1.
図書
edited by Isaac Elishakoff
2.
図書
by Vladimir Fomin
目次情報:
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Preface
Fields and means of describing them / 1：
Models of continuous fields and associated problems / 2：
Filtering of spatio-temporal fields / 3：
Optimal filtering of discrete homogeneous fields / 4：
Fields in electrodynamics / A Appendix：
Spectral analysis of time series / B Appendix：
Spectral analysis of discrete homogeneous fields / C Appendix：
References
Notation
Index
Preface
Fields and means of describing them / 1：
Models of continuous fields and associated problems / 2：
3.
図書
Jiongmin Yong, Xun Yu Zhou
4.
図書
C.T. Kelley
目次情報:
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Preface
How to Get the Software
Optimization of Smooth Functions / Part I：
Basic Concepts / Chapter 1：
Local Convergence of NewtonG++s Method / Chapter 2：
Global Convergence / Chapter 3：
The BFGS Method / Chapter 4：
Simple Bound Constraints / Chapter 5：
Optimization of Noisy Functions / Part II：
Basic Concepts and Goals / Chapter 6：
Implicit Filtering / Chapter 7：
Direct Search Algorithms / Chapter 8：
Bibliography
Index
Preface
How to Get the Software
Optimization of Smooth Functions / Part I：
5.
図書
H.O. Fattorini
目次情報:
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Finite Dimensional Control Problems / Part I：
Calculus of variations and control theory / 1：
Optimal control problems without target conditions / 2：
Abstract minimization problems: the minimum principle for the time optimal problem / 3：
Abstract minimization problems: the minimum principle for general optimal control problems / 4：
Infinite Dimensional Control Problems / Part II：
Differential equations in Banach spaces and semigroup theory / 5：
Abstract minimization problems in Hilbert spaces: applications to hyperbolic control systems / 6：
Abstract minimization problems in Banach spaces: abstract parabolic linear and semilinear equations / 7：
Interpolation and domains of fractional powers / 8：
Linear control systems / 9：
Optimal control problems with state constraints / 10：
Optimal control problems with state constraints: The abstract parabolic case / 11：
Relaxed Controls / Part III：
Spaces of relaxed controls: topology and measure theory / 12：
Relaxed controls in finite dimensional systems: existence theory / 13：
Relaxed controls in infinite dimensional spaces: existence theory / 14：
Finite Dimensional Control Problems / Part I：
Calculus of variations and control theory / 1：
Optimal control problems without target conditions / 2：
6.
図書
G.E. Kolosov
7.
図書
Naum Z. Shor
8.
図書
Miguel A. Goberna and Marco A.López
9.
図書
by E.S. Mistakidis and G.E. Stavroulakis
10.
図書
by Hoang Tuy
11.
図書
Ivan Singer
目次情報:
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Abstract Convexity of Elements of a Complete Lattice
Abstract Convexity of Subsets of a Set
Abstract Convexity of Functions on a Set
Abstract Quasi-Convexity of Functions on a Set
Dualities Between Complete Lattices
Dualities Between Families of Subsets
Dualities Between Sets of Functions
Conjugations. (-Dualities and <$$$>-Dualities
Abstract Subdifferentials
Notes and Remarks
References
Indexes
Abstract Convexity of Elements of a Complete Lattice
Abstract Convexity of Subsets of a Set
Abstract Convexity of Functions on a Set
12.
図書
Robert J. Vanderbei
13.
図書
A.A. Milyutin, N.P. Osmolovskii
目次情報:
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First order conditions: First order conditions
Theory of a weak minimum for the problem on a fixed time interval
Theory of the maximum principle
Extremals and the Hamiltonian of a control system
Hamilton-Jacobi equation and field theory
Transformations of problems and invariance of extremals
Quadratic conditions: Quadratic conditions and conjugate points for broken extremals
Quadratic conditions for a Pontryagin minimum and sufficient conditions for a strong minimum: Proofs
Quadratic conditions in the general problem of the calculus of variations and related optimal control problems
Investigation of extremals by quadratic conditions: Examples
Bibliography
First order conditions: First order conditions
Theory of a weak minimum for the problem on a fixed time interval
Theory of the maximum principle
14.
図書
by Vladimir Fomin
15.
図書
Joseph E. Yukich
16.
図書
Elijah Polak
17.
図書
Tomáš Roubiček
18.
