Abdelazeem, M. M., 2013, Solving ill-posed magnetic inverse problem using a parameterized trust-region sub-problem: Contributions to Geophysics and Geodesy, 43(2), 99–123.
Abdelrahman, E. M., and Sharafeldin, S. M., 1996, An iterative least-squares approach to depth determination from residual magnetic anomalies due to thin dikes: Applied Geophysics, 34, 213–220.
Andrei, N., 2008, An unconstrained optimization test functions collection: Advanced Modeling and Optimization, 10(1), 147-161.
Aster, R. C., Borchers, B., and Thurber, C. H., 2013, Parameter Estimation and Inverse Problems: Elsevier, Amsterdam.
Atchuta, R. D., Ram Babu, H. V., and Sanker Narayan, P. V., 1980, Relationship of magnetic anomalies due to subsurface features and the interpretation of sloping contacts: Geophysics, 25, 32–36.
Azizi, H., Mehrabi, B., and Akbarpour, A., 2009, Genesis of Tertiary magnetite–apatite deposits, Southeast of Zanjan, Iran: Resource Geology, 59(4), 330-341.
Berghen, F. V., 2004, CONDOR: a constrained, non-linear, derivative-free parallel optimizer for continuous, high computing load, noisy objective functions: PhD. thesis, Universite Libre de Bruxelles, Faculte des Sciences Appliquees.
Boyd, S., and Vandenberghe, L., 2004, Convex Optimization: Cambridge.
Conn, A., Gould, N., and Toint, P., 2000, Trust Region Methods: Society for Industrial and Applied Mathematics (SIAM), Philadelphia PA.
Dan, H., Yamashita, N., and Fukushima, M., 2002, Convergence properties of the inexact Levenberg-Marquardt method under local
error bound: Optimization Methods and Software, 17(4), 605–626.
Ekinci, Y. L., 2016, MATLAB-based algorithm to estimate depths of isolated thin dike-like sources using higher-order horizontal derivatives of magnetic anomalies: SpringerPlus, 5(1).
Fan, J. Y., 2003, A modified Levenberg-Marquardt algorithm for singular system of nonlinear equations: Computational Mathematics, 21(5), 625–636.
Fan, J., and Pan, J., 2006, Convergence properties of a self-adaptive Levenberg-Marquardt algorithm under local error bound condition: Computational Optimization and Applications, 34(1), 47–62.
Fletcher, R., 1980, Practical Methods of Optimization, Volume 1: Unconstrained Optimization: John Wiley & Sons.
Gavin, H. P., 2017, The Levenberg-Marquardt method for nonlinear least squares curve-fitting problems: Department of Civil and Environmental Engineering, Duke Unversity.
Gay, D. M., 1981, Computing optimal locally constrained steps: SIAM Journal on Scientific and Statistical Computing, 2(2), 186-197.
Gay, P., 1963, Standard curves for interpretation of magnetic anomalies over long tabular bodies: Geophysics, 28, 161–200.
Ghanati, R., Ghari, H. A., and Fatehi, M., 2017, Regularized nonlinear inversion of magnetic anomalies of simple geometric models using Occam’s method: an application to the Morvarid iron-apatite deposit Iran: Acta Geodaetica et Geophysica, 52(4), 555-580.
Ghanati, R., Ghari, H. A., Mirzaei, M., and Hafizi, M. K., 2015, Nonlinear inverse modeling of magnetic anomalies due to thin sheets and cylinders using Occam’s method: in 8th congress of the Balkan geophysical society, Chania, Greece.
Goldfeld, S. M., Quandt, R. E., and Trotter, H. F., 1966, Maximization by quadratic hill-climbing: Econometrica, 34, 541-551.
Grodzevich, O., 2004, Regularization using Parameterized Trust Region Sub-problem: M.Sc. thesis in mathematics, University of Waterloo, Ontario, Canada.
Gunn, P. J., 1997, Quantitative methods for interpreting aeromagnetic data: a subjective review: AGSO Journal of Australian Geology and Geophysics, 17(2), 105-113.
Hanke, M., 1997, A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems: Inverse Problems, 13(1), 79-95.
Kabanikhin, S. I., 2008, Definitions and examples of inverse and ill-posed problems: Journal of Inverse and Ill-Posed Problems, 16, 317–357.
Karush, W., 1939, Minima of Functions of Several Variables with Inequalities as Side Constraints: M.Sc. Dissertation, Department of Mathematics, University of Chicago, Chicago, Illinois.
