With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence, and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids, and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.

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Iterative methods in combinatorial optimization

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Elements of C*-algebras commuting with their Moore-Penrose inverse

Efficient Hybrid-EAS solid element for accurate stress prediction in thick laminated beams, plates, and shells

Characterizations of EP matrices and weighted-EP matrices

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m,n)-injective in case every right R-homomorphism from an n-generated submodule of Rm to M extends to one from Rm to M. R is said to be left (m,n)-coherent if each n-generated submodule of the left R-module Rm is finitely presented. In this paper, we give some new characterizations of (m,n)-injective modules. We also derive various equivalent conditions for a ring to be left (m,n)-coherent. Some known results on coherent rings are obtained as corollaries.

On (m,n)-Injective Modules and (m,n)-Coherent Rings

Polygons, Circulant Matrices, and Moore-Penrose Inverses

(1986). Does the Generalized Inverse of A Commute with A? Mathematics Magazine: Vol. 59, No. 4, pp. 230-232.

https://www.jstor.org/stable/info/2690317

Does the Generalized Inverse of A Commute with A

Involutory functions and Moore-Penrose inverses of matrices in an arbitrary field

(1960). Row Rank and Column Rank of a Matrix. Mathematics Magazine: Vol. 34, No. 1, pp. 33-34.

Edward T. Wong

Papers

Polygons, Circulant Matrices, and Moore-Penrose Inverses

Does the Generalized Inverse of A Commute with A

Involutory functions and Moore-Penrose inverses of matrices in an arbitrary field

Row Rank and Column Rank of a Matrix