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Continuous Optimization: Current Trends and Modern Applications 2005 ed. [Kõva köide]

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  • Formaat: Hardback, 450 pages, kõrgus x laius: 235x155 mm, kaal: 1840 g, XVIII, 450 p., 1 Hardback
  • Sari: Applied Optimization 99
  • Ilmumisaeg: 10-Aug-2005
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 0387267697
  • ISBN-13: 9780387267692
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Continuous Optimization: Current Trends and Modern Applications 2005 ed.Suurem pilt
  • Formaat: Hardback, 450 pages, kõrgus x laius: 235x155 mm, kaal: 1840 g, XVIII, 450 p., 1 Hardback
  • Sari: Applied Optimization 99
  • Ilmumisaeg: 10-Aug-2005
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 0387267697
  • ISBN-13: 9780387267692
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780387267692.html
Märksõnad:
Continuous optimization is the study of problems in which we wish to opti­ mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in the development of calculus by Newton and Leibniz in the 17*^ century. Nowadys, continuous optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Solution methods for large multivariable constrained continuous optimiza­ tion problems using computers began with the work of Dantzig in the late 1940s on the simplex method for linear programming problems. Recent re­ search in continuous optimization has produced a variety of theoretical devel­ opments, solution methods and new areas of applications. It is impossible to give a full account of the current trends and modern applications of contin­ uous optimization. It is our intention to present a number of topics in order to show the spectrum of current research activities and the development of numerical methods and applications.
Preface xiii
List of Contributors
xv
Part I Surveys
Linear Semi-infinite Optimization: Recent Advances
3(20)
Miguel A. Goberna
Introduction
3(2)
Linear semi-infinite systems
5(3)
Applications
8(3)
Numerical methods
11(2)
Perturbation analysis
13(10)
References
17(6)
Some Theoretical Aspects of Newton's Method for Constrained Best Interpolation
23(228)
Hou-Duo Qi
Introduction
23(3)
Constrained Interpolation in Hilbert Space
26(5)
Nonsmooth Functions and Equations
31(2)
Newton's Method and Convergence Analysis
33(12)
Newton's Method
33(3)
Splitting and Regularity
36(3)
Semismoothness
39(3)
Application to Inequality Constraints
42(2)
Globalization
44(1)
Open Problems
45(172)
References
46(171)
Optimization: the Cutting Angle method
217(7)
Problem formulation
217(1)
The Cutting Angle algorithm
218(1)
Enumeration of local minima
219(3)
Numerical experiments
222(1)
Applications
223(1)
Random variate generation: acceptance/ rejection
224(11)
Problem formulation
224(2)
Log-concave densities
226(1)
Univariate Lipschitz densities
227(3)
Lipschitz densities in Rn
230(1)
Description of the algorithm
231(2)
Numerical experiments
233(2)
Scattered data interpolation: Lipschitz approximation
235(9)
Problem formulation
235(2)
Best uniform approximation
237(1)
Description of the algorithm
238(2)
Numerical experiments
240(4)
Conclusion
244(7)
References
244(7)
Part II Theory and Numerical Methods
A Numerical Method for Concave Programming Problems
251(24)
Altannar Chinchuluun
Enkhbat Rentsen
Panos M. Pardalos
Introduction
251(1)
Global Optimality Condition
252(2)
Approximation Techniques of the Level Set
254(8)
Algorithms and their Convergence
262(8)
Numerical Examples
270(2)
Conclusions
272(3)
References
272(3)
Convexification and Monotone Optimization
275(18)
Xiaoling Sun
Jianling Li
Duan Li
Introduction
275(1)
Monotonicity and convexity
276(5)
Monotone optimization and concave minimization
281(2)
Equivalence to concave minimization
