Isyaku, M.; Tammer, C.; Farajzadeh, A. Existence results and optimization over the set of efficient solutions in vector-valued approximation theory. (English) Zbl 07776544 J. Nonlinear Var. Anal. 7, No. 5, 743-767 (2023). MSC: 90C29 PDFBibTeX XMLCite \textit{M. Isyaku} et al., J. Nonlinear Var. Anal. 7, No. 5, 743--767 (2023; Zbl 07776544) Full Text: DOI
Dinh Nho Hào; Khan, Akhtar A.; Reich, Simeon Convergence rates for nonlinear inverse problems of parameter identification using Bregman distances. (English) Zbl 07776542 J. Nonlinear Var. Anal. 7, No. 5, 715-726 (2023). MSC: 49N45 35R30 PDFBibTeX XMLCite \textit{Dinh Nho Hào} et al., J. Nonlinear Var. Anal. 7, No. 5, 715--726 (2023; Zbl 07776542) Full Text: DOI
Ouakrim, Y.; Boutaayamou, I.; El Yazidi, Y.; Zafrar, A. Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation. (English) Zbl 1521.35208 Inverse Probl. 39, No. 8, Article ID 085011, 33 p. (2023). MSC: 35R30 35J25 65N21 PDFBibTeX XMLCite \textit{Y. Ouakrim} et al., Inverse Probl. 39, No. 8, Article ID 085011, 33 p. (2023; Zbl 1521.35208) Full Text: DOI
Zhu, Xiaopeng; Wu, Zhizhang; Huang, Zhongyi The direct method of lines for forward and inverse linear elasticity problems of composite materials in star-shaped domains. (English) Zbl 1524.65739 Numer. Math., Theory Methods Appl. 16, No. 1, 242-276 (2023). MSC: 65N21 65N40 74A40 74B05 74E30 65N15 65K10 74B10 35Q74 PDFBibTeX XMLCite \textit{X. Zhu} et al., Numer. Math., Theory Methods Appl. 16, No. 1, 242--276 (2023; Zbl 1524.65739) Full Text: DOI
Hoffmann, Heiko; Wald, Anne; Nguyen, Tram Thi Ngoc Parameter identification for elliptic boundary value problems: an abstract framework and applications. (English) Zbl 1491.35458 Inverse Probl. 38, No. 7, Article ID 075005, 49 p. (2022). MSC: 35R30 35D30 35J25 PDFBibTeX XMLCite \textit{H. Hoffmann} et al., Inverse Probl. 38, No. 7, Article ID 075005, 49 p. (2022; Zbl 1491.35458) Full Text: DOI
Jadamba, Baasansuren; Khan, Akhtar A.; Sama, Miguel; Yang, Yidan An iteratively regularized stochastic gradient method for estimating a random parameter in a stochastic PDE. A variational inequality approach. (English) Zbl 07557729 J. Nonlinear Var. Anal. 5, No. 6, 865-880 (2021). MSC: 65C30 35R30 60H15 PDFBibTeX XMLCite \textit{B. Jadamba} et al., J. Nonlinear Var. Anal. 5, No. 6, 865--880 (2021; Zbl 07557729) Full Text: DOI
Hawks, Rachel; Jadamba, Baasansuren; Khan, Akhtar A.; Sama, Miguel; Yang, Yidan A variational inequality based stochastic approximation for inverse problems in stochastic partial differential equations. (English) Zbl 1472.35451 Rassias, Themistocles M. (ed.) et al., Nonlinear analysis and global optimization. Cham: Springer. Springer Optim. Appl. 167, 207-226 (2021). MSC: 35R30 35R60 49N45 65J20 65J22 65M30 PDFBibTeX XMLCite \textit{R. Hawks} et al., Springer Optim. Appl. 167, 207--226 (2021; Zbl 1472.35451) Full Text: DOI
Jadamba, Baasansuren; Khan, Akhtar A.; Sama, Miguel; Starkloff, Hans-Jorg; Tammer, Christiane A convex optimization framework for the inverse problem of identifying a random parameter in a stochastic partial differential equation. (English) Zbl 1471.35332 SIAM/ASA J. Uncertain. Quantif. 9, 922-952 (2021). MSC: 35R30 35R60 49N45 65J20 65J22 65M30 PDFBibTeX XMLCite \textit{B. Jadamba} et al., SIAM/ASA J. Uncertain. Quantif. 9, 922--952 (2021; Zbl 1471.35332) Full Text: DOI
Babaniyi, O.; Jadamba, B.; Khan, A. A.; Richards, M.; Sama, M.; Tammer, C. Three optimization formulations for an inverse problem in saddle point problems with applications to elasticity imaging of locating tumor in incompressible medium. (English) Zbl 1482.35271 J. Nonlinear Var. Anal. 4, No. 2, 301-318 (2020). MSC: 35R30 92C55 74G75 65N30 49N45 PDFBibTeX XMLCite \textit{O. Babaniyi} et al., J. Nonlinear Var. Anal. 4, No. 2, 301--318 (2020; Zbl 1482.35271) Full Text: DOI
