Joydeep Dutta

 

Welcome to my homepage!

Google Scholar

Contact

FB 323 Department of Economic Sciences, IIT Kanpur.
  +91-512-259-7568,   jdutta@iitk.ac.in

   

EDUCATION

ACADEMIC QUALIFICATIONS

  • Ph.D. in Mathematics, Indian Institute of Technology, Kharagpur, 1998.

  • M.Sc. in Mathematics, Indian Institute of Technology, Kharagpur, 1993.

  • B.Sc. (Honours) in Mathematics, St. Xavier's College, University of Calcutta, 1991.

PUBLICATIONS

  1. Co-authored, "Principles of Optimization Theory" with  Professor C. R. Bector (University of Manitoba, Winnipeg, Canada) and Professor Suresh Chandra, (Indian Institute of Technology, Delhi). Published by Narosa Publishers, New Delhi, India, September 2004 and Alpha Science International, Harrow, U. K, 2005. Pages 224. (Revised and Expanded edition under preparation)

  2. Co-authored, "Optimality Conditions in Convex Optimization : A Finite Dimensional View,"  with Anulekha Dhara. , published by CRC/ Taylor and Francis on October 17th 2011.

  3. A monograph titled :  Vector Optmization : A View Through Variational Analaysis, written jointly with Marius Durea and Christiane Tammer. (Under preparation) Publication contract signed with Springer.

Papers in Mathematical Optimization

  1. J. Dutta, V. Vetrivel and S. Nanda, "Semi-invex functions and their subdifferentials," Bulletin of the Australian Mathematical Society, Vol 56, 1997, pp 385-393.

  2. J. Dutta, V. Vetrivel and S. Nanda, "Equivalence of optima and saddle point in nonsmooth nonconvex programs," Optimization, Vol 42, 1997, pp 73-81.

  3. J. Dutta, "On convex vector optimization," Bulletin of the Australian Mathematical Society, Vol 61, 2000, pp 85-83

  4. V. Vetrivel and J. Dutta, "Motzkin type alternative theorem and set-valued optimization," Journal of Analysis, Vol 9, 2001, pp 137-147.

  5. J. Dutta, "On generalized pre-invex functions," Asia Pacific Journal of Operational Research, Vol 18, 2001, pp 257-272.

  6. J. Dutta, and V. Vetrivel, "On approximate minima in vector optimization," Numerical Functional Analysis and Optimization , Vol 22,(7 & 8), 2001, pp 845-859.

  7. J. Dutta and V. Vetrivel, "Mathematical programming with a class of non-smooth functions," Journal of Systems Science and Complexity, Vol 15 No 1, 2002, pp 52-60.

  8. J. Dutta and S. Chandra, "Convexifactors, generalized convexity and optimality conditions," Journal of Optimization Theory and Applications , Vol 113, no 1. 2002, pp 41-64.

  9. A. Rubinov and J. Dutta, "Hadamard type inequality for quasiconvex functions in higher dimensions," Journal of Mathematical Analysis and Applications, Vol 270, No 1, 2002, pp 80-91.

  10. C. S. Lalitha, J. Dutta and M. Govil, "On optimality criteria in set-valued optimization," Journal of Australian Mathematical Society, Vol 75, 2003, pp 221-232.

  11. J. Dutta and S. Chandra, "Convexifactors, generalized convexity and vector optimization," Optimization, Vol 53, 2004, pp 77-94.

  12. J. Dutta, J. E. Martinez-Legaz and A. Rubinov, "Monotonic analysis over cones: I," Optimization, Vol 53, 2004, pp 129-146.

  13. S. S. Dragomir, J. Dutta and A. Rubinov, Hermite-Hadamard type inequalities for increasing and convex-along rays functions, Analysis, Vol 24, 2004, 171-181.

  14. S. Chandra, J. Dutta and C. S. Lalitha, "Regularity Conditions and Optimality in Vector Optimization," Numerical Functional Analysis and Optimization, Vol 25, 2004, pp 479-501.

  15. J. Dutta, J. E. Martinez-Legaz and A, Rubinov, "Monotonic analysis over cones-II," Optimization, Vol 53, 2004, pp 529-547.

  16. J. Dutta, "Necessary optimality conditions and saddle points for approximate optimization in Banach Spaces," TOP, (Trabajos de Investagacion Operativa) (Journal of the Spanish Society of Statistics and Operations Research), Vol 13, 2005, pp 143-127.

  17. J. Dutta, "Optimality conditions for maximizing a locally Lipschitz function," Optimization, Vol 54, 2005, pp 377-389.

  18. J. Dutta, "Generalized derivatives and nonsmooth optimization – a finite dimensional tour," (Invited Survey) , TOP, Vol 13, 2005, pp 185-314.

  19. J. Dutta and C. Tammer, "Lagrangian conditions for vector optimization in Banach Spaces," Mathematical Methods of Operations Research , Vol 64, 2006, 521-540.

