Optimization methods in inverse problems and applications to science and engineering

Aktas FS, Ekmekcioglu O, Pinar MC (2021) Provably optimal sparse solutions to overdetermined linear systems with non-negativity constraints in a least-squares sense by implicit enumeration. Optim Eng. https://doi.org/10.1007/s11081-021-09676-2 Atanasov A, Kanchev A, Georgiev S (2021) Reconstruction analysis of honeybee colony collapse disorder modeling. Optim Eng. https://doi.org/10.1007/s11081-021-09678-0 Barnsley MF (1989) Fractals Everywhere. Academic Press, New York Barnsley MF, Ervin V, Hardin D, Lancaster., J. (1985) Solution of an inverse problem for fractals and other sets. Proc Nat Acad Sci USA 83:1975–1977 Barnsley M.F., Hurd L (1995) Fractal image compression, AK Peters Ltd Banach S (1922) Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales. Fund Math 3:133–181 Berenguer MI, Kunze H, La Torre D, Ruiz Galán M (2015) Galerkin schemes and inverse boundary value problems in reflexive Banach spaces. J Comput Appl Math 275:100–112 Berenguer M.I., Kunze H, La Torre D, Ruiz Galán M (2016) Galerkin method for constrained variational equations and a collage-based approach to related inverse problems, J. Comput. Appl. Math. 292(10207): 67-75 Capasso V, Kunze HE, La Torre D, Vrscay ER (2014) Solving inverse problems for differential equations by a"generalized collage" method and application to a mean field stochastic model. Nonlinear Analy Real World Appl 15(1):276–289 Capasso V, Kunze HE, La Torre D, Vrscay ER (2013) Solving inverse problems for biological models using the collage method for differential equations. J Math Biol 67:25–38 Chaofan Huang C, Ren Y, McGuinness EK, Losego MD, Lively RP, Roshan Joseph V (2021) Bayesian optimization of functional output in inverse problems. Optim Eng. https://doi.org/10.1007/s11081-021-09677-1 Fisher Y (1996) Fractal image compression: theory and applications. Springer, New York Garralda-Guillem A.I., Kunze H, La Torre D, Ruiz Galán M (2020) Using the generalized collage theorem for estimating unknown parameters in perturbed mixed variational equations, Commun Nonlin Sci Num Simulation, 91: 105433 Garralda-Guillem AI, Lopez PM (2021) Numerical solution for an inverse variational problem. Optim Eng. https://doi.org/10.1007/s11081-021-09671-7 Keller JB (1976) Inverse problems. Am Math Mon 83(2):107–118 Kunze H, Vrscay ER (1999) Solving inverse problems for ordinary differential equations using the Picard contraction mapping. Inverse Prob 15:745–770 Kunze H, La Torre D, Mendivil F, Vrscay E.R. (2019) Self-similarity of solutions to integral and differential equations with respect to a fractal measure, Fractals, 27 (2): 1950014 Kunze H, La Torre D, Vrscay ER (2012) Solving inverse problems for DEs using the collage theorem and entropy maximization. Appl Math Lett 25(12):2306–2311 Kunze H, La Torre D, Mendivil F, Vrscay ER (2013) Fractal-based methods in analysis. Fractal Based Methods in Analy 9781461418917:1–408 Kunze H.E., La Torre D (2015)Collage-type approach to inverse problems for elliptic PDEs on perforated domains (2015) Electronic J Diff Equ, 48: 11 Kunze H, La Torre D, Levere K, Ruiz Galán M (2015) Inverse problems via the “generalized collage theorem” for vector-valued lax-milgram-based variational problems, Math Problem Eng 2015: 764643 Jacquin., A. (1992) Image coding based on a fractal theory of iterated contractive image transformations, Image Processing. IEEE Trans Image Proc 1:18–30 Jiang Y, Liu J (2021) A numerical study of single source localization algorithms for phaseless inverse scattering problems. Optim Eng https://doi.org/10.1007/s11081-021-09664-6 Li D, La Torre D, Vrscay ER (2021) The intensity-based measure approach to “Weberize” L2-based methods of signal and image approximation. Optim Eng https://doi.org/10.1007/s11081-021-09639-7 Lu N (1997) Fractal imaging, Morgan Kaufmann Publishers Inc Otero D, La Torre D, Michailovich O et al (2020) Optimization of structural similarity in mathematical imaging. Optim Eng https://doi.org/10.1007/s11081-020-09525-8 Ramzani H, Behroozifar M (2020) A scheme for solving two models of the two-dimensional inverse problem. Optim Eng https://doi.org/10.1007/s11081-020-09537-4 Riane N, David C (2021). An inverse Black-Scholes problem Optim Eng https://doi.org/10.1007/s11081-020-09588-7 Riane N, David C (2021) Optimal control of the heat equation on a fractal set. Optim Eng https://doi.org/10.1007/s11081-021-09625-z Samadhiya A, Namrata K, Gupta D (2021) Uncertainty quantification in deterministic parameterization of single diode model of a silicon solar cell. Optim Eng. https://doi.org/10.1007/s11081-021-09679-z Tadi M, Radenkovic M (2021) New computational methods for inverse wave scattering with a new filtering technique. Optim Eng https://doi.org/10.1007/s11081-021-09638-8 Touqeer M, Umer R, Ahmadian A et al (2021) An optimal solution of energy scheduling problem based on chance-constraint programming model using Interval-valued neutrosophic constraints. Optim Eng https://doi.org/10.1007/s11081-021-09622-2 Tychonoff AN (1963) Solution of incorrectly formulated problems and the regularization method. Dokl Akad Nauk SSSR 151:501–504 Tychonoff AN, Arsenin NY (1977) Solution of Ill-posed problems. Winston, Washington Umer R, Touqeer M, Omar AH et al (2021) Selection of solar tracking system using extended TOPSIS technique with interval type-2 pythagorean fuzzy numbers. Optim Eng https://doi.org/10.1007/s11081-021-09623-1 Urbaniak IA, Kunze A, Li D et al (2021) The use of intensity-dependent weight functions to“Weberize” L2-based methods of signal and image approximation. Optim Eng https://doi.org/10.1007/s11081-021-09630-2 Yan M, Wang J, Dai Y et al (2021) A method of multiple-attribute group decision making problem for 2-dimension uncertain linguistic variables based on cloud model. Optim Eng https://doi.org/10.1007/s11081-021-09670-8