Tyagi, Mohit; Barbone, Paul E.; Oberai, Assad A. Residual-based stabilized formulation for the solution of inverse elliptic partial differential equations. (English) Zbl 1447.65121 Comput. Math. Appl. 80, No. 5, 822-836 (2020). MSC: 65N21 35J57 35R30 65N30 74B10 65N12 PDFBibTeX XMLCite \textit{M. Tyagi} et al., Comput. Math. Appl. 80, No. 5, 822--836 (2020; Zbl 1447.65121) Full Text: DOI
Aquino, Wilkins; Bonnet, Marc Analysis of the error in constitutive equation approach for time-harmonic elasticity imaging. (English) Zbl 1421.49031 SIAM J. Appl. Math. 79, No. 3, 822-849 (2019). MSC: 49N45 49K20 49K40 74J25 PDFBibTeX XMLCite \textit{W. Aquino} and \textit{M. Bonnet}, SIAM J. Appl. Math. 79, No. 3, 822--849 (2019; Zbl 1421.49031) Full Text: DOI arXiv
Clason, Christian; Khan, Akhtar A.; Sama, Miguel; Tammer, Christiane Contingent derivatives and regularization for noncoercive inverse problems. (English) Zbl 1422.90060 Optimization 68, No. 7, 1337-1364 (2019). MSC: 90C33 PDFBibTeX XMLCite \textit{C. Clason} et al., Optimization 68, No. 7, 1337--1364 (2019; Zbl 1422.90060) Full Text: DOI arXiv
Guo, Ruchi; Lin, Tao; Lin, Yanping A fixed mesh method with immersed finite elements for solving interface inverse problems. (English) Zbl 1458.74135 J. Sci. Comput. 79, No. 1, 148-175 (2019). MSC: 74S05 74G75 74P10 PDFBibTeX XMLCite \textit{R. Guo} et al., J. Sci. Comput. 79, No. 1, 148--175 (2019; Zbl 1458.74135) Full Text: DOI arXiv
Liu, Tao A wavelet multiscale method for the inverse problem of a nonlinear convection-diffusion equation. (English) Zbl 1376.65125 J. Comput. Appl. Math. 330, 165-176 (2018). MSC: 65M32 35R30 35K57 65T60 76S05 76M20 PDFBibTeX XMLCite \textit{T. Liu}, J. Comput. Appl. Math. 330, 165--176 (2018; Zbl 1376.65125) Full Text: DOI
Cho, M.; Jadamba, B.; Kahler, R.; Khan, A. A.; Sama, M. First-order and second-order adjoint methods for the inverse problem of identifying non-linear parameters in pdes. (English) Zbl 1396.49028 Manchanda, Pammy (ed.) et al., Industrial mathematics and complex systems. Emerging mathematical models, methods and algorithms. Based on the presentations at the international conference, Greater Noida, India, January 29–31, 2016. Singapore: Springer (ISBN 978-981-10-3757-3/hbk; 978-981-10-3758-0/ebook). Industrial and Applied Mathematics, 147-163 (2017). MSC: 49M30 65M32 49J40 PDFBibTeX XMLCite \textit{M. Cho} et al., in: Industrial mathematics and complex systems. Emerging mathematical models, methods and algorithms. Based on the presentations at the international conference, Greater Noida, India, January 29--31, 2016. Singapore: Springer. 147--163 (2017; Zbl 1396.49028) Full Text: DOI
Jadamba, Baasansuren; Khan, Akhtar A.; Sama, Miguel; Tammer, Christiane On convex modified output least-squares for elliptic inverse problems: stability, regularization, applications, and numerics. (English) Zbl 1400.90303 Optimization 66, No. 6, 983-1012 (2017). MSC: 90C48 PDFBibTeX XMLCite \textit{B. Jadamba} et al., Optimization 66, No. 6, 983--1012 (2017; Zbl 1400.90303) Full Text: DOI
Jadamba, B.; Khan, A. A.; Raciti, F.; Tammer, Christiane; Winkler, B. Iterative methods for the elastography inverse problem of locating tumors. (English) Zbl 1401.92127 Rassias, Themistocles M. (ed.) et al., Essays in mathematics and its applications. In honor of Vladimir Arnold. Cham: Springer (ISBN 978-3-319-31336-8/hbk; 978-3-319-31338-2/ebook). 101-131 (2016). MSC: 92C55 92-04 92C10 74C15 PDFBibTeX XMLCite \textit{B. Jadamba} et al., in: Essays in mathematics and its applications. In honor of Vladimir Arnold. Cham: Springer. 101--131 (2016; Zbl 1401.92127) Full Text: DOI