  20. S. Dempe, J. Dutta and S. Lohse, "Optimality conditions in bilevel programming," Optimization , Vol 55, 2006, pp 505-524.

  21. J. Dutta and C. S. Lalitha, "Bounded sets of KKT multipliers in vector optimization," Journal of Global Optimization, Vol 36, 2006, pp 425-437.

  22. J. Dutta, "Revisiting the Lagrange multiplier rule," Pacific Journal of Optimization, Vol 2, 2006, pp 501-519

  23. S. Dempe, J. Dutta, and B. S. Mordukhovich, "New necessary optimality conditions in optimistic bilevel programming,," Optimization, Vol 56, 2007, pp 577-604

  24. J. Dutta, J. E. Martinez-Legaz and A. M. Rubinov, "Monotonic analysis over cones – III," Vol 15, Journal of Convex Analysis, 2008, pp 561-579

  25. D. Aussel and J. Dutta, "Generalized Nash equilibrium problem, variational inequality and quasiconvexity," Vol 36, Operations Research Letters, 2008, pp 461-464.

  26. M. Durea, J. Dutta and Chr. Tammer, "Bounded sets of Lagrange multipliers for vector optimization problems in infinite dimension," Journal of Mathematical Analysis and Applications, Vol 348, 2008, pp 589-606.

  27. M. Durea and J. Dutta, "Lagrange multipliers for Pareto minimum in general Banach spaces," Pacific Journal of Optimization, Vol 4, 2008, pp 447-463.

  28. M. Durea, J. Dutta and Chr. Tammer, "Lagrange multipliers for epsilon- Pareto solutions in vector optimization with non-solid cones in Banach Spaces," Journal of Optimization Theory and Applications, Vol 145, 2010, pp 196-211.

  29. J. Dutta, S. R. Pattanaik and Michel Thera, "On note on approximate Lagrange multiplier rules, Mathematical Programming," Series B. Vol 123, 2010, pp 161-171.

  30. C. Charitha, and J. Dutta, "Regularized gap functions and error bounds for vector variational inequalities," Pacific Journal of Optimization, Vol 6, 2010, pp 497–510.

  31. Regina Burachik, J. Dutta, "Inexact proximal point methods for variational inequality problems," SIAM Journal of Optimization. Vol 20, 2010, pp 2653–2678.

  32. D. Aussel and J. Dutta, "On gap functions for multivalued Stampacchia variational inequalities," Journal of Optimization Theory and Applications, Vol 149, 2011, 513-527.

  33. M. Durea, J. Dutta and C. Tammer, "Stability properties of KKT points in vector optimization," Optimization, Vol 60, 2011, pp 823-838.

  34. J. Dutta and C. Yalcin Kaya, "A new scalarization and numerical method for constructing weak Pareto front of multi-objective optimization problem," Optimization, Vol 60, 2011. pp 1091-1104.

  35. S. Dempe and J. Dutta, "Is bilevel programming a special case of mathematical program with complementarity constraints?" Mathematical Programming , Series A, Vol 131, 2012, pp 37-48.

  36. J. Dutta, "Gap Functions and Error Bounds for Variational and Generalized Varirational Inequalities," Vietnam Journal of Mathematics , Vol 40, 2012, pp 231-253. (This is a special issue for the 65th birthday of Prof. P. Q. Khanh)

  37. J. Dutta and C. S. Lalitha, "Optimality Conditions for Convex Optimization Revisited," Optimization Letters, Vol 7, 2013, pp 221-229.

  38. J. Dutta, K. Deb, R, Arora and R. Tulshyan, "Approximate KKT conditions: Theory and Numerical Experiments," Journal of Global Optimization, Vol 56, 2013, pp 1463-1499.

  39. C. Charitha, J. Dutta and C. S. Lalitha, "Gap functions for vector variational inequalities," Optimization, Vol 64, 2015.

  40. J. Dutta, "Barrier methods in nonsmooth convex optimization without convex representation," Optimization Letters , Vol 9, 2015, pp 1177-1185.

  41. J. M. Borwein and J. Dutta, Maximal monotone inclusions and Fitzpatrick functions," Journal of Optimization Theory and Application, Vol 171, 2016, 757-784.

  42. C. Charitha, J. Dutta and D. R. Luke, "Lagrange multipliers, (exact) regularization and error bounds for monotone variational inequalities," Mathematical Programming Series A, Vol 171, 2017, 519-549.

Papers in Optimization Heuristics

  1. K. Deb, S. Gupta, J. Dutta, B. Ranjan, Solving dual problem using coevolutionary algorithm, Journal of Global Optimization, Vol 57, 2013, pp 891-933.

