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An Easy path to convex analysis and ...

Mordukhovich, B. Sh.

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An Easy path to convex analysis and applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	An Easy path to convex analysis and applications // Boris S. Mordukhovich, Nguyen Mau Nam.
作者:	Mordukhovich, B. Sh.
其他作者:	Nguyen, Mau Nam.
出版者:	[San Rafael, CA] :Morgan & Claypool, : c2014.,
面頁冊數:	xvi, 202 p. :ill. ;24 cm.
內容註:	1. Convex sets and functions -- 2. Subdifferential calculus -- 3. Remarkable consequences of convexity -- 4. Applications to optimization and location problems.
標題:	Convex functions. -
ISBN:	9781627052375

An Easy path to convex analysis and applications /
Mordukhovich, B. Sh.

An Easy path to convex analysis and applications /Boris S. Mordukhovich, Nguyen Mau Nam. - [San Rafael, CA] :Morgan & Claypool,c2014. - xvi, 202 p. :ill. ;24 cm. - Synthesis lectures on mathematics and statistics,#141938-1743 ;. - Synthesis lectures on mathematics and statistics ;#14..

Includes bibliographical references (p. 195-197) and index.

1. Convex sets and functions -- 2. Subdifferential calculus -- 3. Remarkable consequences of convexity -- 4. Applications to optimization and location problems.

Convex 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.

ISBN: 9781627052375US50.00Subjects--Topical Terms:

544201
Convex functions.

LC Class. No.: QA331.5 / .M67 2014

Dewey Class. No.: 515/.8

An Easy path to convex analysis and applications /
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100 1 $a Mordukhovich, B. Sh. $q (Boris Sholimovich) $3 2184854
245 1 3 $a An Easy path to convex analysis and applications / $c Boris S. Mordukhovich, Nguyen Mau Nam.
260 # $a [San Rafael, CA] : $b Morgan & Claypool, $c c2014.
300 $a xvi, 202 p. : $b ill. ; $c 24 cm.
490 1 $a Synthesis lectures on mathematics and statistics, $x 1938-1743 ; $v #14
504 $a Includes bibliographical references (p. 195-197) and index.
505 0 # $a 1. Convex sets and functions -- 2. Subdifferential calculus -- 3. Remarkable consequences of convexity -- 4. Applications to optimization and location problems.
520 3 $a Convex 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.
650 # 0 $a Convex functions. $3 544201
650 # 0 $a Convex geometry. $3 567300
650 # 0 $a Mathematical optimization. $3 517763
700 1 # $a Nguyen, Mau Nam. $3 2184855
830 0 $a Synthesis lectures on mathematics and statistics ; $v #14. $3 2184856