Author(s) Book
John.E. Dennis, Jr.,
Rice University 
6100 Main St. 
Houston, TX 77005-1892 
(713) 527-4094 
Robert.B. Schnabel,
University of Colorado at Boulder 
Department of Computer Science 
Boulder, CO 80309-0430 
Phone: (303) 492-7554 
Numerical Methods for Unconstrained Optimization and Nonlinear Equations
Prentice-Hall Inc., Englewood Cliffs, New Jersey 07632, (pp. xiii+377), 1983 
ISBN 0-13-627216-9 
Contents  Preface 
1. Introduction 
2. Nonlinear Problems in one Variable 
3. Numerical Linear Algebra Background 
4. Multivariable Calculus Background 
5. Newton’s Method for Nonlinear Equations and Unconstrained Minimization 
6. Globally Convergent Modifications of Newton’s Method 
7. Stopping, Scalling, and Testing 
8. Secant Methods for Systems of Nonlinear Equations 
9. Secant Methods for Unconstrained Minimization 
10. Nonlinear Least Squares 
11. Methods for Problems with Special Structure 
Appendix A. A Modular System of Algorithms for Unconstrained Minimization and Nonlinear Equations (by Robert Schnabel) 
Appendix B. Test Problems (by Robert Schnabel) 
References, Author Index, Subject Index 
Iain S. Duff
Numerical Analysis,
Computer Science and Systems
Harwell Laboratory, Oxfordshire
A.M. Erisman
Engineering Technology Applications
Boeing Computer Services, Seattle
John K. Reid
Numerical Analysis,
Computer Science and Systems
Harwell Laboratory, Oxfordshire
Direct Methods for Sparse Matrices
Clarendon Press - Oxford, xiv + 341 pp, 1989
Oxford Science Publications
ISBN 0-19-853421-3 (pbk)

     Glossary of symbols
  1. Introduction
  2. Sparse matrices: storage schemes and simple operations
  3. Gaussian elimination for dense matrices: the algebraic problem
  4. Gaussian elimination for dense matrices: numerical 
  5. Gaussian elimination for sparse matrices: an introduction
  6. Reduction to block truiangular form
  7. Local pivotal strategies for sparse matrices
  8. Ordering sparse matrices to special forms
  9. Implementing Gaussian elimination: ANALYSE with numerical
10. Implementing Gaussian elimination with symbolic ANALYSE
11. Partitioning, matrix modification, and tearing
12. Other sparsity-oriented issues
    Appendix A: Matrix and vector norms
    Appendix B: The LINPACK condition number esdtimate
    Appendix C: Fortran conventions
    Appendix D: Pictures of sparse matrices
    Solutions to selected exercises
    Author index
    Subject index

Iliya I. Dikin.
Energy Systems Institute,
130 Lermontov street,
Irkutsk, 664033,
Determination of feasible and optimal solutions by the interior points method.
Nauka, Novosibirsk, 1998. 110 pp.
ISBN 5-02-013453-6
Contents Introduction.
1. Determination of an interior point of a system of linear constraints.
1.1. Problem statement.
1.2. An iterative algorithm.
1.3. Examples.
1.4. Technical results.
1.5. Study of consistent systems.
1.6. Analysis of the system inconsistency.
1.7. Main results.
1.8. Quadratic convergence rate of the sequence of dual estimates.
1.9. Proof of Lemma 1.3.
1.10.Limiting behavior of one sequence.
2. Ellipsoid of the affine scaling method.
2.1. Another strategy of determining the step value.
2.2. Proof of Lemma 2.1.
3. Mathematical programming problems with linear constraints.
3.1. Solution of a linear programming problem.
3.2. Fast correction problem of the electric power system.
3.3. Study of convergence.
3.4. Optimization of a smooth function.
3.5. Study of reliability of the electric power system using the method.
3.6. Minimization of Gibbs potential.
4. Nonlinear system of equalities and inequalities.
4.1. Problem statement.
4.2. An iterative algorithm.
4.3. Calculation of electric power system conditions
4.4. Forecasting of power consumption.
4.5. Local convergence.
4.6. Maximization of entropy.
5. Gradient method for determining the saddle point of the Lagrangian function.
5.1. Study of a linear programming problem.
5.2. Biological interpretation of the gradient method.
Abstract: The monograph presents results of studies on creation and substantiation of the effective algorithms for solving optimization problems, elaboration of the procedures for acceleration of computation process convergence. Global convergence of the method for determination of a relatively interior point of the set, prespecified by linear equalities and inequalities, is established. Analysis of the long-term application of the interior points method to practical problems of the electric utility industry, economy and other spheres is given. The book is intended for specialists dealing with the theory or application of the optimization methods.
Dantzig, G.B.,
Stanford University,
Stanford, CA, USA
Thapa, M.N.,
Mountain View, CA, USA
Linear Programming
Springer Verlag,
Springer Series in Operations Research.
1997. XXXVIII, 435 pp. 87 figs., diskette.
ISBN0-387-94833-3, DM 98,-
From the Contents Foreword.
The linear programming problem.
Solving simple linear programs.
The simplex method.
Interior-point methods.
Equivalent formulations.
Price mechanism and sensitivity analysis.
Transportation and assignment problem.
Network flow theory.
Iliya I. Dikin,
Lidiya.V. Shelkunova,
Valentin.P. Skibenko,
Nikolai.I. Voropai

Energy System Institute,
Siberian Branch,
Russian Academy of Sciences,
Irkutsk, Russia
A New Approach to Construction of Optimal Stability Regions of Electric Power Systems on the Base of Quadratic Lyapunov Functions
Energy Systems Institute,
Russian Academy of Sciences,
Irkutsk, Russia, 1999, pp.104
From the Contents Introduction
1. Problem of Electric Power System Stability
1.1. Electric power system and stability studies
1.2. Basic concepts of the method of Lyapunov functions
1.3. Method of Lyapunov functions in the studies of electric power system models
2. Construction of the Lyapunv Functions and the Estimates of Asymptotic Stability Regions
2.1. About quadratic forms
2.2. The optimal quadratic LF
2.3. LF for the system of second-order equations
2.4. Aggregation of LF of subsystems
2.5. Algorithm of the interior points method
3. Methods of Decomposition-Aggregation in Studies of Multimachine Electric Power Systems
3.1. A modified position model of electric power systems
3.2. Model M1
3.3. Model M2
3.4. Comparison of the models
3.5. Model M3
4. General Description of the "Region" Program
4.1. Structure of the software
4.2. Block-diagram of the program
4.3. Short instructions for users of the Region1 program
4.4. Text of the Region1 program
5. Conclusions