Verfügbarkeit: Optimization :: THWS Bibkatalog

Optimization: structure and applications

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Format:	Buch
Sprache:	English
Veröffentlicht:	New York, NY Springer 2009
Schriftenreihe:	Springer optimization and its applications 32
Schlagworte:	Mathematical optimization Optimierung Aufsatzsammlung
Online-Zugang:	Inhaltsverzeichnis Klappentext
Beschreibung:	XXI, 401 S. Ill., graph. Darst.
ISBN:	9780387980959

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Datensatz im Suchindex

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adam_text	Contents List of Figures ................................................ xv List of Tables ................................................. xvii Preface ....................................................... xix Part I Optimization: Structure 1 On the nondifferentiability of cone-monotone functions in Banach spaces ......................................... 3 Jonathan Borwein and Rafal Goebel 1.1 Introduction .......................................... 3 1.2 Examples ............................................ 6 References ................................................. 13 2 Duality and a Farkas lemma for integer programs ...................................... 15 Jean B. Lasserre 2.1 Introduction .......................................... 15 2.1.1 Preliminaries .................................. 16 2.1.2 Summary of content ............................ 17 2.2 Duality for the continuous problems Ρ and 1 .............. 18 2.2.1 Duality for Ρ .................................. 18 2.2.2 Duality for integration .......................... 19 2.2.3 Comparing P,P* and Ι, Γ ...................... 19 2.2.4 The continuous Brion and Vergne formula ......... 20 2.2.5 The logarithmic barrier function ................. 21 2.2.6 Summary ..................................... 22 2.3 Duality for the discrete problems Id and Pd .............. 22 2.3.1 The Z-transform ............................... 23 2.3.2 The dual problem Vd ........................... 24 2.3.3 Comparing I* and Id ........................... 24 Contents 2.3.4 The discrete Brion and Vergne formula ......... 25 2.3.5 The discrete optimization problem Pd ............ 26 2.3.6 A dual comparison of Ρ and Pd ................. 27 2.4 A discrete Farkas lemma ............................... 29 2.4.1 The case when А є Nmxn ...................... 30 2.4.2 The general case ............................... 31 2.5 Conclusion ........................................... 33 2.6 Proofs ............................................... 34 2.6.1 Proof of Theorem 1 ............................ 34 2.6.2 Proof of Corollary 1............................ 35 2.6.3 Proof of Proposition 3.1 ........................ 36 2.6.4 Proof of Theorem 2............................ 37 References ................................................. 38 Some nonlinear Lagrange and penalty functions for problems with a single constraint ......................... 41 J. S. Giri and A. M. Rubinov 3.1 Introduction .......................................... 41 3.2 Preliminaries ......................................... 43 3.3 The relationship between extended penalty functions and extended Lagrange functions ............................ 44 3.4 Generalized Lagrange functions ......................... 47 3.5 Example ............................................. 51 3.5.1 The Lagrange function approach ................. 51 3.5.2 Penalty function approach ...................... 52 References ................................................. 53 Convergence of truncates in Í1 optimal feedback control .. 55 Robert Wenczel, Andrew Eberhard and Robin Hill 4.1 Introduction .......................................... 55 4.2 Mathematical preliminaries ............................. 58 4.3 System-theoretic preliminaries .......................... 60 4.3.1 Basic system concepts .......................... 60 4.3.2 Feedback stabilization of linear systems ........... 62 4.4 Formulation of the optimization problem in Iі ............ 64 4.5 Convergence tools ..................................... 67 4.6 Verification of the constraint qualification ................ 71 4.6.1 Limitations on the truncation scheme ............. 76 4.7 Convergence of approximates ........................... 78 4.7.1 Some extensions ............................... 85 4.8 Appendix ............................................ 88 References ................................................. 92 Contents ¡x 5 Asymptotical stability of optimal paths in nonconvex problems ................................................. 95 Musa A. Mamedov 5.1 Introduction and background ........................... 95 5.2 The main conditions of the turnpike theorem ............. 