図書
東工大
by Hiroshi Konno, Phan Thien Thach, Hoang Tuy
目次情報:
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PREFACE
Part I FOUNDATIONS 1
1 SCOPE OF GLOBAL OPTIMIZATION 3
1.1 Models and Nature of the Problem 4
1.2 Mathematical Structure 10
1.3 Hierarchy of Global Optimization Problems 13
1.4 Transcending Stationarity as the Core of Global Optimization 15
1.5 Problems With Special Structures 18
2 QUASI-CONVEXITY 23
2.1 Quasi-Convex Functions 24
2.2 Quasi-conjugacy 30
2.3 Quasi-biconjugate 39
2.4 Quasi-subdifferential 43
3 D.C. FUNCTIONS AND D.C. SETS 47
3.1 Some Typical Examples 47
3.2 General Properties of D.C. Functions 50
3.3 How to Recognize D.C. Functions 52
3.4 Effective D.C. Representation 56
3.5 D.C. Sets 67
3.6 Global Optimality Criterion 72
4 DUALITY 77
4.1 Quasi-convex Minimization over a Convex Set 78
4.2 Maximization over a Convex Set and Minimization over the Complement of a Convex Set 85
4.3 D.C. Optimization 93
5 LOW-RANK NONCONVEX STRUCTURES 95
5.1 Nonconvexity Rank 96
5.2 Nonconvexity Index 100
5.3 Weakly Convex Functions 108
5.4 D.C. Representation by a Nucleus 113
6 GLOBAL SEARCH METHODS AND BASIC D.C. OPTIMIZATION ALGORITHMS 119
6.1 Outer Approximation 119
6.2 Successive Partition 130
6.3 Dualization 155
Part II METHODS AND ALGORITHMS 167
7 PARAMETRIC APPROACHES IN GLOBAL OPTIMIZATION 169
7.1 Minimization of a Generalized Linear Multiplicative Function and a Sum of Two Linear Fractional Functions 170
7.2 Rank Two and Rank Three Bilinear Programming Problems 177
7.3 Average Performance of Parametric Algorithms 184
7.4 Minimization of Low-Rank Concave Functions 191
8 MULTIPLICATIVE PROGRAMMING PROBLEMS 203
8.1 Convex Multiplicative Programming Problems 204
8.2 Minimization of a Product of Several Convex Functions 213
8.3 Other Problems Related to Multiplicative Functions 220
9 MONOTONIC PROBLEMS 229
9.1 Quasiconcave Monotonic Functions 230
9.2 Basic Structural Properties 234
9.3 Linearly Constrained Problems 240
9.4 Solution Methods for Monotonic Problems 244
9.5 Decomposition by Polyhedral Annexation 247
9.6 Decomposition by Projection 252
9.7 Problems With Monotonic Constraints 258
9.8 Cases of Polynomial Solvability: Network Constraints 264
10 DECOMPOSITION METHODS BY PRICES 273
10.1 Generalized Dantzig-Wolfe's Decomposition Method 274
10.2 Generalized Benders' Partitioning Method 283
10.3 Alternative Variant 291
11 DYNAMIC PROGRAMMING ALGORITHMS IN GLOBAL OPTIMIZATION 297
11.1 Multi-Echelon Production and Inventory Problem 298
11.2 Lot-Sizing Problems with Generalized Concave Cost Functions 303
11.3 Discrete-Variable Multi-Stage Problems 310
Part III SELECTED APPLICATIONS 323
12 LOW RANK NONCONVEX QUADRATIC PROGRAMMING 325
12.1 Concave Quadratic Programming Problems and Bilinear Programming Problems 326
12.2 Low Rank Concave Quadratic Programming Problems 331
12.3 Low Rank Bilinear Programming Problems 343
12.4 General Low Rank Nonconvex Quadratic Programming Problems 349
13 CONTINUOUS LOCATION 353
13.1 Unconstrained Location Problems 354
13.2 Solving Unconstrained Location Problems 362
13.3 Constrained Location Problems 367
13.4 Solving General Constrained Location Problems 371
14 DESIGN CENTERING AND RELATED GEOMETRIC PROBLEMS 375
14.1 Design Centering 375
14.2 Related Geometric Problems 389
15 MULTIOBJECTIVE AND BILEVEL PROGRAMMING 397
15.1 Optimization over the Efficient Set 398
15.2 Bilevel Linear Programming 408
15.3 Relationship between Monotonic, Multiobjective and Bilevel Programming 423
REFERENCES 427
INDEX 455
PREFACE
Part I FOUNDATIONS 1
1 SCOPE OF GLOBAL OPTIMIZATION 3
19.
図書
Immanuel M. Bomze ... [et al.]
