Novel approach to accelerating Newton's method for sup-norm optimization arising inH ?-control

Autor:	O. Merino, J. W. Helton
Rok vydání:	1993
Předmět:	Mathematical optimization Control and Optimization Applied Mathematics Computation Management Science and Operations Research Optimal control symbols.namesake Uniform norm Rate of convergence Theory of computation Convergence (routing) symbols Newton's method Analytic function Mathematics
Zdroj:	Journal of Optimization Theory and Applications. 78:553-578
ISSN:	1573-2878 0022-3239
DOI:	10.1007/bf00939882
Popis:	We present algorithms for solving general sup-norm minimization problems over spaces of analytic functions, such as those arising inH∞ control. We also give an analysis and some theory of these algorithms. Part of this is specific to analytic optimization, while part holds for general sup-norm optimization. In particular, we are proposing a type of Newton-type algorithm which actually uses very high-order terms. The novel feature is that higher-order terms can be chosen in many ways while still maintaining a second-order convergence rate. Then, a clever choice of higher-order terms greatly reduces computation time. Conceivably this technique can be modified to accelerate Newton algorithms in some other circumstances. Estimates of order of convergence as well as results of numerical tests are also presented.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b284b763fa3f1e96828c971d9f22be88 https://doi.org/10.1007/bf00939882 Zobrazit plný text záznamu Full text from SpringerLink