Complexity in numerical optimization:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Singapore u.a.
World Scientific
1993
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 511 S. graph. Darst. |
| ISBN: | 9810214154 |
Staff View
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| 245 | 1 | 0 | |a Complexity in numerical optimization |c ed.: Panos M. Pardalos |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1993 | |
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Record in the Search Index
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| adam_text | Contents
Preface v
Average Performance of a Self Dual Interior Point Algorithm
for Linear Programming 1
K. M. Anstreicher, J. Ji, F. A. Potra, and Y. Ye
1. Introduction 2
2. The HLP problem and the self dual algorithm 3
3. A new projection scheme for finite termination 6
4. Random model and probabilistic analysis 10
References 13
The Complexity of Approximating a Nonlinear Program 16
M. Bellare and P. Rogaway
1. Introduction 17
2. Preliminaries 20
3. The complexity of polynomial programming 25
4. The complexity of quadratic programming 26
References 30
Algorithms for the Least Distance Problem 33
P. Berman, N. Kovoor, and P. M. Pardalos
1. Introduction 33
2. The parametric characterization and its properties 35
3. An algorithm based on construction of arrangements 41
4. Queries and a witness based search scheme 43
5. A linear time recursive algorithm 48
6. Conclusions 53
References 53
Appendix 56
Translational Cuts for Convex Minimization 57
J. V. Burke, A.A. Goldstein, P. Tseng, and Y. Ye
1. Introduction 58
2. Iteration count for the translational cuts algorithm 60
2. Work per iteration for the translational cuts algorithm 63
vii
viii Contents
References 72
Maximizing Concave Functions in Fixed Dimension 74
E. Cohen and N. Megiddo
1. Introduction 75
2. Preliminaries 75
3. Hyperplane queries 80
4. Employing multi dimensional search 81
5. The algorithm 82
6. Correctness 83
7. Complexity 84
8. Parametric extensions of problems ¦ 85
References 87
Approximating the Steiner Minimum Tree 88
D. Z. Du
1. Introduction 88
2. Minimum spanning trees 89
3. MST based heuristics 94
4. Sub SMT based heuristics 99
References 102
The Complexity of Allocating Resources in Parallel: Upper
and Lower Bounds 107
E. J Friedman
1. Introduction 107
2. General convex optimization 108
3. Resource allocation 114
4. Primal algorithms 116
5. Primal dual (price based) algorithms 118
6. Conclusions 121
Appendix 122
References 125
Some Bounds on the Complexity of Gradients, Jacobians,
and Hessians 128
A. Griewank
1. Introduction 129
Contents ix
2. Generalizations of partial separability 136
3. The evaluation program and its complexity 147
4. Results and discussion 154
5. Summary and conclusion 160
References 161
Complexity Issues in Nonconvex Network Flow Problems 163
G. M, Guisewite and P. M. Pardalos
1. Introduction 163
2. The uncapacitated case 165
3. The capacitated case 172
4. Summary 177
References 177
Complexity of Smooth Convex Programming and its Applications ... 180
O. Giiler
1. Introduction 180
2. The algorithm for constrained minimization 183
3. Another algorithm for constrained minimization 188
4. Applications to convex quadratic programs 191
References 194
A Classification of Static Scheduling Problems 203
J. W. Herrmann, C. Y. Lee, and J. L. Snowdon
1. Introduction 203
2. Problem description 204
3. Table organization 207
References 231
An O(nL) Iteration Algorithm for Computing Bounds in Quadratic
Optimization Problems 254
A. P. Kamath and N. K. Karmarkar
1. Outline 254
2. Introduction 255
3. Interior point approach to the problem 256
4. Complexity analysis 261
5. Generalizing the algorithm 263
6. Conclusions 267
x Contents
References 267
Complexity of Single Machine Hierarchical Scheduling: A Survey — 269
C. Y. Lee and G. Vairaktarakis
1. Introduction 269
2. Notation and basic results 270
3 A g {£ Ci, £,• Wid, LmM, /„,«, fUi}
BefEi^EitiAULL} 274
4. A 6 {Ei £, , E* mTi, Ei Tj, Ei mU, E, Ut}
5€{EiCi,E iCi,£max,/max,i;max} 276
«¦ A € {Et C/f, Et lt i* J5 imaxi /man ^maxj
5€{E,JBi,E,«,r»E,ri,E.«.^,E,^} 280
6. A € {£, £, , Ei rmTi, E, Ti, Ei mOi, £; Ut}
B £ {EiEuEiWiTuEiTiiEiWiUuEiUi} 287
7. Complexity tables 294
8. Conclusion 294
References 295
Performance Driven Graph Enhancement Problems 299
D. Paik and S. Sahni
1. Introduction 299
2. DVUP 302
3. LinkDelay(x, S) 309
4. ShortestPath(a;, 6) 310
5. Satellite^) 311
6. LongestPath(i, S) 312
7. DVSP 314
8. DVDP 318
References 320
Efficient Algorithms for 6 Near Planar Graph and
Algebraic Problem 323
V. Radhakrishnan, H. B. Hunt III, and R. E. Steams
1. Introduction 324
2. Preliminaries 326
3. Comparisons with other classes of graphs 328
