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X.-W. Liu and Y.-X. Yuan, “A Null-Space Primal-Dual Interior-Point Algorithm for Nonlinear Optimization with Nice Convergence Properties,” Mathematical Programming, Vol. 125, No. 1, 2010, pp. 163-193. doi:10.1007/s10107-009-0272-y

has been cited by the following article:

• TITLE: Minimizing Complementary Pivots in a Simplex-Based Solution Method for a Quadratic Programming Problem

  AUTHORS: Elias Munapo

  KEYWORDS: Quadratic Programming; Convex; Karusha-Kuhn-Tucker; Simplex Method

  JOURNAL NAME: American Journal of Operations Research, Vol.2 No.3, September 19, 2012

  ABSTRACT: The paper presents an approach for avoiding and minimizing the complementary pivots in a simplex based solution method for a quadratic programming problem. The linearization of the problem is slightly changed so that the simplex or interior point methods can solve with full speed. This is a big advantage as a complementary pivot algorithm will take roughly eight times as longer time to solve a quadratic program than the full speed simplex-method solving a linear problem of the same size. The strategy of the approach is in the assumption that the solution of the quadratic programming problem is near the feasible point closest to the stationary point assuming no constraints.