Logo
 

Akhtar A. Khan: Publications


Research Monographs:

    1. Uncertainty Quantification in Variational Inequalities. Theory, Numerics, and Applications, Baasansuren Jadamba, Akhtar A. Khan, Fabio Raciti, CRC Press, 2019 (in progress).
    2. Introduction to Set-Valued Optimization, Akhtar A. Khan, Christiane Tammer, Constantin Zalinescu, Springer, 2014, 765 pages.


Edited Books:

    1. Variational Analysis and Set Optimization.  Akhtar A. Khan, Elisabeth Koebis, and Christiane Tammer, Taylor & Francis, 2019.
    2. Nonlinear Analysis and Variational Problems, Panos Pardalos, Themistocles M. Rassias, Akhtar A. Khan, Springer, 2009.

 

Edited Journals Special Issues:

 


  1. Variational Analysis and Nonsmooth Optimization. Special issue of the international journal "Optimization" dedicated to the 70th birthday of Prof. Dr. Boris Mordukhovich. Editors:  Akhtar Khan, Mau Nam Nguyen, Christiane Tammer, Bao Troung,  2019.
  2. Biomechanical constitutive model identification. Special issue of the international journal "Mathematical Problems in Engineering", Hindawi Publications. Editors: Guillermo Rus, Akhtar A. Khan, Juan Melchor, Marie Muller. 2019.
  3. Set-Valued Optimization and Variational Analysis. Special issue of the international journal "Optimization" dedicated to the 65th birthday of Prof. Dr. Johannes Jahn. Editors:  Gabriele Eichfelder, Akhtar Khan, Andreas Lohne, Christiane Tammer,  2018.
  4. Variational Analysis and Nonsmooth Optimization.  Special issue of the international journal "Optimization" dedicated to the memory of Jonathan Michael Borwein. Editors: Regina Burachik, Akhtar Khan, Christiane Tammer, Doug Ward,  2018.
  5. Deterministic and Stochastic Variational Principles and Applications. Special issue of the international journal "Journal of Optimization Theory and Applications". Editors: Wilfried Grecksch, Akhtar A. Khan, Hannelore  Lisei, and Christiane Tammer, Springer,  2015.


Research Papers

 

