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Filter-type Algorithms for Solving Systems of Algebraic Equations and Inequalities

  • Roger Fletcher
  • Sven Leyffer
Part of the Applied Optimization book series (APOP, volume 82)

Abstract

The problem of solving a nonlinear system is transformed into a bi-objective nonlinear programming problem, which is then solved by a prototypical trust region filter SQP algorithm. The definition of the bi-objective problems is changed adaptively as the algorithm proceeds. The method permits the use of second order information and hence enables rapid local convergence to occur, which is particularly important for solving locally infeasible problems. A proof of global convergence is presented under mild assumptions.

Keywords

nonlinear systems nonlinear programming global convergence filter multiobjective optimization 

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References

  1. [1]
    Chin C.M. and Fletcher R. (2001), On the Global Convergence of an SLP-filter algorithm that takes EQP steps, Dundee University, Dept. of Mathematics, Report NA/199.Google Scholar
  2. [2]
    Fletcher R. and Leyffer S. (1997), Nonlinear Programming Without a Penalty Function, Dundee University, Dept. of Mathematics, Report NA/171, to appear in Mathematical Programming.Google Scholar
  3. [3]
    Fletcher R., Leyffer S. and Toint Ph.L. (2000), On the Global Convergence of a Filter-SQP Algorithm, Dundee University, Dept. of Mathematics, Report NA/197, to appear in SIAM Journal of Optimization.Google Scholar
  4. [4]
    Gauvin J. (1977), A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming, Mathematical Programming, 12, pp. 136–138.MathSciNetzbMATHCrossRefGoogle Scholar
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    Powell M.J.D. (1970), A hybrid method for nonlinear equations, in Numerical Methods for Nonlinear Algebraic Equations, (Ed. P. Rabinowitz), Gordon and Breach, London.Google Scholar

Copyright information

© Kluwer Academic Publishers B.V. 2003

Authors and Affiliations

  • Roger Fletcher
    • 1
  • Sven Leyffer
    • 1
  1. 1.Department of MathematicsUniversity of DundeeDundeeScotland UK

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