عنوان

Matrices and Simplex Algorithms :

(Number (ISBN

940097941X

(Number (ISBN

9789400979413

Number

b593918

Title Proper

Matrices and Simplex Algorithms :

General Material Designation

[Book]

Other Title Information

a Textbook in Mathematical Programming and Its Associated Mathematical Topics

First Statement of Responsibility

by A.R.G. Heesterman.

Place of Publication, Distribution, etc.

Dordrecht

Name of Publisher, Distributor, etc.

Springer Netherlands

Date of Publication, Distribution, etc.

1983

Specific Material Designation and Extent of Item

(766 pages)

Text of Note

I Matrices, Block-Equations, and Determinants --; I / Equations-Systems and Tableaux --; II / Matrix Notation --; III / Block-Equations and Matrix-Inversion --; IV / Some Operators and Their Use --; V / Determinants and Rank --; II Graphs and Linear Programming --; VI / Vectors and Coordinate-Spaces --; VII / Some Basic Linear Programming Concepts --; VIII / Outline of the Simplex Algorithm --; IX / The Search for a Feasible Solution --; X / Mixed Systems, Upper and Lower Bounds --; XI / Duality --; XII / Linear Programming on the Computer --; XIII / Parametric Variation of the L.P. Problem --; III Some General Mathematical Programming Notions and Related Matrix Algebra --; XIV / Topology of Feasible Space Areas and its Relation to Definiteness --; XV / Optimality Conditions --; IV Quadratic Programming --; XVI / Quadratic Programming with Linear Restrictions --; XVII / Parametric Methods in Quadratic Programming --; XVIII / General Quadratic Programming --; V Integer Programming --; XIX / Integer Programming and Some of its Applications --; XX / Branching Methods --; XXI / The Use of Cuts --; References.

Text of Note

This is a textbook devoted to mathematical programming algorithms and the mathematics needed to understand such algorithms. It was mainly written for economists, but the mathematics itself obviously has relevance for other disciplines. It is a textbook as well a~ in parts, a contribution to new knowledge. There is, accordingly, a broad ordering of climbing sophistication, the earlier chapters being purely for the student, the later chapters being more specialist and containing some element of novelty on certain points. The book is edited in five parts. Part I deals with elementary matrix operations, matrix inversion, determinants, etc. Part II is mainly devoted to linear programming. As far as students' readability is concerned, these two parts are elementary undergraduate material. However, I would claim, in particular with respect to linear programming, that I do things more efficiently than the standard textbook approach has it. This refers mainly to the search for a feasible solution i.e. Chapter 9, and to upper and lower limits, i.e. Chapter 10. I have also argued that the standard textbook treatment of degeneracy misses a relevant problem, namely that of accuracy. In short, I would invite anyone who has the task of writing or designing an LP-code, to first acquaint himself with my ideas. viii INTRODUCTION Parts III and IV are concerned with nonlinear programming.

Matrices.

Programming (Mathematics)

Class number

Book number

by A.R.G. Heesterman.

A R G Heesterman

Electronic name

[Book]

Y