| bibtype |
J -
Journal Article
|
| ARLID |
0648560 |
| utime |
20260417131709.1 |
| mtime |
20260410235959.9 |
| SCOPUS |
105035207662 |
| WOS |
001736106100001 |
| DOI |
10.1080/02331934.2026.2653193 |
| title
(primary) (eng) |
On the Josephy-Halley method for generalized equations |
| specification |
| page_count |
31 s. |
| media_type |
E |
|
| serial |
| ARLID |
cav_un_epca*0258218 |
| ISSN |
0233-1934 |
| title
|
Optimization |
| publisher |
|
|
| keyword |
Halley method |
| keyword |
Josephy-Newton method |
| keyword |
cubic convergence |
| keyword |
generalized equations |
| keyword |
metric regularity |
| author
(primary) |
| ARLID |
cav_un_auth*0497379 |
| name1 |
Roubal |
| name2 |
Tomáš |
| institution |
UTIA-B |
| full_dept (cz) |
Matematická teorie rozhodování |
| full_dept (eng) |
Department of Decision Making Theory |
| department (cz) |
MTR |
| department (eng) |
MTR |
| country |
CZ |
| share |
51 |
| garant |
K |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| author
|
| ARLID |
cav_un_auth*0507856 |
| name1 |
Valdman |
| name2 |
J. |
| country |
CZ |
|
| source |
|
| source |
|
| cas_special |
| abstract
(eng) |
We extend the classical third-order Halley iteration to the setting of generalized equations of the form \[ 0 \in f(x) + F(x), \] 0 is an element of f(x)+F(x), where $ f\colon X\longrightarrow Y $ f:X -> Y is twice continuously Fr & eacute;chet differentiable between Banach spaces and $ F\colon X ightrightarrows Y $ F:X paired right arrows Y is a set-valued mapping with a closed graph. Building on a predictor-corrector framework, our scheme first solves a partially linearized inclusion to produce a predictor $ u_{k+1} $ uk+1, then incorporates second-order information in a Halley-type corrector step to obtain $ x_{k+1} $ xk+1. Under metric regularity of the linearization at a reference solution and H & ouml;lder continuity of $ f'' $ f '' with exponent $ p\in (0,1] $ p is an element of(0,1], we prove that the iterates converge locally with the order 2 + p (cubically when p = 1). Moreover, by constructing a suitable scalar majorant function, we derive Kantorovich-type conditions guaranteeing well-definedness and R-cubic convergence from an explicit neighbourhood of the initial guess. Numerical experiments across one-, two-, and many-dimensional problems validate the theoretical convergence rates and demonstrate the efficiency of the Josephy-Halley method relative to its Josephy-Newton counterpart. |
| result_subspec |
WOS |
| RIV |
BA |
| FORD0 |
10000 |
| FORD1 |
10100 |
| FORD2 |
10101 |
| reportyear |
2027 |
| num_of_auth |
2 |
| inst_support |
RVO:67985556 |
| permalink |
https://hdl.handle.net/11104/0378173 |
| cooperation |
| ARLID |
cav_un_auth*0507857 |
| name |
Czech Technical University, Faculty of Information Technology, Department of Applied Mathematics |
| institution |
FIT CVUT |
| country |
CZ |
|
| confidential |
S |
| mrcbC91 |
C |
| mrcbT16-e |
MATHEMATICS.APPLIED|OPERATIONSRESEARCH&MANAGEMENTSCIENCE |
| mrcbT16-f |
2 |
| mrcbT16-g |
0.3 |
| mrcbT16-h |
6.3 |
| mrcbT16-i |
0.00462 |
| mrcbT16-j |
0.714 |
| mrcbT16-k |
3502 |
| mrcbT16-q |
63 |
| mrcbT16-s |
0.705 |
| mrcbT16-y |
33.62 |
| mrcbT16-x |
1.88 |
| mrcbT16-3 |
914 |
| mrcbT16-4 |
Q2 |
| mrcbT16-5 |
1.600 |
| mrcbT16-6 |
189 |
| mrcbT16-7 |
Q1 |
| mrcbT16-C |
60.7 |
| mrcbT16-M |
0.62 |
| mrcbT16-N |
Q2 |
| mrcbT16-P |
77.5 |
| arlyear |
2026 |
| mrcbU14 |
105035207662 SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
001736106100001 WOS |
| mrcbU63 |
cav_un_epca*0258218 Optimization IN PRINT 2026 0233-1934 1029-4945 Taylor & Francis |
|