Linear programming: mathematics, theory and algorithms
type: Item
instance of: scholarly article
title: Linear programming: mathematics, theory and algorithms
zbMATH Open document ID: 0870.90082
author: Michael J. Panik
published in: Applied Optimization
publication date: 1996-08-26T00:00:00Z
review text: The purpose of this book is to present to the students the salient features of the theory and computational aspects of linear programming. Linear programming is one of the most versatile and powerful mathematical programming techniques that can be employed for efficiently solving a stylized class of decision problems of the form \[ \max f(X)=C'X\quad\text{subject to } AX\leq b,\quad X\geq 0, \] where \(C\), \(X\in \mathbb{R}^p\), \(b\in\mathbb{R}^m\), \(A\) is a matrix of order \((m\times n)\), and a prime denotes transposition. The book has 14 chapters: Chapter 1: Introduction and overview; Chapter 2: Preliminary mathematics; Chapter 3: Introduction to linear programming; Chapter 4: Duality theory; Chapter 5: The theory of linear programming; Chapter 6: Duality theory revisited; Chapter 7: Computational aspects of linear programming; Chapter 8: One-phase, two-phase, and composite methods of linear programming; Chapter 9: Computational aspects of linear programming: selected transformation; Chapter 10: The dual simplex, primal-dual, and complementary pivot methods; Chapter 11: Postoptimality analysis I; Chapter 12: Postoptimality analysis II; Chapter 13: Interior point methods; Chapter 14: Interior point algorithms for solving linear complementarity problems. The bibliography contains 155 items. Chapter 2 reviews the mathematical tools needed to study linear programming. Chapter 3 presents the canonical and standard forms of a linear programming problem and the concepts of feasibility and optimality. In chapter 4, the fundamental theorems of linear programming, namely the weak duality theorem, the strong duality theorem, the existence theorem, and weak and strong complementary slackness theorems are discussed. Chapter 5 presents the primal simplex method for solving linear programming problems. In chapter 6, duality theory revisited (the geometry of duality and optimality and Lagrangean saddle-points) is discussed. Chapter 7 deals with the computational aspepts of l…
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 90-02
zbMATH DE Number: 920117
zbMATH Keywords: duality
zbMATH Keywords: postoptimality analysis
zbMATH Keywords: interior point methods
zbMATH Keywords: simplex
reviewed by: Dorel I. Duca
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 920117