Applications of discrete mathematics

127

Book Announcements

Uniform

Perfectness.

a Solution cedure.

Theory

GAME-THEORETIC RATIONALITY. Payoff

Based Solely on Risk Dominance

The Role of Strategic

J.L. Nazareth, Oxford, 1987)

Net Distance.

Computer

Solution

Possible

timality.

Associating

Method.

The Simplex Method

Multipliers

tion. The Simplex Method: Complexity External

Problem.

on the Canonical

Form.

Algebraic

Program.

Internal

Representation

4: The Basis Matrix:

Numerical

Number

Representation.

Analysis

of Op-

Column-Oriented 3: Problem Program.

of Numerical

of Basic Arithmetic

Descrip-

Convergence

of a Linear

Fundamentals

The Diet Pro2: The Simplex

Simplex Algorithm.

PART II: PRACTICAL ASPECTS. Chaper

Chapter

Pro-

Press,

Characterization Chapter

The Simplex Method:

Details of Implementation. Linear Algebra.

University

and Their Solution.

Interpretation.

The Primal

Would

and the Tracing

(Oxford

Geometry. Their

Description.

Simplex Algorithm. of a Linear

and

Priors

to Our Theory.

1: Linear Programs

a Vertex

Row-Oriented

of the Primal Representation

with

Refinements

The Underlying

and Risk Dominance.

Bicentric

of Linear Programs

PART 1: BASIC THEORY AND METHOD. Chapter blem. The Linear Programming

Dominance

be Preferable?

and Setup.

Practical

Computation

Operations.

and

Analysis

of Sequences of Arithmetic Operations and Attendant Difficulties. Analysis of Algorithms. Theory and Stability of Problems. Summary. Chapter 5: The Basis Matrix: Factorizing

Perturbation and Solving.

Prerequisites.

Interchanges.

Pivoting

The LU Factorization.

Strategies

During

LU Factorization.

Computed

Solution.

Basis Matrix: Golub

to Ensure Variants

Practical

Exiting

Variables.

Choosing

the Exiting

Chapter gramming

Issues. Systems.

Chapter

7: Selection

Update.

Strategies. Chapter

When

Choosing the Basis

the Entering

10: Mathematical

Model Specification

Method.

timality

Conditions

Programming

Systems The Linear

Details

of Implementation.

troduction.

Algorithm.

Chapter

Decomposition

tions. Variants. Chapter

The Diet Problem

Numerical

Behavior

Practical

Details

with Row Partitions. of Decomposition

Principle

binatorial

and

and the Simplex

Ringeisen and Fred (SIAM, Philadelphia,

Results

Geometry

Principle

Method.

of Updates

and

the Entering

and

Details

the Exiting

Variable Finding

of Implementation.

in Practice.

Theory.

Sensitivity

Practical

PART

Principle

Ties to Op-

Analysis.

and the Simplex Method

ImPro-

Optimizer.

11: The Duality

and Duality

Introduction.

Further

Mathematical

Programming

Decomposition

Algorithms.

Sequences Choosing

Practical

Method.

with Column

InParti-

Details of Implementation. The Self-Dual

Simplex

of Implementation.

PART 1: PLENARV SESSIONS. The

Methods

Dual Programs

6: The

The Bartels-

Simplex Algorithm.

Solving the Dual Program.

12: The Decomposifion

Method

13: The Homotopy

Richard D. Mathematics

Revisited.

Chapter

When the Basis Is Infeasible.

Practical

of the Primal

and Interpretation.

and Simplex Algorithms.

of the

Choosing

III: OPTIMIZAXON PRINCIPLE + SIMPLEX METHOD = LP ALGORITHM. Chapter

and the Simplex

Fill-in

The Accuracy

8: Selection Strategies:

Variable

Is Infeasible.

An Implementation

to Control

the LU Factors.

Strategies:

Selection

9: Practical Implementation.

plementation

Updating

Details of Implementation.

Background.

Variable

of Equations.

The Fletcher-Matthews

Variable.

Column

Strategies

Details of Implementation.

Form Update.

Chapter

the Entering Practical

an Initial Feasible Solution. Choosing

Update.

Pivoting

Systems

Practical

The Product

Details of Implementation.

When the Basis Is Feasible.

Solving

on LU Factorization.

The Forrest-Tomlin

Solving.

Strategies.

and Solving.

with Row and/or

of the LU Factorization.

Combined

Updating

Update.

The LU Factorization

Stability

in Cryptography (Paul Erd6s).

S. Roberts, eds., Applications PA, 1988) 230 pages

of

Cryptanalysis of Knapsack Cryptosystems (Ernest F. (Don Coppersmith). Some Old and New Problems

A Survey

of Applications

of Operations

Research

Discrete

Brickell). in Com-

in the Airline

In-

dustry Jr.).

(Kevin K. Gillette). Recent

Results

“Locator’s”

Interval

Graphs,

in the Theory

Dilemma

(Christoph

Interval

of Random

J. Witzgall

Orders, Orders

and Patsy

Bienstock).