目次情報:
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Preface
NOP - A Compact Input Format for Nonlinear Optimization Problems / A. Neumaier1：
GLOPT - A Program for Constrained Global Optimization / S. Dallwig, et al.2：
Global Optimization for Imprecise Problems / M.N. Vrahatis, et al.3：
New Results on Gap-Treating Techniques in Extended Interval Newton Gauss-Seidel Steps for Global Optimization / D. Ratz4：
Quadratic Programming with Box Constraints / P.L. De Angelis5：
Evolutionary Approach to The Maximum Clique Problem: Empirical Evidence on a Larger Scale / I. Bomze, et al.6：
Interval and Bounding Hessians / C. Stephens7：
On Global Search for Non-Convex Optimal Control Problems / A. Strekalovsky ; I. Vasiliev8：
A Multistart Linkage Algorithm Using First Derivatives / C.J. Price9：
Convergence Speed of an Integral Method for Computing the Essential Supremum / J. Hichert, et al.10：
Complexity Analysis Integrating Pure Adaptive Search (PAS) and Pure Random Search (PRS) / Z.B. Zabinsky ; B.P. Kristinsdottir11：
LGO - A Program System for Continuous and Lipschitz Global Optimization / J.D. Pintèr12：
A Method Using Local Tuning For Minimizing Functions with Lipschitz Derivatives / Ya.D. Sergeyev13：
Molecular Structure Prediction by Global Optimization / K.A. Dill, et al.14：
Optimal Renewal Policy for Slowly Degrading Systems / A. Pfening ; M. Telek15：
Numerical Prediction of Crystal Structures by Simulated Annealing / W. Bollweg, et al.16：
Multidimensional Optimization in Image Reconstruction from Projections / I. Garciacute;a, et al.17：
Greedy Randomized Adaptive Search for a Location Problem with Economies of Scale / K. Holmqvist, et al.18：
An Algorithm for Improving the Bounding Procedure in Solving Process Network Synthesis by a B&B Method / B. Imreh, et al.19：
Preface
NOP - A Compact Input Format for Nonlinear Optimization Problems / A. Neumaier1：
GLOPT - A Program for Constrained Global Optimization / S. Dallwig, et al.2：
20.
図書
by Diethard Pallaschke and Stefan Rolewicz
21.
図書
edited by Reiner Horst and Panos M. Pardalos
22.
図書
by A.G. Kusraev, S.S. Kutateladze
23.
図書
Roman B. Statnikov, Joseph B. Matusov
出版情報:
New York : Chapman & Hall, c1995 xiv, 236 p. ; 24 cm
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24.
図書
E.G. Golshtein and N.V. Tretyakov ; translated by N.V. Tretyakov
目次情報:
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Introduction to Convex Analysis
Modified Lagrangian Functions for Convex Programming Problems
Dual Methods
Monotone Maps
Gradient-Type Methods and Modification of a Monotone Map
Saddle Gradient Methods
Modified Lagrangian Functions for Smooth Mathematical Programming Problems and Related Dual Methods
Bibliographic Comments
References
Index
Introduction to Convex Analysis
Modified Lagrangian Functions for Convex Programming Problems
Dual Methods
25.
図書
Vadim F. Krotov
目次情報:
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Control Processes
Optimal Control
Problem Bounding and Solving
Functions Sufficient Conditions of Optimality
Some Special Optimal Control Problems
Direct Application of the Sufficient
Optimality Conditions
Sufficient Optimality Conditions and Basic Equations of the Variational Calculus and Optimal
Control Theory
Optimal Feeback Policy Hamilton-Jacobi Method Computer Methods for Successive
Improvements in a ControlProgram Dual Computational
Algorithms for Solving and Optimizing of
Control Processes
Optimal Control
Problem Bounding and Solving
26.
図書
edited by Ding-Zhu Du and Panos M. Pardalos
27.
図書
edited by Roberto Lucchetti and Julian Revalski
28.
図書
by Reiner Horst, Panos M. Pardalos, and Nguyen V. Thoai
29.
図書
Gennadii A. Mikhailov ; translated by Karl K. Sabelfeld
30.
図書
E.N. Chukwu
31.
図書
Marko M. Mäkelä and Pekka Neittaanmäki
出版情報:
Singapore ; New Jersey : World Scientific, c1992 xii, 254 p. ; 23 cm
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32.
図書
by Anatoly A. Zhigljavsky ; edited by J. Pintér
33.
図書
Tamer Bașar, Pierre Bernhard
出版情報:
Boston : Birkhäuser, 1991 xii, 224 p. ; 25 cm
シリーズ名:
Systems & control
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34.
図書
V.M. Tikhomirov ; translated from the Russian by Abe Shenitzer
出版情報:
Providence, R.I. : American Mathematical Society, c1990 xi, 187 p. ; 26 cm
シリーズ名:
Mathematical world ; v. 1
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Ancient maximum and minimum problems / Part 1：
Why do we solve maximum and minimum problems?
