31
Zusatzinfo	XXIV, 518 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Theorie / Studium ► Algorithmen
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Mathematik / Informatik ► Mathematik ► Graphentheorie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	1-4419-4808-2 / 1441948082
ISBN-13	978-1-4419-4808-3 / 9781441948083
Zustand	Neuware