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ABS Methods for Nonlinear Optimization

  • Emilio Spedicato
  • Zunquan Xia
Part of the NATO ASI Series book series (ASIC, volume 434)

Abstract

ABS methods have been introduced by Abaffy, Broyden and Spedicato (1984) initially for solving general linear systems and have been later extended to solving linear least squares and nonlinear systems. Applications to nonlinear optimization have been considered recently mainly by Chinese researchers. In this paper we present the basic results on ABS methods for linear systems and then we consider in more detail a number of applications to nonlinear optimization, particularly the construction of general Quasi-Newton updates, subject possibly to sparsity, and a unified formulation of feasible descent direction methods for linearly constrained optimization.

Keywords

Gradient Projection Method Nest Dissection Search Vector Symmetric Algorithm Feasible Descent Direction 
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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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Emilio Spedicato
    • 1
  • Zunquan Xia
    • 2
  1. 1.Department of MathematicsUniversity of BergamoBergamoItaly
  2. 2.Department of Applied MathematicsDalian University of TechnologyDalianP.R. China

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