  1. B. Jadamba, A. A. Khan, and M. Sama, Stable Conical Regularization by Constructible Dilating Cones with an Application to Lp-Constrained Optimization Problems (revised version under review), 2018.
  2. L. Huerga, A. A. Khan, M. Sama, A Henig Conical Regularization Approach for Circumventing the Slater Conundrum in Linearly lp-Constrained Least Squares (under review), 2018.
  3. A. A. Khan, S. Migorski, and M. Sama,  Inverse Problems for Multi-Valued Quasi Variational Inequalities and Noncoercvie Variational Inequalities With Noisy Data, (under review), 2018.
  4. N. Hebestreit, A. A. Khan, E. Koebis, and C. Tammer, Existence Theorems and Regularization Methods for Non-Coercive Vector Variational and Vector Quasi-Variational Inequalities, (under review), 2018.
  5. B. Jadamba, A. A. Khan, R. Lopez, and M. Sama, Conical Regularization for Multi-Objective Optimization Problems, (under review), 2018.
  6. C. Clason, A. A. Khan, M. Sama, and C. Tammer, Contingent Derivatives and Regularization for Noncoercive Inverse Problems. DOI: 10.1080/02331934.2018.1442448.
  7. D. N. Hao, A. A. Khan, M. Sama, and C. Tammer, Inverse Problems in Variational Inequalities by Minimizing Energy. Accepted (at press, 2018).
  8. B. Jadamba, A. A. Khan, R. Kahler, and M. Sama, Elliptic Inverse Problems of Identifying Nonlinear Parameters, Pure and Applied Functional Analysis,  3, 309--326 2018.
  9. M. Cho, A. A. Khan, T. Malysheva, M. Sama, and L. White,  Stability Analysis of the Inverse Problem of Parameter Identification in Mixed Variational Problems, Applications of Nonlinear Analysis, Springer, 134, 61--100, 2018.
  10. A. A. Khan, D. Motreanu, Inverse problems for quasi-variational inequalities, Journal of Global Optimization, 70, 401--411, 2018.
  11. B. Jadamba, A. A. Khan, M. Sama, C. Tammer, On convex modified output least-squares for elliptic inverse problems: stability, regularization, applications, and numerics, Optimization, 60, 983--1012, 2017.
  12. J. Gwinner, B. Jadamba, A. A. Khan, M. Sama, Identification in variational and quasi-variational inequalities, Journal of Convex Analysis, 25, 1--26, 2018.
  13. B. Jadamba, A. A. Khan, A. Oberai, M. Sama, First-Order and Second-Order Adjoint Methods For Parameter Identification Problems with an Application to the Elasticity Imaging Inverse Problem, Inverse Problems in Science and Engineering, 1-20, 2017. DOI: 10.1080/17415977.2017.1289195.
  14. A. A. Khan, B. Solemani, Chr. Tammer,  Second-Order Optimality Conditions in Set-Valued Optimization with Variable Ordering Structure, Pure and Applied Functional Analysis,  Volume 2, No. 2, 305--316, 2017.
  15. M. Cho, B. Jadamba, A. A. Khan, A. A. Oberai, and M. Sama, Identification in Mixed Variational Problems by Adjoint Methods with Applications, Modeling and Optimization: Theory and Applications,  Springer, 213, 65-84, 2017.
  16. M. Cho, B. Jadamba, R. Kahler, A. A. Khan, and M. Sama, First-order and second-order adjoint methods for the inverse problem of identifying nonlinear parameters in PDEs, Industrial Mathematics and Complex systems, Springer, pp. 147--163, 2017.
  17. A. Gibali, B. Jadamba, A. A. Khan, C. Tammer, W. Winkler, Gradient and Extragradient Methods for the Elasticity Imaging Inverse Problem Using an Equation Error Formulation: A Comparative Numerical Study, Contemporary Mathematics, 659, 65--89, 2016.
  18. B. Jadamba, A. A. Khan, F. Raciti, C. Tammer, B. Winkler, Iterative Methods for the Elastography Inverse Problem of Locating Tumors, Essays in Mathematics and its Applications, Springer, 109-141, 2016.
  19. B. Jadamba, A. A. Khan, M. Sama, C. Tammer, An Optimization Framework for Elliptic Inverse Problems: Stability, Optimality, Regularization, Discretization, and Applications. (Revised version submitted on 10th November, 2016).