Kuhn, H. W., Tucker, A. W., 1951, Nonlinear programming: Proceedings of 2nd Berkeley Symposium, Berkeley: University of California Press, 481–492.
Marquardt, D., 1963, An Algorithm for Least-Squares Estimation of Nonlinear Parameters, SIAM Journal on Applied Mathematics:
11 (2): 431–441.
Martinez, J. M., 1994, Local minimizers of quadratic functions on Euclidean balls and spheres: SIAM Journal of Optimization, 4(1), 159-176.
Mazaheri, M. S., Ghaderi, M., and Karimpour, M. H., 2010, Aliabad-Morvarid iron-apatite deposit, a Kiruna type example in Iran: 1st International Applied Geological Congress, Department of Geology at Islamic Azad University, Mashhad Branch, Iran.
Menke, W., 1984, Geophysical Data Analysis: Discrete Inverse Theory: Academic Press, Cambridge.
Moré, J. J., and Sorensen, D. C., 1983, Computing a trust region step: SIAM Journal on Scientific and Statistical Computing, 4(3), 553-572.
Nabighian, M. N., Grauch, V. J. S., Hansen, R. O., LaFehr, T. R., Li, Y., Peirce, J. W., Phillips, J. D., and Ruder, M. E., 2005, The historical development of the magnetic method in exploration: Geophysics, 70(6), 33-61.
Nocedal, J., and Wright, S. J., 1999, Numerical Optimization: Springer series in operations research edition.
Petrov, Y. P., and Sizikov, V. S., 2005, Well-Posed, Ill-Posed, and Intermediate Problems with Applications: Berlin, Boston: De Gruyter.
Powell, M. J. D., 1975, Convergence properties of a class of minimization algorithms: in Nonlinear Programming 2, 0. L. Mangasarian, R. R. Myer, and S. M. Robinsons, Eds., Academic Press, New York, 1-27.
Prakas Rao, T. K. S, Subrahmanyam, M., and Srikrishna Murthy, A., 1986, Nomograms for direct interpretation of magnetic anomalies due to long horizontal cylinders: Geophysics, 51(11), 2150–2159.
Raju, D. C. V., 2003, LIMAT: a computer program for least-squares inversion of magnetic anomalies over long tabular bodies: Computer and Geoscience, 29, 91–98.
Shan, Sh., 2008, A Levenberg-Marquardt Method For Large-Scale Bound-Constrained Nonlinear Least-Squares Master of Science thesis: The Faculty of Graduate Studies (Computer Science), The University of British Columbia.
Sorensen, D. C., 1980, Newton’s method with a model trust region modification: SIAM Journal on Numerical Analysis, 19(2), 409–426.
Stanley, J. M., 1977, Simplified gravity and magnetic interpretation of contact and dyke-like structures: Bulletin of the Australian Society of Exploration Geophysicists, 8(3), 60–64.
Telford, W. M., Geldart, L. P., and Sheriff, R. E., 1990, Applied Geophysics, 2nd Edition: Cambridge University Press, Cambridge.
Tikhonov, A. N., and Arsenin, V. Y., 1977, Solutions of Ill-Posed Problems: Winston and Sons, Washington DC.
Tlas, M., and Asfahani, J., 2011, Fair function minimization for interpretation of magnetic anomalies due to thin dikes, spheres and faults: Applied Geophysics, 75(1), 237-243.
Wang, Y., and Ma, Sh., 2009, A fast subspace method for image deburring: Applied Mathematics and Computation, 215, 2359–2377.
Wang, Y., and Yuan, Y., 2001, A trust region method for solving distribute parameter identification problems: Journal of Computational Mathematics, 21(6), 759-772.
Wang, Y., and Yuan, Y., 2005, Convergence and regularity of trust region methods for nonlinear ill-posed inverse problems: Inverse Problems, 21(3), 821–838.
Yamashita, N., and Fukushima, M., 2001, On the rate of convergence of the Levenberg-Marquardt method: Computing (Suppl.), 15, 239–249.
Yuan, Y., 2000, A review of trust region algorithms for optimization: in: Ball, J. M., Hunt, J. C. R. (eds.) ICIAM 99, Proceedings of the Fourth International Congress on Industrial and Applied Mathematics, 271–282, Oxford University Press, Oxford.
Yuan, Y., 2015, Recent advances in trust region algorithms: Mathematical Programming, 151(1), 249–281.