Algorithms for Continuous Optimization pp 333-356 | Cite as

# ABS Methods for Nonlinear Optimization

## 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## Preview

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## References

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