Download Acta Numerica 1995 (Volume 4) by Arieh Iserles PDF

By Arieh Iserles

Acta Numerica has validated itself because the top discussion board for the presentation of definitive reports of numerical research issues. Highlights of this year's factor comprise articles on sequential quadratic programming, mesh adaption, unfastened boundary difficulties, and particle equipment in continuum computations. The invited papers will let researchers and graduate scholars alike to quick snatch the present tendencies and advancements during this box.

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Additional resources for Acta Numerica 1995 (Volume 4)

Example text

2). This implies that the active sets are the same and that strict complementary slackness (assumption A3) holds for both. 1) is minimize V/(x fc ) t d x + ^dx Bf-dx dx subject to: Vflr(a;fc)tdx + g(xk) < 0. 2). 4) are the same. 4) will identify the correct active set. 3) will be satisfied if the Bk are always positive definite or if they satisfy the condition lim Vk(Bk - HC*)Vk = 0. 5) k—>oo This latter condition implies two-step superlinear convergence by Theorem 5. Prom Section 3 linear, superlinear or two-step superlinear convergence is ensured if Bk approaches HC* in one of the ways hypothesized in Theorems 2-5.

Overton (1985), 'Projected Hessian updating algorithms for nonlinearly constrained optimization problems', SIAM Journal on Numerical Analysis 22, 821-850. E. M. Omojokun (1989), 'Trust region algorithms for optimization with nonlinear equality and inequality constraints', PhD thesis, University of Colorado. J. M. Ortega and W. C. Rheinboldt (1970), Iterative Solution of Nonlinear Equations In Several Variables, Academic Press, New York. E. R. Panier and A. L. Tits (1993), 'On combining feasibility, descent and superlinear convergence in inequality constrained optimization', Mathematical Programming 59, 261-276.

R. A. Tapia (1977), 'Diagonalized multiplier methods and quasi-Newton methods for constrained optimization', Journal of Optimization Theory and Applications 22, 135-194. R. A. Tapia (1978), 'Quasi-Newton methods for equality constrained optimization: Equivalence of existing methods and a new implementation', in Nonlinear Programming 3 (O. Mangasarian, R. Meyer and S. ), Academic Press, New York, pp. 125-164. R. A. Tapia (1988), 'On secant updates for use in general constrained optimization', Mathematics of Computation 51, 181-202.

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