Luo, Honglin; Wang, Xianfu; Yang, Xinmin Various notions of nonexpansiveness coincide for proximal mappings of functions. (English) Zbl 07809686 SIAM J. Optim. 34, No. 1, 642-653 (2024). MSC: 49J53 46N10 47H09 47H05 26B25 PDFBibTeX XMLCite \textit{H. Luo} et al., SIAM J. Optim. 34, No. 1, 642--653 (2024; Zbl 07809686) Full Text: DOI
Bauschke, Heinz H.; Singh, Shambhavi; Wang, Xianfu The splitting algorithms by Ryu, by Malitsky-Tam, and by Campoy applied to normal cones of linear subspaces converge strongly to the projection onto the intersection. (English) Zbl 07700282 SIAM J. Optim. 33, No. 2, 739-765 (2023). Reviewer: Ravindra Kishor Bisht (Pune) MSC: 41A50 49M27 65K05 47H05 15A10 47H09 49M37 90C25 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., SIAM J. Optim. 33, No. 2, 739--765 (2023; Zbl 07700282) Full Text: DOI arXiv
Bauschke, Heinz H.; Krishan Lal, Manish; Wang, Xianfu Directional asymptotics of Fejér monotone sequences. (English) Zbl 1515.90098 Optim. Lett. 17, No. 3, 531-544 (2023). MSC: 90C25 47H09 47J26 47H05 65K10 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., Optim. Lett. 17, No. 3, 531--544 (2023; Zbl 1515.90098) Full Text: DOI arXiv
Bauschke, Heinz H.; Ouyang, Hui; Wang, Xianfu On circumcenter mappings induced by nonexpansive operators. (English) Zbl 1491.47042 Pure Appl. Funct. Anal. 6, No. 2, 257-288 (2021). MSC: 47H09 47H04 41A50 90C25 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., Pure Appl. Funct. Anal. 6, No. 2, 257--288 (2021; Zbl 1491.47042) Full Text: arXiv Link
Bauschke, Heinz H.; Moursi, Walaa M.; Wang, Xianfu Generalized monotone operators and their averaged resolvents. (English) Zbl 1515.47068 Math. Program. 189, No. 1-2 (B), 55-74 (2021). MSC: 47H05 47H09 49N15 90C25 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., Math. Program. 189, No. 1--2 (B), 55--74 (2021; Zbl 1515.47068) Full Text: DOI arXiv
Alwadani, Salihah; Bauschke, Heinz; Wang, Xianfu Attouch-Théra duality, generalized cycles, and gap vectors. (English) Zbl 07384486 SIAM J. Optim. 31, No. 3, 1926-1946 (2021). MSC: 47H05 49J53 47H09 47N10 49N15 47A06 47J25 90C25 PDFBibTeX XMLCite \textit{S. Alwadani} et al., SIAM J. Optim. 31, No. 3, 1926--1946 (2021; Zbl 07384486) Full Text: DOI arXiv
Alwadani, Salihah; Bauschke, Heinz H.; Revalski, Julian P.; Wang, Xianfu Resolvents and Yosida approximations of displacement mappings of isometries. (English) Zbl 1487.47080 Set-Valued Var. Anal. 29, No. 3, 721-733 (2021). MSC: 47H05 47H09 47A06 90C25 PDFBibTeX XMLCite \textit{S. Alwadani} et al., Set-Valued Var. Anal. 29, No. 3, 721--733 (2021; Zbl 1487.47080) Full Text: DOI arXiv
Bauschke, Heinz H.; Ouyang, Hui; Wang, Xianfu Circumcentered methods induced by isometries. (English) Zbl 07341166 Vietnam J. Math. 48, No. 3, 471-508 (2020). MSC: 47H09 65K10 41A50 65K05 90C25 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., Vietnam J. Math. 48, No. 3, 471--508 (2020; Zbl 07341166) Full Text: DOI arXiv
Wang, Dongying; Wang, Xianfu A parameterized Douglas-Rachford algorithm. (English) Zbl 1461.90104 Comput. Optim. Appl. 73, No. 3, 839-869 (2019). MSC: 90C25 47H05 65K05 PDFBibTeX XMLCite \textit{D. Wang} and \textit{X. Wang}, Comput. Optim. Appl. 73, No. 3, 839--869 (2019; Zbl 1461.90104) Full Text: DOI
Bauschke, Heinz H.; Wang, Caifang; Wang, Xianfu; Xu, Jia Subgradient projectors: extensions, theory, and characterizations. (English) Zbl 1422.49014 Set-Valued Var. Anal. 26, No. 4, 1009-1078 (2018). Reviewer: Gerhard-Wilhelm Weber (Poznań and Ankara) with Nadi Serhan Aydın (Istanbul) MSC: 49J52 49J53 47H04 47H05 47H09 49S05 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., Set-Valued Var. Anal. 26, No. 4, 1009--1078 (2018; Zbl 1422.49014) Full Text: DOI
Planiden, Chayne; Wang, Xianfu Epi-convergence: the Moreau envelope and generalized linear-quadratic functions. (English) Zbl 1507.47006 J. Optim. Theory Appl. 177, No. 1, 21-63 (2018). MSC: 47A06 52A41 47H05 90C31 PDFBibTeX XMLCite \textit{C. Planiden} and \textit{X. Wang}, J. Optim. Theory Appl. 177, No. 1, 21--63 (2018; Zbl 1507.47006) Full Text: DOI arXiv
