What's New

Version 021215

  • Material in appendix on derivatives of eigenvalues
  • Expanded bibliography
  • Added "What's New" chapter
  • Wrote intro to taylor majorization
  • Some shaky stuff on Lipschitz

Version 021315

  • Added folium in coordinate descent chapter

Version 021415

  • Added univariate cubic in local majorization
  • Revisiting the reciprocal in higher order majorization

Version 021515

  • Various small editorial changes throughout
  • Version numbering by date
  • Appendix on cobweb plotter
  • Moved the graphics from an external server to the book
  • Added some section headers in ALS chapter
  • Removed shaky Lipschitz stuff

Version 021615

  • Cleanup first chapters

Version 021715

  • Some stuff for section on product of derivatives of block mappings - representation as cyclic matrix

Version 021815

  • Added some detail to the SVD example
  • Added material on Dinkelbach majorization

Version 021915

  • L-majorization and D-majorization

Version 022015

  • Calculations for derivatives of general block methods
  • Reorganized examples in block chapter

Version 022115

  • Updated material on derivatives of algorithmic map for block methods
  • Block Newton methods section
  • Formulas for rate of block optimization
  • Defined and used the LU-form and product form

Version 022215

  • Removed Gauss-Jordan from multiple block LS
  • Convergence rate of CCD for the Rayleigh quotient
  • added blockRate.R function
  • added mls.R function for multiple block LS
  • various small edits

Version 022315

  • Expanded bibliography
  • Put LaTeX macros in header.md to be included on every page
  • Tentatively started HTML cross-referencing of sections
  • Clarified block relaxation derivatives
  • Started some material on block Newton.

Version 022415

  • Defined iteration map, iteration function, iteration matrix and iteration radius
  • Add material on comparing majorizers (may have to be moved to composition section)
  • Simple quartic example in neighborhood majorization

Version 022515

  • No changes

Version 022615

  • No changes

Version 022715

  • Some changes in the definition section of majorization

Version 022815

  • More majorization definition changes
  • Majorization duality
  • Graphics for majorization
  • Moved code and graphics to better places

Version 030115

  • More meat on D-majorization
  • Additions to mean value section
  • Separate section on majorizing value functions
  • logit example with higher derivatives
  • Mean value and taylor majorization material

Version 030215

  • Higher derivatives for the logit plots and formulas
  • Higher derivatives for the probit, empty section
  • Changed the order of some sections and chapters
  • Cleanup of various sections
  • Consistent notation for block least squares
  • Consistent notation in tomography section
  • Split convexity in convexity and linear majorization
  • Moved EM into convexity

Version 030315

  • Notation in EM sums and integrals
  • Notation is now a separate chapter -- I intend to make a big deal out of this
  • Moved appendices to background chapter
  • Plan: merge silly README and introduction files for each chapter
  • Added matrix background
  • Added canonical correlation background section
  • cover page !
  • DC example
  • Added probit calculations to sharp quadratic

Version 030415

  • Moved last graphics from gifi into book
  • Moved bibliography and notation files to top level
  • Checked and corrrected chapter and section headers
  • Background on singular value decomposition - start
  • Background on canonical correlation - start
  • Background on eigen value decomposition - start

Version 030515

  • Split eigen background in symmetric and asymmetric
  • Background on symmetric eigen decomposition
  • Started background asymmetric eigen problem
  • Changed chapter title from linear to tangential majorization.
  • Added necessary condition from tangential majorization of concave function.
  • Changed chapter title to higher order majorization.

Version 030615

  • More on asymmetric eigenproblems.
  • Changed names: Sub-level majrization, Dinkelbach majorization, Nesterov Majorization.
  • Added even higher order Nesterov majorization.
  • Added multivariate quadratic sub-level majorization -- start.
  • Nesterov majorization definition and implementation.
  • Rearranged background chapter, new empty sections in matrices and inequalities.
  • Introduced majorization scheme or majorization coupling
  • Decomposition section with examples added.

Version 030715

  • Defined majorizaton coupling.
  • Redid coupling plot for log-logit in rgl.
  • I will start moving figures back into the text, instead of putting them at the end of the page. Markdown and HTML are not LaTeX, there are no floats.
  • Background section on necessary and suffficient conditions for a minimum, added some material on quadratics.
  • Background section on generalized inverses. Still empty.
  • Necessary conditions for minimum on sphere or ball.
  • Insert stuff on partial majorization in value functions.

Version 030815

  • I am experimenting with cross-referencing chapters, sections, theorems, figures, maybe even paragraphs and formulas, using the html name attribute.
  • I am experimenting with pretty printing and executing R code in the pages, by using Rgitbook.

Version 030915

  • Replaced some figure with code for knitr
  • Added bibliography items
  • Changed preface name in book.json
  • Added link to my bibliography in preface
  • Replaced all md files by Rmd files
  • Pasted in sharp majorization of even functions
  • Pasted in sharp majorization in two points
  • Material on first secular equation in modified eigenvalues background
  • Must remember to name my chunks

Version 031015

  • Added material on modifed eigen problem
  • Added material on quadratics on a sphere

Version 031115

  • Added more material on quadratics on a sphere
  • Included LaTeX macros on pages
  • Replaced more figures by code
  • Expanded glossary
  • ALS intro
  • Add knitr caches for computations

Version 031215

  • ALS intro edited
  • ALS rate of convergence edited
  • ALSOS section edited
  • Continue cosmetics, cross referencing, glossary, caches
  • Renamed news.md, bibliography.md, notation.md using caps
  • Include LaTeX macros on each page
  • Update README.md in all directories
  • Update book.json to gitbook 2.0.0-beta.3

Version 031315

  • Added some material to majorizing value functions
  • Experimenting with how to link to R code files
  • Thinking about merging subsections into a single section file

Version 031415 (day of pi)

  • Added section on projection vs block relaxation

Version 031515

  • Rewrote section on missing data in linear models (Yates)
  • Redid plots in quadratic majorization of normal distribution and density

Version 031615

  • Try out variables in book.json for chapter and section cross references

Version 031715

  • Moved HEADER.md to the top of all Rmd files.

Version 031815

  • Some experimenting with variables and arrays in book.json

Version 031915

  • No changes

Version 032015

  • Sections rasch and morerasch edited
  • Section on Block Newton edited

Version 032115

  • Added derivatives of implicit functions

Version 032215

  • Added material on marginal functions and solution maps (changed section title)
  • Added classical implicit function theorem

Version 032315

  • No changes

Version 032415

  • Added S-majorization and D-majorization example, with figures and code to Dinkelbach section
  • Graphics for Chebyshev example in 2.8.2 replaced by code, graphics in 2 x 2 plot matrix
  • Started adding section and chapter numbers
  • Graphics for folium redone with code and cache

Version 032515

  • Section on univariate and separable functions
  • Updated book.json to gitbook 2.0.0

Version 032615

  • Add material on Concave-Convex Procedure
  • S-majorization by a quadratic: multivariate case
  • Started section on majorization on a hyperrectangle

Version 032715

  • Add material on location problem
  • Add section on Generalized Weiszfeld Methods

Version 032815

  • Background on liminf/limsup
  • Rearranged some background sections

Version 032915

  • Definition section Majorization Algorithm
  • Replaced more plots with knitr chunks of R code
  • Started section on matrix derivatives

Version 033015

  • Material on matrix derivatives
  • Started section on directional derivatives

Version 033115

  • More on directional derivatives
  • Shift focus to functions with values in extended reals

Version 040115

  • Section on derivates between directional and Taylor

Version 040215

  • More on derivatives
  • book.json gitbook updated to version 2.0.1