The oldest problem-Dido's problem Maxima and minima in nature ( optics$)$
Maxima and minima in geometry
Maxima and minima in algebra and in analysis Kepler's problem
The brachistochrone Newton's aerodynamical problem
Methods of solution of extremal problems / Part 2：
What is a function?
What is an extremal problem?
Extrema of functions of one variable
Extrema of functions of many variables
Lagrange's principle More problem solving
What happened later in the theory of extremal problems?
More accurately, a discussion
Ancient maximum and minimum problems / Part 1：
Why do we solve maximum and minimum problems?
The oldest problem-Dido's problem Maxima and minima in nature ( optics$)$
35.
図書
Mario Fedrizzi, Janusz Kacprzyk, Marc Roubens, (eds.)
36.
図書
K.L. Teo, C.J. Goh, and K.H. Wong
37.
図書
Peter Whittle
38.
図書
edited by H.J. Sussmann
目次情報:
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Synthesis, presynthesis, sufficient conditions for optimality and subanalytic sets / H. J. Sussmann
upper and lower semicontinuous differential inclusions - a unified approach / Alberto Bressan
global controllability by nice controls / Kevin A. Grasse
integrability of certain distributions associated with actions on manifolds and applications to control problems / Eduardo D. Sontag
right and left invertibility of nonlinear control systems / Witold Respondek
Bressan
Synthesis, presynthesis, sufficient conditions for optimality and subanalytic sets / H. J. Sussmann
upper and lower semicontinuous differential inclusions - a unified approach / Alberto Bressan
global controllability by nice controls / Kevin A. Grasse
39.
図書
Brian D.O. Anderson, John B. Moore
40.
図書
Leslie M. Hocking
目次情報:
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Optimal control problems; Systems of differential equations, matrices, and sets
Time-Optimal Control of Linear Systems: Controllability / Part A：
Time-optimal control
Further examples
The Pontryagin Maximum Principle: The basic Pontryagin Maximum Principle (PMP) / Part B：
Extensions to the PMP
Linear state equations with quadratic costs
Proof of the Pontryagin Maximum Principle
Further applications and extensions
Applications of Optimal Control Theory: Some applied optimal control problems / Part C：
Numerical methods for optimal control problems
Bibliography
Outline solutions to the exercises
Index
Optimal control problems; Systems of differential equations, matrices, and sets
Time-Optimal Control of Linear Systems: Controllability / Part A：
Time-optimal control
41.
図書
C.A. Floudas, P.M. Pardalos
42.
図書
with foreword by Wassily Leontief ; edited by Lev J. Leifman
出版情報:
New York : Oxford University Press, 1990 xiv, 341 p. ; 25 cm
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目次情報:
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Academician L. V. Kantorovich (19 January 1912 to 7 April 1986) / V. L. Markarov ; S. L. Sobolev1.：
My Journey in Science (Supposed Report to the Moscow Mathematical Society) / L. V. Kantorovich2.：
Silver Medal / J. V. Rosenhead ; Natalie Iljina-Kantorovich3.：
On L. V. Kantorovich's Research in the Field of Computer Architecture / Ya. I. Fet4.：
On Special Representations of Polynomials that are Positive on a System of Closed Intervals, and Some Applications / M. G. Krein ; B. Ya. Levin ; A. A. Nudel'Man5.：
New Possibilities of K-spaces / S. S. Kutateladze6.：
The Integral Representability of Extended Functionals on Vector Lattices and Cones / A. I. Veksler7.：
When Each Continuous Operator Is Regular / Yuri A. Abramovich8.：
General Monge-Kantorovich Problem and Its Applications in Measure Theory and Mathematical Economics / V. L. Levin9.：
A Lagrangian Transportation Problem Relaxation Method for Solving Problem A of L. V. Kantorovich / G. L. Thompson10.：
Some Numerical and Practical Problems in Linear Programming / Horst Hollatz11.：
Totally Positive Linear Programming Problems / Andras Prekopa12.：
Minimum Norm Solution to the Linear Complementarity Problem / J. B. Rosen13.：
Least Norm Solution of Nonmonotone Linear Complementarity Problems / O. L. Mangasarian14.：
A Case for Interactive Multiobjective Linear Programming / Moshe Dror ; Saul I. Gass15.：
On Duality Results in Nonconvex Optimization / K.-H. Elster16.：
On Polyhedral Annexation Method for Concave Minimization / Hoang Tuy17.：
Combinatorial Optimization: Accuracy Versus Complexity and Stability / Lev J. Leifman18.：
On the Core of the Assignment Game / M. L. Balinski ; David Gale19.：
Fields of Convex Polyhedra and the Pareto-Smale Optimum / A. M. Vershik ; A. G. Chernyakov20.：
Optimal Patterns of Capital Accumulation and External Indebtness in a Two-Sector Model of Economic Growth / H. Uzawa21.：
About the Authors
Index
Academician L. V. Kantorovich (19 January 1912 to 7 April 1986) / V. L. Markarov ; S. L. Sobolev1.：
My Journey in Science (Supposed Report to the Moscow Mathematical Society) / L. V. Kantorovich2.：
Silver Medal / J. V. Rosenhead ; Natalie Iljina-Kantorovich3.：
43.