Bauschke, Heinz H.; Schaad, Jason; Wang, Xianfu On Douglas-Rachford operators that fail to be proximal mappings. (English) Zbl 1514.47092 Math. Program. 168, No. 1-2 (B), 55-61 (2018). MSC: 47J25 47H09 47H05 90C25 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., Math. Program. 168, No. 1--2 (B), 55--61 (2018; Zbl 1514.47092) Full Text: DOI arXiv
Bartz, Sedi; Bauschke, Heinz H.; Wang, Xianfu The resolvent order: a unification of the orders by Zarantonello, by Loewner, and by Moreau. (English) Zbl 1425.47006 SIAM J. Optim. 27, No. 1, 466-477 (2017). MSC: 47H05 47H09 26B25 15B57 47L07 52A41 90C25 PDFBibTeX XMLCite \textit{S. Bartz} et al., SIAM J. Optim. 27, No. 1, 466--477 (2017; Zbl 1425.47006) Full Text: DOI arXiv
Bauschke, Heinz H.; Wang, Caifang; Wang, Xianfu; Xu, Jia On subgradient projectors. (English) Zbl 1316.47043 SIAM J. Optim. 25, No. 2, 1064-1082 (2015). MSC: 47H05 47H09 47N10 49J50 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., SIAM J. Optim. 25, No. 2, 1064--1082 (2015; Zbl 1316.47043) Full Text: DOI arXiv
Bauschke, Heinz H.; Bello Cruz, J. Y.; Nghia, Tran T. A.; Phan, Hung M.; Wang, Xianfu The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle. (English) Zbl 1307.49030 J. Approx. Theory 185, 63-79 (2014). Reviewer: Ctirad Matonoha (Prague) MSC: 49M27 90C25 49M37 47H05 47H09 65K05 65K10 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., J. Approx. Theory 185, 63--79 (2014; Zbl 1307.49030) Full Text: DOI arXiv
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin Rectangularity and paramonotonicity of maximally monotone operators. (English) Zbl 06315981 Optimization 63, No. 4, 487-504 (2014). MSC: 47H05 47A06 47B25 47H09 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., Optimization 63, No. 4, 487--504 (2014; Zbl 06315981) Full Text: DOI arXiv
Wang, Xianfu Most maximally monotone operators have a unique zero and a super-regular resolvent. (English) Zbl 1300.47058 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 87, 69-82 (2013). Reviewer: Yuqiang Feng (Wuhan) MSC: 47H05 47H10 54E52 47H09 54E50 PDFBibTeX XMLCite \textit{X. Wang}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 87, 69--82 (2013; Zbl 1300.47058) Full Text: DOI arXiv
Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu Near equality, near convexity, sums of maximally monotone operators, and averages of firmly nonexpansive mappings. (English) Zbl 1321.47113 Math. Program. 139, No. 1-2 (B), 55-70 (2013). Reviewer: Orestes Bueno (Lima) MSC: 47H05 47H09 47H10 52A20 90C25 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., Math. Program. 139, No. 1--2 (B), 55--70 (2013; Zbl 1321.47113) Full Text: DOI arXiv
Bauschke, Heinz H.; Martín-Márquez, Victoria; Moffat, Sarah M.; Wang, Xianfu Compositions and convex combinations of asymptotically regular firmly nonexpansive mappings are also asymptotically regular. (English) Zbl 1300.47056 Fixed Point Theory Appl. 2012, Paper No. 53, 11 p. (2012). Reviewer: Vasile Berinde (Baia Mare) MSC: 47H05 47H09 47H10 90C25 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., Fixed Point Theory Appl. 2012, Paper No. 53, 11 p. (2012; Zbl 1300.47056) Full Text: DOI arXiv
Bauschke, Heinz H.; Wang, Xianfu; Wylie, Calvin J. S. Fixed points of averages of resolvents: geometry and algorithms. (English) Zbl 1263.47064 SIAM J. Optim. 22, No. 1, 24-40 (2012). Reviewer: Narin Petrot (Phitsanulok) MSC: 47H05 47H09 47J25 65K05 65K10 90C25 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., SIAM J. Optim. 22, No. 1, 24--40 (2012; Zbl 1263.47064) Full Text: DOI arXiv
Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality. (English) Zbl 1263.47066 Set-Valued Var. Anal. 20, No. 1, 131-153 (2012). Reviewer: Rita Pini (Milano) MSC: 47H09 47H05 90C25 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., Set-Valued Var. Anal. 20, No. 1, 131--153 (2012; Zbl 1263.47066) Full Text: DOI arXiv
Wang, Xianfu; Bauschke, Heinz H. Compositions and averages of two resolvents: relative geometry of fixed points sets and a partial answer to a question by C.Byrne. (English) Zbl 1228.47052 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 13, 4550-4572 (2011). Reviewer: Nicolas Hadjisavvas (Hermoupolis) MSC: 47H05 47H09 26B25 47H10 47J25 90C25 PDFBibTeX XMLCite \textit{X. Wang} and \textit{H. H. Bauschke}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 13, 4550--4572 (2011; Zbl 1228.47052) Full Text: DOI arXiv