  20. A. A. Khan, D. Motreanu, Existence Theorems for Elliptic and Evolutionary Variational and Quasi-Variational Inequalities, Journal of Optimization Theory and Application, 167, 1136--1161, 2015.
  21. B. Jadamba, A. A. Khan, M. Sama, Error estimates for integral constraint regularization of state-constrained elliptic control problems, Computational Optimization and Application, 2016. pp. 1-33. DOI 10.1007/s10589-016-9885-2.
  22. B. Jadamba, A. A. Khan, M. Sama, Stability of the Conical Regularization for Constructible Dilating Cones (Under review for Optimization Letters, 2016).
  23. E. Koebis, A. A. Khan, C. Tammer, Scalarization Methods in Multiobjective Optimization, Robustness, Risk Theory and Finance, Springer, 135-157, 2015.
  24. B. Jadamba, A. A. Khan, R. Kahler, F. Raciti, B. Winkler, Identification of Flexural Rigidity in a Kirchhoff Plates Model Using a Convex Objective and Continuous Newton Method, Mathematical Problems in Engineering, Article ID 290301, 11 pages, 2015.
  25. P. Caya, B. Jadamba, A. A. Khan, F. Raciti, B. Winkler, An Equation Error Approach for the Identification of Elastic Parameters in Beams and Plates with $H_1$-Regularization, Lecture Notes in Computer Sciences, Springer, 2015.
  26. A. A. Khan, C. Tammer, C. Zalinescu, Regularization of Quasi variational inequalities, Optimization, 64 (2015), 1703--1724.
  27. N. Bush, B. Jadamba, A. A. Khan, F. Raciti, Identification of a Parameter in Fourth-Order Partial Differential Equations by an Equation Error Approach, Mathematica Slovaca, 65 (2015), No. 5, 1--13.
  28. M. Gockenbach, B. Jadamba, A. A. Khan, C. Tammer, W. Winkler, Proximal Method for the Elastography Inverse problem of Tumor Identification Using an Equation Error Approach, Advances in Variational and Hemivariational Inequalities, 169--192, Springer, 2015.
  29. B. Jadamba, A. A. Khan, G. Rus, M. Sama, B. Winkler, A New Convex Inversion Framework for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location, SIAM J. Appl. Math., 74(5), 1486--1510, 2014.
  30. M. Doyley, B. Jadamba, A. A. Khan, M. Sama, B. Winkler, A New Energy Inversion Framework for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location, Numerical Functional Analysis and Application, 35, 984--1017, 2014.
  31. E. Crossen, M. S. Gockenbach, B. Jadamba, A. A. Khan, B. Winkler, An Equation Error Approach for the Elasticity Imaging Inverse Problem for Predicting Tumor Location, Computers Math. Appl. 67 (2014) 122--135.
  32. B. Jadamba, A. A. Khan, F. Raciti, Regularization of stochastic variational inequalities and a comparison of an $L_p$ and a sample path approach, Nonlinear Analysis, 94 (2014) 65--83.
  33. A. A. Khan, M. Sama, A New Conical Regularization for Some Optimization and Optimal Control Problems: Convergence Analysis and Finite Element Discretization, Numerical Functional Analysis and Optimization, 34 (2013) 861--895.
  34. N. Cahill, B. Jadamba, A. A. Khan, M. Sama, and B. Winkler, A First-Order Adjoint and a Second-Order Hybrid Method for an Energy Output Least Squares Elastography Inverse Problem of Identifying Tumor Location, Boundary Value Problems, 2013, 2013:263.
  35. A. Gibali, B. Jadamba, A. A. Khan, J. Oleksyn, Gradient and Extragradient Methods for an Elliptic Inverse Problem of Parameter Identification: A Numerical Study, I. J. Pure and Applied Mathematics, 4 (2013), 33--51.
  36. A. A. Khan, C. Tammer, Generalized Dubovitskii-Milyutin Approach in Set-Valued Optimization, Vietnam Journal of Mathematics, 40, 285--304, 2012.
  37. A. A. Khan, D. Motreanu, Local Minimizers Versus X-Local Minimizers, Optimization Letters, 7, 1027--1033, 2013.