281(1)
Outer approximation algorithm for concave minimization problems
281(2)
Polyblock outer approximation method
283(3)
A hybrid method
286(2)
Conclusions
288(1)
Acknowledgement
289(4)
References
289(4)
Generalized Lagrange Multipliers for Nonconvex Directionally Differentiable Programs
293(28)
Nguyen Dinh
Gue Myung Lee
Le Anh Tuan
Introduction and Preliminaries
293(3)
Generalized Lagrange Multipliers
296(8)
Necessary conditions for optimality
296(5)
Sufficient condition for optimality
301(3)
Special Cases and Applications
304(10)
Problems with convexlike directional derivatives
304(1)
Composite nonsmooth programming with Gateaux differentiability
305(4)
Quasidifferentiable problems
309(5)
Directionally Differentiable Problems with DSL-approximates
314(7)
References
317(4)
Slice Convergence of Sums of Convex functions in Banach Spaces and Saddle Point Convergence
321(22)
Robert Wenczel
Andrew Eberhard
Introduction
321(2)
Preliminaries
323(4)
A Sum Theorem for Slice Convergence
327(9)
Saddle-point Convergence in Fenchel Duality
336(7)
References
341(2)
Topical Functions and their Properties in a Class of Ordered Banach Spaces
343(22)
Hossein Mohebi
Introduction
343(1)
Preliminaries
344(3)
Plus-Minkowski gauge and plus-weak Pareto point for a downward set
347(2)
Xφ-subdifferential of a topical function
349(4)
Fenchel-Moreau conjugates with respect to φ
353(4)
Conjugate of type Lau with respect to φ
357(8)
References
360(5)
Part III Applications
Dynamical Systems Described by Relational Elasticities with Applications
365(22)
Musa Mammadov
Alexander Rubinov
John Yearwood
Introduction
365(2)
Relationship between two variables: relational elasticity
367(2)
Some examples for calculating relational elasticities
369(1)
Dynamical systems
370(4)
Classification Algorithm based on a dynamical systems approach
374(3)
Algorithm for global optimization
377(3)
Results of numerical experiments
380(1)
Conclusions and future work
381(6)
References
383(4)
Impulsive Control of a Sequence of Rumour Processes
387(22)
Charles Pearce
Yalcin Kaya
Selma Belen
Introduction
387(2)
Single-Rumour Process and Preliminaries
389(2)
Scenario 1
391(4)
Monotonicity of ξ
395(4)
Convexity of ξ
399(3)
Scenario 2
402(3)
Comparison of Scenarios
405(4)
References
406(3)
Minimization of the Sum of Minima of Convex Functions and Its Application to Clustering
409(26)
Alexander Rubinov
Nadejda Soukhoroukova
Julien Ugon
Introduction
409(1)
A class of sum-min functions
410(1)
Functions represented as the sum of minima of convex functions
410(1)
Some properties of functions belonging to F
411(1)
Examples
411(4)
Cluster functions and generalized cluster functions
412(1)
Bradley-Mangasarian approximation of a finite set
412(1)
Skeleton of a finite set of points
413(1)
Illustrative examples
414(1)
Minimization of sum-min functions belonging to class F
415(2)
Minimization of generalized cluster function
417(2)
Construction of generalized cluster functions
417(1)
Initial points
418(1)
Numerical experiments with generalized cluster function
419(5)
Datasets
419(1)
Numerical experiments: description
419(1)
Results of numerical experiments
420(4)
Skeletons
424(6)
Introduction
424(3)
Numerical experiments: description
427(2)
Numerical experiments: results
429(1)
Other experiments
430(1)
Conclusions
430(5)
Optimization
430(1)
Clustering
431(2)
References
433(2)
Analysis of a Practical Control Policy for Water Storage in Two Connected Dams
435(15)
Phil Howlett
Julia Piantadosi
Charles Pearce
Introduction
435(1)
Problem formulation
436(2)
Intuitive calculation of the invariant probability
438(2)
Existence of the inverse matrices
440(1)
Probabilistic analysis
441(4)
The expected long-term overflow
445(1)
Extension of the fundamental ideas
445(5)
References
450