97 5.3 Definition of the set V and some of its properties ..........100 5.4 Transformation of Condition H3 .........................101 5.5 Sets of 1st and 2nd type: Some integral inequalities ........105 5.5.1 .............................................105 5.5.2 .............................................106 5.5.3 .............................................107 5.5.4 .............................................108 5.5.5 .............................................113 5.6 Transformation of the functional (5.2) ...................117 5.6.1 .............................................117 5.6.2 .............................................119 5.7 The proof of Theorem 13.6.............................123 5.7.1 .............................................123 5.7.2 .............................................129 References .................................................133 6 Pontryagin principle with a PDE: a unified approach .....135 B. D. Craven 6.1 Introduction ..........................................135 6.2 Pontryagin for an ODE ................................136 6.3 Pontryagin for an elliptic PDE ..........................138 6.4 Pontryagin for a parabolic PDE .........................139 6.5 Appendix ............................................140 References .................................................141 7 A turnpike property for discrete-time control systems in metric spaces ..........................................143 Alexander J. Zaslavski 7.1 Introduction ..........................................143 7.2 Stability of the turnpike phenomenon ....................146 7.3 A turnpike is a solution of the problem (P) ...............149 7.4 A turnpike result ......................................151 References .................................................155 8 Mond-Weir Duality ......................................157 B. Mond 8.1 Preliminaries .........................................157 8.2 Convexity and Wolfe duality ............................158 8.3 Fractional programming and some extensions of convexity ..........................................159 x Contents 8.4 Mond-Weir dual ...................................... 160 8.5 Applications .......................................... 160 8.6 Second order duality ................................... 162 8.7 Symmetric duality ..................................... 163 References ................................................. 165 9 Computing the fundamental matrix of an M/G/1-type Markov chain .............................................167 Emma Hunt 9.1 Introduction ..........................................167 9.2 Algorithm H: Preliminaries .............................170 9.3 Probabilistic construction ..............................172 9.4 Algorithm H ..........................................174 9.5 Algorithm H: Preliminaries .............................175 9.6 H, G and convergence rates ............................178 9.7 A special case: The QBD ...............................181 9.8 Algorithms CR and H .................................185 References .................................................187 10 A comparison of probabilistic and invariant subspace methods for the block M/G/l Markov chain ..............189 Emma Hunt 10.1 Introduction ..........................................189 10.2 Error measures ........................................190 10.3 Numerical experiments .................................192 10.3.1 Experiment Gl ................................193 10.3.2 Experiment G2 ................................194 10.3.3 The Daigle and Lucantoni teletrafik problem ......196 10.3.4 Experiment G6 ................................201 10.3.5 Experiment G7 ................................202 References .................................................204 11 Interpolating maps, the modulus map and Hadamard s inequality .................................................207 S. S. Dragomir, Emma Hunt and C. E. M. Pearce 11.1 Introduction ..........................................207 11.2 A refinement of the basic inequality .....................210 11.3 Inequalities for G¡ and Hf .............................216 11.4 More on the identric mean .............................217 11.5 The mapping h¡ ......................................220 References .................................................223 Contents xj Part II Optimization: Applications 12 Estimating the size of correcting codes using extremal graph problems ...........................................227 Sergiy Butenko, Panos Pardalos, Ivan Sergienko, Vladimir Shylo and Petro Stetsyuk 12.1 Introduction ..........................................227 12.2 Finding lower bounds and exact solutions for the largest code sizes using a maximum independent set problem ......229 12.2.1 Finding the largest correcting codes ..............232 12.3 Lower Bounds for Codes Correcting One Error on the Z-Channel ........................................236 12.3.1 The partitioning method ........................237 12.3.2 The partitioning algorithm ......................239 12.3.3 Improved lower bounds for code sizes .............239 12.4 Conclusions ..........................................241 References .................................................242 13 New perspectives on optimal transforms of random vectors ...................................................245 P. G. Howlett, C. E. M. Pearce and A. P. Torokhti 13.1 Introduction and statement of the problem ...............245 13.2 Motivation of the statement of the problem ...............247 13.3 Preliminaries .........................................248 13.4 Main results ..........................................249 13.5 Comparison of the transform T° and the GKLT ...........251 13.6 Solution of the unconstrained minimization problem (13.3) . 