図書
by J. Guddat, F. Guerra Vazquez, with H. Th. Jongen
出版情報:
Stuttgart : B. G. Teubner , Chichester ; New York : J. Wiley & Sons, c1990 viii, 191 p. ; 24 cm
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44.
図書
Dan Tiba
45.
図書
Uwe Helmke and John B. Moore ; with a foreword by R. Brockett
46.
図書
P. Neittaanmäki, D. Tiba
47.
図書
J.L. Nazareth
48.
図書
edited by Ding-Zhu Du and Jie Sun
49.
図書
Stephen Boyd ... [et al.]
目次情報:
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Preface
Introduction / 1：
Overview
A Brief History of LMIs in Control Theory
Notes on the Style of the Book
Origin of the Book
Some Standard Problems Involving LMIs / 2：
Linear Matrix Inequalities
Some Standard Problems
Ellipsoid Algorithm
Interior-Point Methods
Strict and Nonstrict LMIs
Miscellaneous Results on Matrix Inequalities
Some LMI Problems with Analytic Solutions
Some Matrix Problems / 3：
Minimizing Condition Number by Scaling
Minimizing Condition Number of a Positive-Definite Matrix
Minimizing Norm by Scaling
Rescaling a Matrix Positive-Definite
Matrix Completion Problems
Quadratic Approximation of a Polytopic Norm
Ellipsoidal Approximation
Linear Differential Inclusions / 4：
Differential Inclusions
Some Specific LDIs
Nonlinear System Analysis via LDIs
Analysis of LDIs: State Properties / 5：
Quadratic Stability
Invariant Ellipsoids
Analysis of LDIs: Input/Output Properties / 6：
Input-to-State Properties
State-to-Output Properties
Input-to-Output Properties
State-Feedback Synthesis for LDIs / 7：
Static State-Feedback Controllers
State Properties
Observer-Based Controllers for Nonlinear Systems
Lur+1/4 and Multiplier Methods / 8：
Analysis of Lur+1/4 Systems
Integral Quadratic Constraints
Multipliers for Systems with Unknown Parameters
Systems with Multiplicative Noise / 9：
Analysis of Systems with Multiplicative Noise
State-Feedback Synthesis
Miscellaneous Problems / 10：
Optimization over an Affine Family of Linear Systems
Analysis of Systems with LTI Perturbations
Positive Orthant Stabilizability
Linear Systems with Delays
Interpolation Problems
The Inverse Problem of Optimal Control
System Realization Problems
Multi-Criterion LQG
Nonconvex Multi-Criterion Quadratic Problems
Notation
List of Acronyms
Bibliography
Index
Preface
Introduction / 1：
Overview
50.
図書
by Constantin Udrişte
51.
図書
A. Cichocki, R. Unbehauen
出版情報:
New York : J. Wiley, 1993 xvii, 526 p. ; 24 cm
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Mathematical Preliminaries of Neurocomputing
Architectures and Electronic Implementation of Neural Network Models
Unconstrained Optimization and Learning Algorithms
Neural Networks for Linear, Quadratic Programming and Linear Complementarity Problems
A Neural Network Approach to the On-Line Solution of a System of Linear Algebraic Equations and Related Problems
Neural Networks for Matrix Algebra Problems
Neural Networks for Continuous, Nonlinear, Constrained Optimization Problems
Neural Networks for Estimation, Identification and Prediction
Neural Networks for Discrete and Combinatorial Optimization Problems
Appendices
Subject Index
Mathematical Preliminaries of Neurocomputing
Architectures and Electronic Implementation of Neural Network Models
Unconstrained Optimization and Learning Algorithms
52.
図書
Masatoshi Sakawa
53.
図書
A.L. Dontchev, T. Zolezzi
54.
図書
by Ignacy Kaliszewski
出版情報:
Boston : Kluwer Academic Publishers, c1994 xiv, 160 p. ; 24 cm
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55.
図書
Philip E. Gill, Walter Murray, Margaret H. Wright
出版情報:
Redwood City, Calif. : Addison-Wesley Pub. Co., Advanced Book Program, c1991 xvii, 426 p. ; 24 cm
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56.
