Linear and combinatorial optimization in ordered algebraic structures. (English) Zbl 0466.90045

Zimmermann, U.

Annals of Discrete Mathematics 10, 380 p. (1981).

MSC:

90C48	Programming in abstract spaces
06Fxx	Ordered structures
90-02	Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
05C35	Extremal problems in graph theory
90C05	Linear programming
06B99	Lattices
20M14	Commutative semigroups
90C09	Boolean programming
90C10	Integer programming
90B10	Deterministic network models in operations research
90C35	Programming involving graphs or networks
05B35	Combinatorial aspects of matroids and geometric lattices
05B40	Combinatorial aspects of packing and covering
05C05	Trees
05C25	Graphs and abstract algebra (groups, rings, fields, etc.)
05C30	Enumeration in graph theory
05C38	Paths and cycles
05C50	Graphs and linear algebra (matrices, eigenvalues, etc.)
05C70	Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)

Keywords:

combinatorial optimization; algebraic optimization; semigroups; semirings; semimodules; ordered algebraic systems; lattices; graph theory; matroid theory; duality; stability of matrices; algebraic path problems; algebraic flow problems; independence systems; algebraic matching problems; maximum spanning tree; greedy method; branch and bound method; relaxations