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.
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References
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.
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.
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.
Gauvin J. (1977), A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming, Mathematical Programming, 12, pp. 136–138.
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.
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© 2003 Kluwer Academic Publishers B.V.
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Fletcher, R., Leyffer, S. (2003). Filter-type Algorithms for Solving Systems of Algebraic Equations and Inequalities. In: Di Pillo, G., Murli, A. (eds) High Performance Algorithms and Software for Nonlinear Optimization. Applied Optimization, vol 82. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0241-4_12
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DOI: https://doi.org/10.1007/978-1-4613-0241-4_12
Publisher Name: Springer, Boston, MA
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