Harry Markowitz and the Early History of Quadratic Programming

  • Richard W. Cottle
  • Gerd Infanger


Despite his fame as the father of modern portfolio selection theory, Harry Markowitz’s pioneering efforts in the methodology of quadratic programming are surprisingly obscure. This article is primarily about Markowitz’s critical line algorithm as a contribution to the early history of quadratic programming (as distinct from the more specialized portfolio selection problem). After documenting our claim that the critical line algorithm received scant attention around the time of its introduction, we discuss some factors that may have led to this state of affairs. We then elaborate an argument for the repeatedly made assertion that Markowitz’s critical line algorithm and Philip Wolfe’s simplex method for quadratic programming are equivalent. We do this by relating both of them to the parametric principal pivoting method of quadratic programming and linear complementarity theory.


Quadratic Programming Portfolio Selection Basic Variable Simplex Method Linear Complementarity Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Management Science and EngineeringStanford UniversityStanfordUSA

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