  38. A. A. Khan, C. Tammer, Second-Order Optimality Conditions in Set-valued Optimization via Asymptotic Derivatives, Optimization, 62, 743--758, 2013.
  39. B. Jadamba, A. A. Khan, M. Paulhamus and M. Sama, Proximal Point Methods for the Inverse Problem of Identifying Parameters in Beam Models, Emerging Applications of Wavelet Methods, American Institute of Physics, 1463 (2012) 16--38.
  40. A. A. Khan. M. Sama, Regularization for State Constrained Optimal Control Problems by Half Spaces Based Decoupling, Systems Control Letters, 61 (2012) 707–-713.
  41. A. A. Khan, M. Sama, Optimal Control of Multivalued Quasi Variational Inequalities, Nonlinear Analysis, 75 (2012) 1419–-1428.
  42. A. A. Khan. M. Sama, A Multiplier Rule for Stable Problems in Vector Optimization, J. Convex Analysis, 19 (2012) 525--539.
  43. A. A. Khan, D. Ward, Toward Second-Order Sensitivity Analysis in Set-Valued Optimization, Journal of Nonlinear and Convex Analysis, 13, 65-83, 2012.
  44. B. Jadamba, A. A. Khan, M. Sama, Inverse Problems on Parameter Identification in Partial Differential Equations, Mathematical Methods, Models and Algorithms in Science and Technology, World Scientific, 228--258, 2011.
  45. B. Jadamba, A. A. Khan, M. Sama, Generalized Solutions of Quasi Variational Inequalities, Optimization Letters, 6, 1221--1231, 2012.
  46. B. Jadamba, M.S. Gockenbach, A. A. Khan, A Comparative Numerical Study of Optimization Approaches for elliptic Inverse Problems, JMI International Journal of Mathematical Sciences, 1 (2010) 35--56.
  47. B. Jadamba, B.D. Rouhani, A. A. Khan, F. Raciti, Generalized Solutions of Multi-valued Monotone Quasi Variational Inequalities. Optimization and Optimal Control: Theory and Applications, edited by A. Chinchuluun, P.M. Pardalos, R. Enkhbat and I, Tseveendorj, Springer, 227-240, 2010.
  48. M.S. Gockenbach, A. A. Khan, An Abstract Framework for Elliptic Inverse Problems. Part 2: An Augmented Lagrangian Approach, Mathematics and Mechanics of Solids, 14 (2009) 517--539.
  49. E. Hernandez, A. A. Khan, L. Rodriguez-Marin, M. Sama, Computation Formulas and Multiplier Rules for Graphical Derivatives in Separable Banach Spaces, Nonlinear Analysis, 71 (2009) 4241--4250.
  50. G. Isac, A. A. Khan, Second-order Optimality Conditions in Set-valued Optimization by a New Tangential Derivative, Acta Mathematica Vietnamica, 34 (2009) 81--90.
  51. F. Giannessi, A. A. Khan, On the Envelope of a Variational Inequality, Nonlinear Analysis and Variational Problems, Springer-Verlag, 2009, 285--294.
  52. A. Caruso A. A. Khan, F. Raciti, Continuity Results for a Class of Variational Inequalities with Application to Time Dependent Network Problems, Numerical Functional Analysis and Optimization, 30 (2009) 1278--1288.
  53. G. Isac, A. A. Khan, Dubovitski-Milutin Approach in Set-valued Optimization, SIAM Journal on Control and Optimization, 47 (2008) 144--162.
  54. B. Jadamba, A. A. Khan, Error Estimates for the Inverse Problem of Identifying Variable Coefficients by the Modified Least-squares, Indian J. Industrial and Applied Mathematics, 1 (2008) 1--9. B. Djafari Rouhani, A. A. Khan, F. Raciti, Penalization and Regularization for Multi-valued Pseudo-monotone Variational Inequalities with Mosco Approximation on Constraint Sets, J. Global Optimization, 40 (2008) 147--153.
  55. M. S. Gockenbach, B. Jadamba, A. A. Khan, Equation Error Approach for Elliptic Inverse Problems with an Application to the Identification of Lam\'e Parameters, Inverse Problems in Science and Engineering, 16 (2008) 349--367.
  56. B. Jadamba, A. A. Khan, F. Raciti, On the Inverse Problem of Identifying Lam'e coefficients in Linear Elasticity, Computer and Mathematics with Applications, 56 (2008) 431--443.