Caya, P.; Jadamba, B.; Khan, A. A.; Raciti, F.; Winkler, B. An equation error approach for the identification of elastic parameters in beams and plates with \(H_1\) regularization. (English) Zbl 1382.74135 Kozubek, Tomáš (ed.) et al., High performance computing in science and engineering. Second international conference, HPCSE 2015, Soláň, Czech Republic, May 25–28, 2015. Revised selected papers. Cham: Springer (ISBN 978-3-319-40360-1/pbk; 978-3-319-40361-8/ebook). Lecture Notes in Computer Science 9611, 60-67 (2016). MSC: 74S30 74G75 74K10 74K20 PDFBibTeX XMLCite \textit{P. Caya} et al., Lect. Notes Comput. Sci. 9611, 60--67 (2016; Zbl 1382.74135) Full Text: DOI
Jadamba, B.; Kahler, R.; Khan, A. A.; Raciti, F.; Winkler, B. Identification of flexural rigidity in a Kirchhoff plates model using a convex objective and continuous Newton method. (English) Zbl 1394.74100 Math. Probl. Eng. 2015, Article ID 290301, 11 p. (2015). MSC: 74K20 35J40 35R30 PDFBibTeX XMLCite \textit{B. Jadamba} et al., Math. Probl. Eng. 2015, Article ID 290301, 11 p. (2015; Zbl 1394.74100) Full Text: DOI
Gockenbach, Mark S.; Jadamba, Baasansuren; Khan, Akhtar A.; Tammer, Christiane; Winkler, Brian Proximal methods for the elastography inverse problem of tumor identification using an equation error approach. (English) Zbl 1319.35297 Han, Weimin (ed.) et al., Advances in variational and hemivariational inequalities. Theory, numerical analysis, and applications. Cham: Springer (ISBN 978-3-319-14489-4/hbk; 978-3-319-14490-0/ebook). Advances in Mechanics and Mathematics 33, 173-197 (2015). MSC: 35R30 49J40 65N30 92C50 PDFBibTeX XMLCite \textit{M. S. Gockenbach} et al., Adv. Mech. Math. 33, 173--197 (2015; Zbl 1319.35297) Full Text: DOI
Zhao, Jingjun; Liu, Tao; Liu, Songshu Identification of space-dependent permeability in nonlinear diffusion equation from interior measurements using wavelet multiscale method. (English) Zbl 1308.65162 Inverse Probl. Sci. Eng. 22, No. 4, 507-529 (2014). MSC: 65M32 65M06 65T60 PDFBibTeX XMLCite \textit{J. Zhao} et al., Inverse Probl. Sci. Eng. 22, No. 4, 507--529 (2014; Zbl 1308.65162) Full Text: DOI
Cahill, Nathan D.; Jadamba, Baasansuren; Khan, Akhtar A.; Sama, Miguel; Winkler, Brian C. A first-order adjoint and a second-order hybrid method for an energy output least-squares elastography inverse problem of identifying tumor location. (English) Zbl 1292.35323 Bound. Value Probl. 2013, Paper No. 263, 19 p. (2013). MSC: 35R30 49N45 65N21 65N30 92C55 PDFBibTeX XMLCite \textit{N. D. Cahill} et al., Bound. Value Probl. 2013, Paper No. 263, 19 p. (2013; Zbl 1292.35323) Full Text: DOI
Zhao, Jingjun; Liu, Tao; Liu, Songshu An adaptive homotopy method for permeability estimation of a nonlinear diffusion equation. (English) Zbl 1279.35063 Inverse Probl. Sci. Eng. 21, No. 4, 585-604 (2013). MSC: 35K60 35R30 65M32 76S05 PDFBibTeX XMLCite \textit{J. Zhao} et al., Inverse Probl. Sci. Eng. 21, No. 4, 585--604 (2013; Zbl 1279.35063) Full Text: DOI
Puel, G.; Aubry, D. Using mesh adaption for the identification of a spatial field of material properties. (English) Zbl 1242.74151 Int. J. Numer. Methods Eng. 88, No. 3, 205-227 (2011). MSC: 74S05 74G75 PDFBibTeX XMLCite \textit{G. Puel} and \textit{D. Aubry}, Int. J. Numer. Methods Eng. 88, No. 3, 205--227 (2011; Zbl 1242.74151) Full Text: DOI Link