図書
Christodoulos A. Floudas and Panos M. Pardalos, editors
57.
図書
J.E. Dennis, Jr., Robert B. Schnabel
目次情報:
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Preface
Introduction. Problems to be considered / 1：
Characteristics of 'real-world' problems
Finite-precision arithmetic and measurement of error
Exercises
Nonlinear Problems in One Variable / 2：
What is not possible
Newton's method for solving one equation in one unknown
Convergence of sequences of real numbers
Convergence of Newton's method
Globally convergent methods for solving one equation in one uknown
Methods when derivatives are unavailable
Minimization of a function of one variable
Numerical Linear Algebra Background / 3：
Vector and matrix norms and orthogonality
Solving systems of linear equations'matrix factorizations
Errors in solving linear systems
Updating matrix factorizations
Eigenvalues and positive definiteness
Linear least squares
Multivariable Calculus Background / 4：
Derivatives and multivariable models
Multivariable finite-difference derivatives
Necessary and sufficient conditions for unconstrained minimization
Newton's Method for Nonlinear Equations and Unconstrained Minimization / 5：
Newton's method for systems of nonlinear equations
Local convergence of Newton's method
The Kantorovich and contractive mapping theorems
Finite-difference derivative methods for systems of nonlinear equations
Newton's method for unconstrained minimization
Finite difference derivative methods for unconstrained minimization
Globally Convergent Modifications of Newton's Method / 6：
The quasi-Newton framework
Descent directions
Line searches
The model-trust region approach
Global methods for systems of nonlinear equations
Stopping, Scaling, and Testing / 7：
Scaling
Stopping criteria
Testing
Secant Methods for Systems of Nonlinear Equations / 8：
Broyden's method
Local convergence analysis of Broyden's method
Implementation of quasi-Newton algorithms using Broyden's update
Other secant updates for nonlinear equations
Secant Methods for Unconstrained Minimization / 9：
The symmetric secant update of Powell
Symmetric positive definite secant updates
Local convergence of positive definite secant methods
Implementation of quasi-Newton algorithms using the positive definite secant update
Another convergence result for the positive definite secant method
Other secant updates for unconstrained minimization
Nonlinear Least Squares / 10：
The nonlinear least-squares problem
Gauss-Newton-type methods
Full Newton-type methods
Other considerations in solving nonlinear least-squares problems
Methods for Problems with Special Structure / 11：
The sparse finite-difference Newton method
Sparse secant methods
Deriving least-change secant updates
Analyzing least-change secant methods
A Modular System of Algorithms for Unconstrained Minimization and Nonlinear Equations / Robert SchnabelAppendix A：
Test Problems / Appendix B：
References
Author Index
Subject Index
Preface
Introduction. Problems to be considered / 1：
Characteristics of 'real-world' problems
58.
図書
edited by Athanasios Migdalas, Panos M. Pardalos and Peter Värbrand
59.
図書
edited by Roman Słowiński
目次情報:
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Series Foreword / D. Dubois ; H. Prade
Preface / R. Slowinski
Decision Making / Part I：
Fuzzy Preference Modeling / P. Perny ; M. Roubens1：
Fuzzy Aggregation of Numerical Preferences / M. Grabisch, et al.2：
The Use of Fuzzy Preference Models in Multiple Criteria Choice, Ranking and Sorting / J. Fodor, et al.3：
Group Decision Making Under Fuzziness / J. Kacprzyk ; H. Nurmi4：
Elements of Fuzzy Game Theory / A. Billot5：
Mathematical Programming / Part II：
Fuzzy Linear Programming with Single or Multiple Objective Functions / H. Rommelfanger6：
Fuzzy Nonlinear Programming with Single or Multiple Objective Functions / M. Sakawa7：
Discrete Fuzzy Optimization / S. Chanas ; D. Kuchta8：
Fuzzy Dynamic Programming / A.O. Esogbue9：
Statistics and Data Analysis / Part III：
Fuzzy Set-Theoretic Methods in Statistics / J. Gebhardt, et al.10：
Fuzzy Regression Analysis / P. Diamond ; H. Tanaka11：
Reliability, Maintenance and Replacement / Part IV：
Reliability / E. Kerre, et al.12：
Maintenance and Replacement Models under a Fuzzy Framework / W.E. Hearnes II13：
Index
Series Foreword / D. Dubois ; H. Prade
Preface / R. Slowinski
Decision Making / Part I：
60.
