510 Mathematik
Refine
Has Fulltext
- yes (197)
Is part of the Bibliography
- yes (197)
Year of publication
Document Type
- Doctoral Thesis (114)
- Journal article (64)
- Book (6)
- Other (3)
- Report (3)
- Conference Proceeding (2)
- Preprint (2)
- Book article / Book chapter (1)
- Master Thesis (1)
- Review (1)
Keywords
- Optimale Kontrolle (8)
- Nash-Gleichgewicht (7)
- Optimierung (7)
- Extremwertstatistik (6)
- Newton-Verfahren (6)
- Nichtlineare Optimierung (6)
- Mathematik (5)
- optimal control (5)
- Differentialgleichung (4)
- MPEC (4)
Institute
Sonstige beteiligte Institutionen
ResearcherID
- B-4606-2017 (1)
In distance geometry problems and many other applications, we are faced with the optimization of high-dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well-known preconditioning techniques for the conjugate gradient method remain applicable. Very-largescale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the algorithm.
In this paper, convex approximation methods, suclt as CONLIN, the method of moving asymptotes (MMA) and a stabilized version of MMA (Sequential Convex Programming), are discussed with respect to their convergence behaviour. In an extensive numerical study they are :finally compared with other well-known optimization methods at 72 examples of sizing problems.
In Janssen and Reiss (1988) it was shown that in a location model of a Weibull type sample with shape parameter -1 < a < 1 the k(n) lower extremes are asymptotically local sufficient. In the present paper we show that even global sufficiency holds. Moreover, it turns out that convergence of the given statistical experiments in the deficiency metric does not only hold for compact parameter sets but for the whole real line.