252 13.7 Applications and further modifications and extensions .....253 13.8 Simulations ...........................................254 13.9 Conclusion ...........................................258 References .................................................258 14 Optimal capacity assignment in general queueing networks ..................................................261 P. K. Pollett 14.1 Introduction ..........................................261 14.2 The model ...........................................262 14.3 The residual-life approximation .........................263 14.4 Optimal allocation of effort .............................264 14.5 Extensions ...........................................267 14.6 Data networks ........................................268 14.7 Conclusions ..........................................271 References .................................................271 x¡¡ Contents 15 Analysis of a simple control policy for stormwater management in two connected dams ......................273 Julia Piantadosi and Phil Howlett 15.1 Introduction ..........................................273 15.2 A discrete-state model .................................274 15.2.1 Problem description ............................274 15.2.2 The transition matrix for a specific control policy .. 275 15.2.3 Calculating the steady state when 1 < m < к...... 276 15.2.4 Calculating the steady state for m = 1............279 15.2.5 Calculating the steady state for m = к............ 280 15.3 Solution of the matrix eigenvalue problem using Gaussian elimination for 1 < m < к.............................. 280 15.3.1 Stage 0.......................................281 15.3.2 The general rules for stages 2 to m - 2 ...........281 15.3.3 Stage m - 1...................................283 15.3.4 The general rules for stages m to к - 2m ..........284 15.3.5 Stage fc - 2m + 1 ..............................285 15.3.6 The general rule for stages к — 2m + 2 tok-m-2 ..................................286 15.3.7 The final stage k-m-l .......................287 15.4 The solution process using back substitution for 1 < m < к . 287 15.5 The solution process for m = 1..........................290 15.6 The solution process for m = к.......................... 292 15.7 A numerical example ..................................292 15.8 Justification of inverses ................................295 15.8.1 Existence of the matrix Wo ......................296 15.8.2 Existence of the matrix Wp for 1 < ρ < m - 1.....296 15.8.3 Existence of the matrix Wq ioxm<q<k-m-l ..........................298 15.9 Summary ............................................305 References .................................................306 16 Optimal design of linear consecutive-fc-out-of-n systems . 307 Małgorzata O Reilly 16.1 Introduction ..........................................307 16.1.1 Mathematical model ...........................307 16.1.2 Applications and generalizations of linear consecutive-fc-out-of-n systems .................308 16.1.3 Studies of consecutive-fc-out-of-n systems ........309 16.1.4 Summary of the results .........................311 16.2 Propositions for R and M ..............................312 16.3 Preliminaries to the main proposition ....................315 16.4 The main proposition ..................................318 16.5 Theorems ......................................... 321 Contents x¡¡¡ 16.6 Procedures to improve designs not satisfying necessary conditions for the optimal design ........................324 References .................................................325 17 The (fc+l)-th component of linear consecutive-fc-out-of-n systems ...................................................327 Małgorzata O Reilly 17.1 Introduction ..........................................327 17.2 Summary of the results ................................329 17.3 General result for η > 2k, к > 2.........................330 17.4 Results for η = 2k + 1, к > 2...........................334 17.5 Results for η = 2k + 2, к > 2...........................337 17.6 Procedures to improve designs not satisfying the necessary conditions for the optimal design ........................340 References .................................................341 18 Optimizing properties of polypropylene and elastomer compounds containing wood flour .........................343 Pavel Spiridonov, Jan Budin, Stephen Clarke and Jani Matisons 18.1 Introduction ..........................................344 18.2 Methodology .........................................344 18.2.1 Materials .....................................344 18.2.2 Sample preparation and tests ....................345 18.3 Results and discussions ................................345 18.3.1 Density of compounds ..........................345 18.3.2 Comparison of compounds obtained in a Brabender mixer and an injection-molding machine ..........346 18.3.3 Compatibilization of the polymer matrix and wood flour ................................349 18.3.4 Optimization of the compositions ................350 18.4 Conclusions ..........................................352 References .................................................353 19 Constrained spanning, Steiner trees and the triangle inequality .................................................355 Prabhu Manyem 19.1 Introduction ..........................................355 19.2 Upper bounds for approximation ........................359 19.2.1 The most expensive edge is at most a minimum spanning tree ..................................359 19.2.2 MaxST is at most (n - l)MinST .................359 19.3 Lower bound for a CSP approximation ...................360 19.3.1 E-Reductions: Definition ........................360 19.3.2 SET COVER ..................................361 19.3.3 Reduction from SET COVER ...................361 19.3.4 Feasible Solutions ..............................362 x¡v Contents 19.3.5 Proof of E-Reduction ...........................365 19.4 Conclusions ..........................................366 References .................................................366 20 Parallel line search .......................................369 Т. С Peachey, D. Abramson and A. Lewis 20.1 Line searches .........................................369 20.2 Nimrod/0 ............................................370 20.3 Execution time .......................................373 20.3.1 A model for execution time .....................373 20.3.2 Evaluation time a Bernoulli variate ...............373 20.3.3 Simulations of evaluation time ...................375 20.3.4 Conclusions ...................................375 20.4 Accelerating convergence by incomplete iterations .........377 20.4.1 Strategies for aborting jobs ......................377 20.4.2 Experimental results ...........................378 20.4.3 Conclusions ...................................381 References .................................................381 21 Alternative Mathematical Programming Models: A Case for a Coal Blending Decision Process .....................383 Ruhul A. Sarker 21.1 Introduction ..........................................383 21.2 Mathematical programming models ......................385 21.2.1 Single period model (SPM) ......................386 21.2.2 Multiperiod nonlinear model (MNM) .............389 21.2.3 Upper bound linear model (MLM) ...............390 21.2.4 Multiperiod linear model (MLM) ................391 21.3 Model flexibility .......................................392 21.3.1 Case-1 ........................................392 21.3.2 Case-2 ........................................394 21.3.3 Case-3 ........................................395 21.4 Problem size and computation time ......................395 21.5 Objective function values and fluctuating situation ........396 21.6 Selection criteria ......................................397 21.7 Conclusions ..........................................398 References .................................................398 About the Editors ............................................401 Springer Opti publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and applications involving such problems. Some of the topics include optimization, network flow problems, optimal control, multi-objective programming, approximation and heuristic approaches. _ Charles Pearce · Emma Hunt (Editors) Optimization: Structure and Applications Optimization: Structure and Applications presents selected contributions from renowned researchers in the fields of operations research and industrial engineering. The text is divided into two parts: the first focuses on mathematical structure, and the second, on real-world applications. The book includes recent developments in several optimization-related topics such as decision theory, linear programming, turnpike theory, duality theory, convex analysis, and queueing theory. The applications presented include, but are not limited to, data imaging, network capacity allocation, water system management, and materials design. The 21 self-contained chapters in this volume are devoted to the examination of modern trends and open problems in the field of optimization. This book will be a valuable tool ~ ot only to specialists interested in the technical detail and various applications presented, but also to researchers interested in building upon the book s theoretical results.
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spellingShingle	Optimization structure and applications Springer optimization and its applications Mathematical optimization Optimierung (DE-588)4043664-0 gnd
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title	Optimization structure and applications
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work_keys_str_mv	AT pearcecharles optimizationstructureandapplications

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