4. Path problems and systems of linear equations 330
5. Structure trees, weighted depth, generalized satisfiability 336
6. Summary and open problems 348
Contents xi
References 349
Parametric Flows, Weighted Means of Cuts, and Fractional
Combinatorial Optimization 351
T. Radzik
1. Introduction 351
2. The maximum mean weight cut problem and related network flow problems. .356
3. Linear fractional combinatorial optimization problems 362
4. Analysis of Newton s method for the PF problem 372
5. Analysis of Newton s method for the uniform PF problem 377
6. Concluding remarks 383
References 383
Analysis of a Random Cut Test Instance Generator for the TSP 387
R. L. Rardin, C. A. Tovey, and M. G. Pitcher
1. Introduction 388
2. Versions of the general TSP and class Dp 389
3. Polyhedral relaxations and random cut generators 391
4. Exposed instances 395
5. Intermediate TSP s 398
6. Well formed instances and promises 400
References 403
Some Complexity Issues Involved in the Construction of Test
Cases for NP hard Problems 406
L. A. Sanchis
1. Introduction 406
2. Definitions 408
3. Generability 409
4. Generation of hard instances 417
References 426
Maximizing Non Linear Concave Functions in Fixed Dimension 429
5. Toledo
1. Introduction 429
2. Maximizing one dimensional concave functions 432
3. A two dimensional algorithm 435
4. The general algorithm 438
xii Contents
5. Applications 445
References 446
A Note on the Complexity of Fixed Point Computation for
Noncontractive Maps 448
C. W. Tsay and K. Sikorski
1. Introduction 448
2. Main results 450
3. Complexity for the class F ,h 452
4. Complexity for the class i^.i 454
5. Conclusion 459
References 459
A Technique for Bounding the Number of Iterations in Path
Following Algorithms 462
P. M. Vaidya and D. S. Atkinson
1. Introduction 462
2. Generic path following 464
3. A mathematical framework 467
4. Two old barrier functions 475
5. The hybrid barrier function 484
6. Conclusions 488
References 488
Polynomial Time Weak Approximation Algorithms for Quadratic
Programming 490
5. A. Vavasis
1. Nonconvex quadratic programming 490
2. A weak approximation in polynomial time 492
3. Picking a random point 495
4. Conclusions 498
References 499
Complexity Results for a Class of Min Max Problems with Robust
Optimization Applications 501
G. Yu and P. Kouvelis
1. Introduction 501
2. The min max assignment problem 503
Contents xiii
3. The min max shortest path problem 504
4. The min max resource allocation problem 505
5. The min max knapsack problem 507
6. The min max flow shop scheduling problem 508
7. Remarks 509
References 509
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| spelling | Complexity in numerical optimization ed.: Panos M. Pardalos Singapore u.a. World Scientific 1993 XIII, 511 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Complexité calcul Complexité de calcul (informatique) ram Optimisation mathématique ram Optimisation numérique Computational complexity Mathematical optimization Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Optimierung (DE-588)4043664-0 s Numerische Mathematik (DE-588)4042805-9 s DE-604 Pardalos, Panos M. 1954- Sonstige (DE-588)115385827 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006921498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Complexity in numerical optimization Complexité calcul Complexité de calcul (informatique) ram Optimisation mathématique ram Optimisation numérique Computational complexity Mathematical optimization Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4043664-0 (DE-588)4143413-4 |
| title | Complexity in numerical optimization |
| title_auth | Complexity in numerical optimization |
| title_exact_search | Complexity in numerical optimization |
| title_full | Complexity in numerical optimization ed.: Panos M. Pardalos |
| title_fullStr | Complexity in numerical optimization ed.: Panos M. Pardalos |
| title_full_unstemmed | Complexity in numerical optimization ed.: Panos M. Pardalos |
| title_short | Complexity in numerical optimization |
| title_sort | complexity in numerical optimization |
| topic | Complexité calcul Complexité de calcul (informatique) ram Optimisation mathématique ram Optimisation numérique Computational complexity Mathematical optimization Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Complexité calcul Complexité de calcul (informatique) Optimisation mathématique Optimisation numérique Computational complexity Mathematical optimization Numerical analysis Numerische Mathematik Optimierung Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006921498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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