McCullers Provan

Probabilistic

Analysis

and R. Kevin Wood).

and Michael

of Fault

Efficient

0. Ball). Algebraic

Aspects

Chemical Graph Theory. Facile Calculation Grahps

in

Dynamic

TcpalagicaI in Graphs

Systems.

&dices (Dennis

(R.

of Computing

King).

(W.T.

Electronic

Pivotal

Network

Reliability

(Jerry

Characterization

(D.W. Bange, A.E. Barkauskas

and P.J. Slater).

&he

(Douglas

Ray Dias).

Recent Problems

T.

(J. Scott R. Shier).

Signed

of Molecular

Graphs

(William

Systems

Directed

Branching

Top&s on Domirtaf
H. Rauvray).

and

of Halin

Decomposition

and 2-Monotonic

Eigenvalues

Trotter,

Mail

PART II: MINISYMPOSIA. Com-

of Generalizations

Using

of Matroid

of Graph

Bruce

Analysis

Trees

Recognition

Winkler).

B. Saunders).

binatorial Aspects of Network Reliability. On Reliability (Daniel

and Their Generalizations (Peter

Using

Daminating

and Results about

Sets Kernels

in Directed Graphs (C. Berge and P. Duchet). Recent Results and Open Problems in Domination Theory (S.T. Hedetniemi and R. Laskar). PART Ill: OPEN PROBLEMS. Problem Session (D.J. Kleitman). PART IV: LIST OF PRESENTEDPAPERS.

Gerard Hegron,

Image Synthesis:

Elementary

Algorithms

(MIT Press, Cambridge,

MA, 1988) 216 pages Chapter 1: General Problems of Elementary Processing in Image Synthesis. Algorithms processing.

Image information.

Codifying

the image.

Gtener ation on n Surf ace r$ Dots. \nQo&&cn. of straight G~x?&xI,

line segments. -Z 4cq-fi&1&.

C(olouim_e. polygaual

Zone zaues.

Classifying segment

Generation

cutout

Generation

of ellipses.

<~Qx^J&, 4& -ir,%vc*i?~+.alar+&+??,

Co nc&ia

Comparison

contour.

window.

03 po>ysonal

methohs.

Generation

Generailon

of parabolas.

. ,3l&iYZ7 I;. Z-&%5~,%ii~. ~~r~Y??~~X!?YI,.

zones

‘m’lo sjmple

of a point and a polygonal

Using a polygonal

Cutting

and elementary

Chapter 2: Curve

&emems.

Cross-hatc%jns

4: CU?OUCAlgariTkrns and Geometric Processing. Introduction.

ct. Ck@er

problems.

in image synthesis.

GeneTti c~a~~~~~~a~%sn. IntTementa\

of circles.

‘ill’n_e. Decompo3~on

with a polygonal

using a polygonal c~oncsuslDJI.

Processing

window

contour.

Cutting

to cut out a polygon.

out of one zone by another.

Generalization

out a straight Cutting

to non-polygonal

zones.

Anthony L. Peressini, Francis E. Sullivan and J.J. Uhl Jr, The Mathematics Nonlinear Programming (Springer, Berlin, 1988) 273 pages Chapter 1: Unconstrained Optimization via Calculus. Functions variables.

Positive

minimizers. Convex functions.

and

Eigenvalues

sets.

Some

negative

and positive

illustrations

Convexity

definite

and

matrices

definite

of convex

and

of one variable.

optimization.

Coercive

of

of several and

global

Chapter 2: Convex Sets and Convex Functions.

matrices.

sets in economics-Linear

the arithmetic-geometric

Functions functions

line

out a zone

mean

production

inequality-An

models.

introduction

Convex

to geometric

programming. Unconstrained geometric programming. Convexity and other inequalities. Chapter 3: Iterative Methods for Unconstrained Optimization. Newton’s method. The method of steepest descent. Beyond steepest descent. Broyden’s method. Secant methods for minimization. Chnpler 4: Leasf Squares Optimization. Least squares fit. Subspaces and projections. Minimum norm solutions of underde&s&r&

9ic-u. ‘~~%%xz.

‘,-VA&Trrcr~pxGi-m% %im!~‘mm~-; &I%~mak Gkmrakzc-,

Convex Programming and the Karush-Kuhn-Tucker Convex .Drogramtij,n2.:

canvex

sns.

theorem

and constrajned

geometrjc

Conditions. Separation

%he Xarush-X-in-7 programmjng.

Dual

ucker convex

$9x&m.. c%&‘q*- I :

and support

theorems

for

%heoTem. The Xarush-Xuhn-Tucker programs.

Trust re.gions.

CYzapfer 6:

Penalty Methods. Penalty functions. The penalty method. Applications of the penalty function method to convex programs. Chapter 7: Optimization with Equality Constraints. Surfaces and their tangent