Acceleration of the Cutting-Plane Algorithm: Primal Forms of Bundle Methods

  • Jean-Baptiste Hiriart-Urruty
  • Claude Lemaréchal
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 306)


Chapter VI (subdifferentials and their elementary properties) is essential and Chap. VII or XII (minimality conditions and elementary duality for simple convex minimization problems) will suffice for a superficial reading. However, practically all the book is useful for a complete understanding of every detail; in particular: Chap. 11 (basic principies for minimization algorithms), Chap. IV (properties ofperspective-functions), Chap. IX (bundling mechanism for descent algorithms), Chap. X (conjugacy, smoothness of the conjugate), Chap. XI (approximate subdifferentials, infimal convolution), Chap. XII (classical algorithms for convex minimization, duality schemes in the convex case), Chap. XIV (general principles of dual bundle methods).


Primal Form Proximal Point Algorithm Stability Center Bundle Method Aggregate Linearization 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Jean-Baptiste Hiriart-Urruty
    • 1
  • Claude Lemaréchal
    • 2
  1. 1.Département de MathématiquesUniversité Paul SabatierToulouseFrance
  2. 2.INRIA, RocquencourtDomaine de VoluceauLe ChesnayFrance

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