Foundations of Mathematical Optimization: Convex Analysis without Linearity

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Springer Science & Business Media, Feb 28, 1997 - Mathematics - 585 pages
Many books on optimization consider only finite dimensional spaces. This volume is unique in its emphasis: the first three chapters develop optimization in spaces without linear structure, and the analog of convex analysis is constructed for this case. Many new results have been proved specially for this publication. In the following chapters optimization in infinite topological and normed vector spaces is considered. The novelty consists in using the drop property for weak well-posedness of linear problems in Banach spaces and in a unified approach (by means of the Dolecki approximation) to necessary conditions of optimality. The method of reduction of constraints for sufficient conditions of optimality is presented. The book contains an introduction to non-differentiable and vector optimization.
Audience: This volume will be of interest to mathematicians, engineers, and economists working in mathematical optimization.
 

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Contents

II
1
III
16
IV
21
V
23
VI
28
VII
37
VIII
40
IX
50
XXXV
305
XXXVI
313
XXXVII
336
XXXVIII
341
XXXIX
364
XL
374
XLI
390
XLII
396

X
56
XI
61
XII
67
XIII
76
XIV
97
XV
110
XVI
130
XVII
135
XVIII
141
XIX
150
XX
171
XXI
184
XXII
197
XXIII
206
XXIV
212
XXV
223
XXVI
231
XXVII
240
XXVIII
248
XXIX
254
XXX
261
XXXI
273
XXXII
287
XXXIII
294
XXXIV
296
XLIII
403
XLIV
412
XLV
432
XLVI
441
XLVII
448
XLVIII
455
XLIX
458
L
464
LI
469
LII
475
LIII
483
LIV
486
LV
491
LVI
497
LVII
512
LVIII
517
LIX
522
LX
529
LXI
539
LXII
543
LXIII
551
LXIV
571
LXV
577
LXVI
581
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