図書
Manfred Padberg
目次情報:
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Introduction / 1：
Some Issues in Linear Computation / 1.1：
Three Examples of Linear Computation / 1.2：
Gargantuan Liquids, Inc / 1.2.1：
Oil Refineries, bpd / 1.2.2：
Save Berlin, usw / 1.2.3：
The Linear Programming Problem / 2：
Standard and Canonical Forms / 2.1：
Matrices, Vectors, Scalars / 2.2：
Basic Concepts / 3：
A Fundamental Theorem / 3.1：
Notational Conventions and Illustrations / 3.2：
Five Preliminaries / 4：
Bases and Basic Feasible Solutions / 4.1：
Detecting Optimality / 4.2：
Detecting Unboundedness / 4.3：
A Rank-One Update / 4.4：
Changing Bases / 4.5：
Simplex Algorithms / 5：
Notation, Reading Instructions, Updating / 5.1：
Big M or How to Get Started / 5.2：
Selecting a Pivot Row and Column / 5.3：
Data Structures, Tolerances, Product Form / 5.4：
Equation Format and Cycling / 5.5：
Finiteness of a Simplex Algorithm / 5.6：
Canonical Form / 5.7：
A Worst-Case Example for a Simplex Algorithm / 5.7.1：
Block Pivots and Structure / 5.8：
A Generalized Product Form / 5.8.1：
Upper Bounds / 5.8.2：
Primal-Dual Pairs / 6：
Weak Duality / 6.1：
Strong Duality / 6.2：
Economic Interpretation and Applications / 6.2.1：
Solvability, Redundancy, Separability / 6.3：
A Dual Simplex Algorithm / 6.4：
Correctness, Finitenoss, Initialization / 6.4.1：
Post-Optimality / 6.5：
A Dynamic Simplex Algorithm / 6.6：
Analytical Geometry / 7：
Points, Linos, Subspaces / 7.1：
Polyhedra, Ideal Descriptions, Cones / 7.2：
Faces, Valid Equations, Affine Hulls / 7.2.1：
Facets, Minimal Complete Descriptions, Quasi-Uniqueness / 7.2.2：
Asymptotic Cones and Extreme Rays / 7.2.3：
Adjacency I, Extreme Rays of Polyhedra, Homogenization / 7.2.4：
Point Sets, Affine Transformations, Minimal Generators / 7.3：
Displaced Cones, Adjacency II, Images of Polyhedra / 7.3.1：
Carathéodory, Minkowski, Weyl / 7.3.2：
Minimal Generators, Canonical Generators, Quasi-Uniqueness / 7.3.3：
Double Description Algorithms / 7.4：
Correctness and Finitenoss of the Algorithm / 7.4.1：
Geometry, Euclidean Reduction, Analysis / 7.4.2：
The Basis Algorithm and All-Integer Inversion / 7.4.3：
An All-Integer Algorithm for Double Description / 7.4.4：
Digital Sizes of Rational Polyhedra and Linear Optimization / 7.5：
Facet Complexity, Vertex Complexity, Complexity of Inversion / 7.5.1：
Polyhedra and Related Polytopes for Linear Optimization / 7.5.2：
Feasibility, Binary Search, Linear Optimization / 7.5.3：
Perturbation, Uniqueness, Separation / 7.5.4：
Geometry and Complexity of Simplex Algorithms / 7.6：
Pivot Column Choice, Simplex Paths, Big M Revisited / 7.6.1：
Gaussian Elimination, Fill-In, Scaling / 7.6.2：
Iterative Step I, Pivot Choice, Cholesky Factorization / 7.6.3：
Cross Multiplication, Iterative Step II, Integer Factorization / 7.6.4：
Division Free Gaussian Elimination and Cramer's Rule / 7.6.5：
Circles, Spheres, Ellipsoids / 7.7：
Projective Algorithms / 8：
A Basic Algorithm / 8.1：
The Solution of the Approximate Problem / 8.1.1：
Convergence of the Approximate Iterates / 8.1.2：
Correctness, Finiteness, Initialization / 8.1.3：
Analysis, Algebra, Geometry / 8.2：
Solution to the Problem in the Original Space / 8.2.1：
The Solution in the Transformed Space / 8.2.2：
Geometric Interpretations and Properties / 8.2.3：
Extending the Exact Solution and Proofs / 8.2.4：
Examples of Projective Images / 8.2.5：
The Cross Ratio / 8.3：
Reflection on a Circle and Sandwiching / 8.4：
The Iterative Step / 8.4.1：
A Projective Algorithm / 8.5：
Centers, Barriers, Newton Steps / 8.6：
A Method of Centers / 8.6.1：
The Logarithmic Barrier Function / 8.6.2：
A Newtonian Algorithm / 8.6.3：
Coda / 8.7：
Ellipsoid Algorithms / 9：
Matrix Norms, Approximate Inverses, Matrix Inequalities / 9.1：
Ellipsoid "Halving" in Approximate Arithmetic / 9.2：
Polynomial-Time Algorithms for Linear Programming / 9.3：
Linear Programming and Binary Search / 9.3.1：
Deep Cuts, Sliding Objective, Large Steps, Line Search / 9.4：
Linear Programming the Ellipsoidal Way: Two Examples / 9.4.1：
