Acta Numerica 1995 (Volume 4) by Arieh Iserles

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By Arieh Iserles

Acta Numerica has verified itself because the major discussion board for the presentation of definitive studies of numerical research subject matters. Highlights of this year's factor comprise articles on sequential quadratic programming, mesh adaption, loose boundary difficulties, and particle equipment in continuum computations. The invited papers will permit researchers and graduate scholars alike to speedy clutch the present traits and advancements during this box.

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Acta Numerica 1995: Volume 4 (v. 4)

Acta Numerica has verified itself because the top discussion board for the presentation of definitive studies of numerical research subject matters. Highlights of this year's factor contain articles on sequential quadratic programming, mesh adaption, loose boundary difficulties, and particle tools in continuum computations.

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Also assume that the columns of Z^ are orthogonal. Z& and Yk could be obtained, for example, by a QR factorization of Vh(xk). SEQUENTIAL QUADRATIC PROGRAMMING 25 Definition 3 Let (xk,uk) be a given solution-multiplier pair and assume that Vh(xk) has full rank. The matrix is called a reduced Hessian for the Lagrangian function at (xk,uk). (a;fc)t. Since by A4 a reduced Hessian at the solution is positive definite, it follows that if (xk,uk) is close enough to (x*,u*) then the reduced Hessian at (xk, uk) is positive definite.

Schnabel (1986), 'Continuity of the null space basis and constrained optimization', Mathematical Programming 35, 32-41. R. H. Byrd, R. B. Schnabel and G. A. Schultz (1985), 'A trust-region strategy for nonlinearly constrained optimization', SIAM Journal on Numerical Analysis 24, 1152-1170. R. H. Byrd, R. A. Tapia and Y. Zhang (1992), 'An SQP augmented Lagrangian BFGS algorithm for constrained optimization', SIAM Journal on Optimization 2, 210-241. M. R. Celis, J. E. Dennis, Jr. and R. A. Tapia (1985), 'A trust-region strategy for nonlinear equality constrained optimization', in Numerical Optimization 1984 (P.

K—HX k This implies that {x } converges to a critical point of 4>F. 12) holds. 14) is globally convergent to a critical point of' 4>F. If the critical points of p, is guaranteed. It is easy to see from the following example that convergence can occur to a local maximum of (NLP).

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