Author(s)  Book 

John.E. Dennis,
Jr.,
Rice University 6100 Main St. Houston, TX 770051892 (713) 5274094 Robert.B. Schnabel, University of Colorado at Boulder Department of Computer Science Boulder, CO 803090430 Phone: (303) 4927554 Email: bobby@cs.colorado.edu 
Numerical Methods for Unconstrained Optimization and Nonlinear Equations
PrenticeHall Inc., Englewood Cliffs, New Jersey 07632, (pp. xiii+377), 1983 ISBN 0136272169 Contents 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 Division, Harwell Laboratory, Oxfordshire A.M. Erisman Engineering Technology Applications Division Boeing Computer Services, Seattle John K. Reid Numerical Analysis, Computer Science and Systems Division, Harwell Laboratory, Oxfordshire 
Direct Methods for Sparse Matrices
Clarendon Press  Oxford, xiv + 341 pp, 1989 Oxford Science Publications ISBN 0198534213 (pbk) Contents:

Iliya I. Dikin.
Energy Systems Institute, 130 Lermontov street, Irkutsk, 664033, Russia. 
Determination of feasible and optimal solutions by the interior points method.
Nauka, Novosibirsk, 1998. 110 pp. ISBN 5020134536 Contents 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. References. 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 longterm 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. ISBN0387948333, DM 98, From the Contents The linear programming problem. Solving simple linear programs. The simplex method. Interiorpoint methods. Duality. Equivalent formulations. Price mechanism and sensitivity analysis. Transportation and assignment problem. Network flow theory. References 
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 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 secondorder equations 2.4. Aggregation of LF of subsystems 2.5. Algorithm of the interior points method 3. Methods of DecompositionAggregation 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. Blockdiagram of the program 4.3. Short instructions for users of the Region1 program 4.4. Text of the Region1 program 5. Conclusions References Contents 