On the use of quadratic models in unconstrained minimization without derivatives

Optimization Methods and Software

Volumn 19, Issue 3-4, 2004, Pages 399-411

  Powell, M J D ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Frobenius norm updating; No derivatives; Quadratic models; Trust regions; Unconstrained minimization

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; FUNCTIONS; INTERPOLATION; ITERATIVE METHODS; MATHEMATICAL MODELS;

FROBENIUS NORM UPDATING; NO DERIVATIVES; QUADRATIC MODELS; TRUST REGIONS; UNCONSTRAINED MINIMIZATION;

QUADRATIC PROGRAMMING;

EID: 3042692074     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/10556780410001661450     Document Type: Conference Paper

References (8)

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2. A.R. Conn, N.I.M. Gould and Ph.L. Toint (2000). Trust-Region Methods. MPS-SIAM Series on Optimization, Philadelphia.
3. J.E. Dennis and R.B. Schnabel (1983). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice Hall, Englewood Cliffs.
4. R. Fletcher (1987). Practical Methods of Optimization. John Wiley & Sons, Chichester.
5. J.J. Moré and D.C. Sorensen (1983). Computing a trust region step. SIAM J. Sci. Stat. Comput., 4, 553-572.
6. M.J.D. Powell (2002a). UOBYQA: unconstrained optimization by quadratic approximation. Math. Programming, 92, 555-582.
7. M.J.D. Powell (2002b). Least Frobenius norm updating of quadratic models that satisfy interpolation conditions. Report No. DAMTP 2002/NA08, University of Cambridge (to be published in Math. Programming).
8. M.J.D. Powell (2003). On trust region methods for unconstrained minimization without derivatives. Math. Programming, 97, 605-623.