  57. A. A. Khan, B.D. Rouhani, Iterative Regularization for Elliptic Inverse Problems, Computer and Mathematics with Applications, 54 (2007) 850--860.
  58. M. S. Gockenbach, A. A. Khan, An Abstract Framework for Elliptic Inverse Problems. Part 1: An Output Least-squares Approach, Mathematics and Mechanics of Solids, 12 (2007) 259--276.
  59. M. S. Gockenbach, B. Jadamba, A. A. Khan, Numerical Estimation of Discontinuous Coefficients by the Method of Equation Error, International Journal of Mathematics and Computer Science, 1 (2006) 343--359.
  60. B. Jadamba and V.V. Kalashnikov, A. A. Khan, First and Second Order Optimality Condition in Set-Optimization. In: Optimization with multivalued mappings, S.~Dempe et. al., Springer, 265--276, 2006.
  61. M. S. Gockenbach, A. A. Khan, Identification of Lam\'e Parameters in Linear Elasticity: A Fixed Point Approach, Journal of Industrial and Management Optimization, 1 (2005) 487--497.
  62. J. Jahn, A. A. Khan, P. Zeilinger, Second order optimality conditions in set-valued optimization, Journal of Optimization Theory and Applications, 125 (2005) 331--347.
  63. M. S. Gockenbach, A. A. Khan, A Convex Objective Functional for Elliptic Inverse Problems, In: Mathematical models and methods for real world systems, K.M. Furuti, M.Z. Nashed and A.H. Siddiqi (eds.), Chapman \& Hall/CRC,
    389--419, 2005.
  64. A. A. Khan, F. Raciti, On Traffic Equilibrium Problems: Further Models. In: Variational analysis and applications, F. Giannessi and A. Maugeri, Kluwer Academic Publishers, 579--588, 2005.
  65. J. Jahn, A. A. Khan, Some Calculus Rules for Contingent Epiderivatives, Optimization, 52 (2003) 113--125.
  66. A. A. Khan, F. Raciti, A Multiplier Rule in Set-valued Optimization, Bulletin of the Australian Mathematical Society, 68 (2003) 93--100.
  67. B. Djafari Rouhani, A. A. Khan, On the Embedding of Variational Inequalities, Proceedings of the American Mathematical Society, 131 (2003) 3861--3871.
  68. J. Jahn, A. A. Khan, On the Existence of Contingent Epiderivatives for Set-valued Maps, Applied Mathematics Letters, 16 (2003) 1179--1185.
  69. J. Jahn, A. A. Khan, Generalized Contingent Epiderivatives in Set-valued Optimization: Optimality Conditions, Numerical Functional Analysis and Optimization, 28 (2002) 807--831.
  70. J. Jahn, A. A. Khan, Existence Theorems and Characterizations of Generalized Contingent Epiderivatives, Journal of Nonlinear and Convex Analysis, 3 (2002) 1--15.
  71. A. A. Khan, A Regularization Approach for Variational Inequalities, Computers and Mathematics with Applications, 42 (2001) 65--74.
  72. F. Giannessi, A. A. Khan, Regularization of Non-coercive Quasi Variational Inequalities, Control and Cybernetics, 29 (2000) 91--110.
  73. V. V. Kalashniko, A. A. Khan, A Regularization Approach for Variational Inequalities with Pseudo-monotone Operators. In: Operations research proceedings 1999. Selected papers of the symposium, Magdeburg, Germany,
    K.~Inderfurth (ed.), Springer Berlin, 19--22, 2000.
  74. K. Ahmad, A. A. Khan, Study of Variational Inequalities with Monotone Operators. In: Industrial and applied mathematics, A.H.~Siddiqi and K.Ahmad (eds.), Narosa Publishing House, London, 116--127, 1998.
  75. K. Ahmad, A. A. Khan, Solution of Variational Inequalities by Operator Method of Regularization. In: Functional analysis. Selected topics, P.~K.~Jain (ed.), Narosa Publishing House, London, 140--151, 1998.
  76. B. Jadamba, A. A. Khan, Regularized Auxiliary Problem Principle for Variational Inequalities, Computers and Mathematics with Applications, 4 (2000) 995--1002.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RIT Logo

COPYRIGHT © ROCHESTER INSTITUTE OF TECHNOLOGY
ALL RIGHTS RESERVED | Disclaimer | Copyright Information