This book is an abridged version of the two volumes "Convex Analysis and Minimization Algorithms I and II" (Grundlehren der mathematischen Wissenschaften Vol. 305 and 306). It presents an introduction to the basic concepts in convex analysis and a study of convex minimization problems (with an emphasis on numerical algorithms). The "backbone" of bot volumes was extracted, some material deleted which was deemed too advanced for an introduction, or too closely attached to numerical algorithms. Some exercises were included and finally the index has been considerably enriched, making it an excellent choice for the purpose of learning and teaching.
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"... Das vorliegende Buch, das eine abgemagerte Version des grossen zweibändigen Werkes ist, hilft dem Mange, dass bisher kein einfuehrendes Lehrbuch fuer dieses wichtige Gebiet vorhanden war, in gelungener Weise ab. Ausgehend von konvexen Mengen werden konvexe Funktionen, sublineare Funktionen, Subdifferentiale und schliesslich konjugierte Funktionen behandelt. Ein Werk, das viele Geometer und Analytiker und alle Mathematiker, die sich mit Optimierung und Kontrolltheorie beschaeftigen, ansprechen sollte." P.M. Gruber, International Mathematische Nachrichten, 2002
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First Sentence:
1.1 In the totally ordered set R, inf E and sup E are respectively the greatest lower bound - the infimum - and least upper bound - the supremum - of a nonempty subset E, when they exist (as real numbers). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
closed sublinear functions, epigraphical hull, same relative interior, infimal convolution, conjugacy operation, finite convex function, strict epigraph, convex epigraph, closed convex function, infimal value, polyhedral function, closed convex polyhedron, positive homogeneity, conical hull, affine manifold, asymptotic cone, closed convex set containing, qualification assumption, convex quadratic functions, affine hull, subspace parallel, polar cone, nonempty convex set, calculus rules, closed convex cone Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Take, Remembering Example, Using Example New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
1.1 In the totally ordered set R, inf E and sup E are respectively the greatest lower bound - the infimum - and least upper bound - the supremum - of a nonempty subset E, when they exist (as real numbers). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
closed sublinear functions, epigraphical hull, same relative interior, infimal convolution, conjugacy operation, finite convex function, strict epigraph, convex epigraph, closed convex function, infimal value, polyhedral function, closed convex polyhedron, positive homogeneity, conical hull, affine manifold, asymptotic cone, closed convex set containing, qualification assumption, convex quadratic functions, affine hull, subspace parallel, polar cone, nonempty convex set, calculus rules, closed convex cone Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Take, Remembering Example, Using Example New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
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- Variational Analysis (Grundlehren der mathematischen Wissenschaften) by R. Tyrrell Rockafellar in Back Matter
- Information and Exponential Families in Statistical Theory (Wiley series in probability & mathematical statistics) by Ole E. Barndorff-Nielsen in Back Matter
- Convex Analysis (Princeton Landmarks in Mathematics and Physics) by Ralph Tyrell Rockafellar in Back Matter
- Convexity in the Theory of Lattice Gases [Princeton Series in Physics] by Robert B. Israel in Back Matter
- Optima and Equilibria: An Introduction to Nonlinear Analysis (Graduate Texts in Mathematics) by Jean-Pierre Aubin in Back Matter
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- Advances in Economics and Econometrics: Volume 1: Theory and Applications, Ninth World Congress (Econometric Society Monographs) by Richard Blundell on page 133
- Computational Combinatorial Optimization: Optimal or Provably Near-Optimal Solutions (Lecture Notes in Computer Science) by Michael Jünger on page 154
- The Science of Hysteresis: Volume 1 of 3-volume set by Author Unknown on page 124
- Convex Optimization & Euclidean Distance Geometry by Jon Dattorro in Back Matter
- Convex Optimization by Stephen Boyd in Back Matter
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