| 000 | 05884nam a2200889 i 4500 | ||
|---|---|---|---|
| 001 | 6813202 | ||
| 003 | IEEE | ||
| 005 | 20200413152912.0 | ||
| 006 | m eo d | ||
| 007 | cr cn |||m|||a | ||
| 008 | 140113s2014 caua foab 001 0 eng d | ||
| 020 |
_a9781627052382 _qebook |
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| 020 |
_z9781627052375 _qpaperback |
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| 024 | 7 |
_a10.2200/S00554ED1V01Y201312MAS014 _2doi |
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| 035 | _a(CaBNVSL)swl00403028 | ||
| 035 | _a(OCoLC)868155830 | ||
| 040 |
_aCaBNVSL _beng _erda _cCaBNVSL _dCaBNVSL |
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| 050 | 4 |
_aQA639.5 _b.M674 2014 |
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| 082 | 0 | 4 |
_a516.08 _223 |
| 090 |
_a _bMoCl _e201312MAS014 |
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| 100 | 1 |
_aMordukhovich, B. Sh. _q(Boris Sholimovich), _eauthor. |
|
| 245 | 1 | 3 |
_aAn easy path to convex analysis and applications / _cBoris S. Mordukhovich, Nguyen Mau Nam. |
| 264 | 1 |
_aSan Rafael, California (1537 Fourth Street, San Rafael, CA 94901 USA) : _bMorgan & Claypool, _c2014. |
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| 300 |
_a1 PDF (xvi, 202 pages) : _billustrations. |
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| 336 |
_atext _2rdacontent |
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| 337 |
_aelectronic _2isbdmedia |
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| 338 |
_aonline resource _2rdacarrier |
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| 490 | 1 |
_aSynthesis lectures on mathematics and statistics, _x1938-1751 ; _v# 14 |
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| 538 | _aMode of access: World Wide Web. | ||
| 538 | _aSystem requirements: Adobe Acrobat Reader. | ||
| 500 | _aPart of: Synthesis digital library of engineering and computer science. | ||
| 500 | _aSeries from website. | ||
| 504 | _aIncludes bibliographical references (pages 195-197) and index. | ||
| 505 | 0 | _a1. Convex sets and functions -- 1.1 Preliminaries -- 1.2 Convex sets -- 1.3 Convex functions -- 1.4 Relative interiors of convex sets -- 1.5 The distance function -- 1.6 Exercises for chapter 1 -- | |
| 505 | 8 | _a2. Subdifferential calculus -- 2.1 Convex separation -- 2.2 Normals to convex sets -- 2.3 Lipschitz continuity of convex functions -- 2.4 Subgradients of convex functions -- 2.5 Basic calculus rules -- 2.6 Subgradients of optimal value functions -- 2.7 Subgradients of support functions -- 2.8 Fenchel conjugates -- 2.9 Directional derivatives -- 2.10 Subgradients of supremum functions -- 2.11 Exercises for chapter 2 -- | |
| 505 | 8 | _a3. Remarkable consequences of convexity -- 3.1 Characterizations of differentiability -- 3.2 Carathéodory theorem and Farkas Lemma -- 3.3 Radon theorem and Helly theorem -- 3.4 Tangents to convex sets -- 3.5 Mean value theorems -- 3.6 Horizon cones -- 3.7 Minimal time functions and Minkowski gauge -- 3.8 Subgradients of minimal time functions -- 3.9 Nash equilibrium -- 3.10 Exercises for chapter 3 -- | |
| 505 | 8 | _a4. Applications to optimization and location problems -- 4.1 Lower semicontinuity and existence of minimizers -- 4.2 Optimality conditions -- 4.3 Subgradient methods in convex optimization -- 4.4 The Fermat-Torricelli problem -- 4.5 A generalized Fermat-Torricelli problem -- 4.6 A generalized Sylvester problem -- 4.7 Exercises for chapter 4 -- | |
| 505 | 8 | _aSolutions and hints for exercises -- Bibliography -- Authors' biographies -- Index. | |
| 506 | 1 | _aAbstract freely available; full-text restricted to subscribers or individual document purchasers. | |
| 510 | 0 | _aCompendex | |
| 510 | 0 | _aINSPEC | |
| 510 | 0 | _aGoogle scholar | |
| 510 | 0 | _aGoogle book search | |
| 520 | 3 | _aConvex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build the theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the Fermat-Torricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications. | |
| 530 | _aAlso available in print. | ||
| 588 | _aTitle from PDF title page (viewed on January 13, 2014). | ||
| 650 | 0 | _aConvex geometry. | |
| 653 | _aAffine set | ||
| 653 | _aCarathéodory theorem | ||
| 653 | _aconvex function | ||
| 653 | _aconvex set | ||
| 653 | _adirectional derivative | ||
| 653 | _adistance function | ||
| 653 | _aFenchel conjugate | ||
| 653 | _aFermat-Torricelli problem | ||
| 653 | _ageneralized differentiation | ||
| 653 | _aHelly theorem | ||
| 653 | _aminimal time function | ||
| 653 | _aNash equilibrium | ||
| 653 | _anormal cone | ||
| 653 | _aRadon theorem | ||
| 653 | _aoptimal value function | ||
| 653 | _aoptimization | ||
| 653 | _asmallest enclosing ball problem | ||
| 653 | _aset-valued mapping | ||
| 653 | _asubdifferential | ||
| 653 | _asubgradient | ||
| 653 | _asubgradient algorithm | ||
| 653 | _asupport function | ||
| 653 | _aWeiszfeld algorithm | ||
| 700 | 1 |
_aNam, Nguyen Mau., _eauthor. |
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| 776 | 0 | 8 |
_iPrint version: _z9781627052375 |
| 830 | 0 | _aSynthesis digital library of engineering and computer science. | |
| 830 | 0 |
_aSynthesis lectures on mathematics and statistics ; _v# 14. _x1938-1751 |
|
| 856 | 4 | 2 |
_3Abstract with links to resource _uhttp://ieeexplore.ieee.org/servlet/opac?bknumber=6813202 |
| 856 | 4 | 0 |
_3Abstract with links to full text _uhttp://dx.doi.org/10.2200/S00554ED1V01Y201312MAS014 |
| 999 |
_c562045 _d562045 |
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