0648560 20260417131709.120260410235959.9 105035207662 001736106100001 10.1080/02331934.2026.2653193 31 s. E cav_un_epca*02582180233-1934Taylor & Francis Halley method Josephy-Newton method cubic convergence generalized equations metric regularity cav_un_auth*0497379 Roubal Tomáš UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR CZ 51 K Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0507856 Valdman J. CZ PDF 1.71 MB https://www.tandfonline.com/eprint/JWVSDAFMUAQNN3HKXJY4/full?target=10.1080/02331934.2026.2653193#d1e231 https://library.utia.cas.cz/separaty/2026/MTR/roubal-0648560.pdf 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. WOS BA 10000 10100 10101 2027 2 RVO:67985556 https://hdl.handle.net/11104/0378173 cav_un_auth*0507857 Czech Technical University, Faculty of Information Technology, Department of Applied Mathematics FIT CVUT CZ S C MATHEMATICS.APPLIED|OPERATIONSRESEARCH&MANAGEMENTSCIENCE 2 0.3 6.3 0.00462 0.714 3502 63 0.705 33.62 1.88 914 Q2 1.600 189 Q1 60.7 0.62 Q2 77.5 2026 105035207662 SCOPUS PUBMED 001736106100001 WOS cav_un_epca*0258218 Optimization IN PRINT 2026 0233-1934 1029-4945 Taylor & Francis