Correctness and Finiteness of the DCS Ellipsoid Algorithm / 9.4.2：
Optimal Separators, Most Violated Separators, Separation / 9.5：
?-Solidification of Flats, Polytopal Norms, Rounding / 9.6：
Rational Rounding and Continued Fractions / 9.6.1：
Optimization and Separation / 9.7：
?-Optimal Sets and ?-Optimal Solutions / 9.7.1：
Finding Direction Vectors in the Asymptotic Cone / 9.7.2：
A CCS Ellipsoid Algorithm / 9.7.3：
Linear Optimization and Polyhedral Separation / 9.7.4：
Combinatorial Optimization: An Introduction / 10：
The Berlin Airlift Model Revisited / 10.1：
Complete Formulations and Their Implications / 10.2：
Extremal Characterizations of Ideal Formulations / 10.3：
Blocking and Antiblocking Polyhedra / 10.3.1：
Polyhedra with the Integrality Property / 10.4：
Appendices
Short-Term Financial Management / A：
Operations Management in a Refinery / B：
Automatized Production: PCBs and Ulysses' Problem / C：
References
Bibliography
Index
Introduction / 1：
Some Issues in Linear Computation / 1.1：
Three Examples of Linear Computation / 1.2：
61.
図書
Morton I. Kamien and Nancy L. Schwartz
出版情報:
Amsterdam ; Tokyo : North-Holland , New York, N.Y. : Elsevier Science [distributors outside the United States and Canada], c1991 xvii, 377 p. ; 24 cm
シリーズ名:
Advanced textbooks in economics ; v. 31
子書誌情報:
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Preface to the Fourth Printing
Preface to the Second Edition
Preface to the First Edition
Calculus of Variations / Part I：
Introduction / Section 1：
Example Solved / Section 2：
Simplest Problem-Euler Equation / Section 3：
Examples and Interpretations / Section 4：
Solving the Euler Equation in Special Cases / Section 5：
Second Order Conditions / Section 6：
Isoperimetric Problem / Section 7：
Free End Value / Section 8：
Free Horizon-Transversality Conditions / Section 9：
Equality Constrained Endpoint / Section 10：
Salvage Value / Section 11：
Inequality Constraint Endpoints and Sensitivity Analysis / Section 12：
Corners / Section 13：
Inequality Constraints in (t, x) / Section 14：
Infinite Horizon Autonomous Problems / Section 15：
Most Rapid Approach Paths / Section 16：
Diagrammatic Analysis / Section 17：
Several Functions and Double Integrals / Section 18：
Optimal Control / Part II：
Simplest Problem-Necessary Conditions
Sufficiency
Interpretations
Several Variables
Fixed Endpoint Problems
Various Endpoint Conditions
Discounting, Current Values, Comparative Dynamics
Equilibria in Infinite Horizon Autonomous Problems
Bounded Controls
Further Control Constraint
Discontinuous and Bang-Bang Control
Singular Solutions and Most Rapid Approach Paths
The Pontryagin Maximum Principle, Existence
Further Sufficiency Theorems
Alternative Formulations
State Variable Inequality Constraints
Jumps in the State Variable, Switches in State Equations
Delayed Response / Section 19：
Optimal Control with Integral State Equations / Section 20：
Dynamic Programming / Section 21：
Stochastic Optimal Control / Section 22：
Differential Games / Section 23：
Calculus and Nonlinear Programming / Appendix A：
Calculus Techniques
Mean-Value Theorems
Concave and Convex Functions
Maxima and Minima
Equality Constrained Optimization
Inequality Constrained Optimization
Line Integrals and Green's Theorem
Differential Equations / Appendix B：
Linear First Order Differential Equations
Linear Second Order Differential Equations
Linear nth Order Differential Equations
A Pair of Linear Equations
Existence and Uniqueness of Solutions
References
Author Index
Subject Index
Preface to the Fourth Printing
Preface to the Second Edition
Preface to the First Edition
62.
図書
Rangarajan K. Sundaram
出版情報:
New York ; Cambridge : Cambridge University Press, 1996 xvii, 357 p. ; 26-27 cm
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63.
図書
Christos H. Papadimitriou, Kenneth Steiglitz
出版情報:
Mineola, New York : Dover Publications, 1998 xvi, 496 p. ; 22 cm
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64.
図書
Dimitris Bertsimas, John N. Tsitsiklis
図書