RESEARCH PUBLICATIONS ( Mathematical Optimization)

  1. V. Vetrivel and J. Dutta, "Necessary optimality conditions with subdifferentials of semi-invex functions." Proceedings of the ASME Conference on Nonsmooth /Nonconvex Modelling , Theory and Applications, Chapter 20, pp 427 - 436, 2000, Kluwer Academic Publishers.

  2. A.Rubinov and J. Dutta, "Abstract convexity," Handbook of Generalized Convexity and Generalized Monotonicity,  (Series : Nonconvex Optimization and Applications 76), pp 293-333, 2005, Springer, New York.

  3. J. Dutta and S. Dempe, "Bilevel programming with convex lower level problems,'' Optimization with multivalued mappings, pp 51-71, Springer Optim. Appl., 2, 2006, Springer, New York.

  4. S. Dempe, J. Dutta and B. S. Mordukhovich, "Variational analysis in bilevel programming," Mathematical Programming and Game Theory for Decision Making, pp 257-277, 2008, World Scientific, Singapore.

  5. S. Dempe, N. Dinh and J. Dutta, "Optimality condition for a simple convex bilevel programming problem," Varitaional Analysis and Generalized Differentiaition in Optimization and Control, (In honour of Boris. S. Mordukhovich), Eds R. S. Burachik and J. C. Yao., Springer Optimization and Its Applications, Vol 47, 2010, Springer.

  6. J. Dutta, Strong KKT, Second order conditions and nonsolid cones in vector optimization, Recent Advances in Vector Optimization (Multi-authored book on vector optimization) Edited by Q. H. Ansari and J. C. Yao, Chapter 5, October 2011, Springer.

  7. J. Dutta, "Convex functions in optimization," Decision Sciences: Theory and Practice, Chapter 1, pp 1-78, 2016, CRC Press.

RESEARCH PUBLICATIONS (Optimization Heuristics)

  1. K. Deb, R. Tewari, M. Dixit and J. Dutta, "Finding trade-off solutions close to KKT points using evolutionary multi-objective optimization," Proceedings of the Congress on Evolutionary Computation, pp 2109-2116, CEC-2007, Singapore.

  2. R. Arora, U. Upaadhyay R. Tulshyan and J. Dutta, A parallel algorithm for solving large scale convex minimax problems, Proceedings of SEAL, Edited by K. Deb, et al, pp 35-44, 2010.

  3. K. Deb, M. Abouhawwash and J. Dutta, An optimality theory based proximity measure for evolutionary multiobjective and many objective optimization. Evolutionary Multiobjective Optimization , Lecture Notes in Computer Science, Vol 9019, pp 18-33, 2015.

PROJECTS

SPONSORED PROJECTS/ MOBILITY PROJECTS

  1. Increasing and convex functions along rays: A study in monotonic analysis.
    Funded by the National Board for Higher Mathematics, India (2003-2006).

  2. Indo-French Institute of Mathematics, Mobility Project to visit University of Limoges, France, 2006

  3. Optimizing Engineering Design, DST (Department of Science and Technology, India) sponsored project, 2009-2012 (jointly with Professor Kalyanmoy Deb)

  4. Multiobjective Multidiscplinary Optimization, DST sponsored project, 2010-2013  (jointly with Professor Kalyanmoy Deb).

  5. FM-Radio project for celebrating 150 the birth centenary of the legendary mathematician Srinivasa Ramanujan through 90, radio episodes of 15 minutes each. (jointly with Dr. Satyaki Roy).

  6. IFCAM (Indo-French Center for Applied Mathematics), Mobility Grant for the project titled: Local Nash Equilibrium in Electricity Markets. French participant: Professor Didier Aussel, PROMES, Energy Lab (CNRS), Perpignan, France. Granted: March 2016.

  7. EUPHRATES-ERASMUS Faculty Mobility project to visit LAB PROMES, Eneryg Lab (CNRS), France.Granted May 2016.

FELLOWSHIPS

  1. Visiting Fellowship of the Spanish Ministry of Education and Culture, June 2000.

  2. Post-Doctoral Fellowship of the National Board for Higher Mathematics (NBHM), India, December 1998.

  3. Junior Research Fellowship, University Grants Commission, Government of India, 1993.

  4. Graduate Aptitude Test in Engineering Scholarship, Government of India,1993.

TEACHING

Indian Institute of Technology, Kharagpur

  • MATHS 101 -  Basic Engineeing Mathematics (Instructor)
  • Optimization Methods (Instructor)
  • Numerical Analysis (Instructor)

Indian Institute of Technology, Kanpur

  • ESO 209: Probability and Statistics (Tutorial Instructor)
  • MTH-102: Linear Algebra and Complex Variables (Tutorial Instructor)
  • MTH  506: Principles of Optimization (Instructor)
  • MTH 101: Calculus (Institute Core-Course) (Instructor/ Tutorial Instructor)
  • MTH 306: Linear Programming and Extensions(Instructor)
  • MTH203: Ordinary and partial differential equations (Tutorial Instructor)
  • MTH102: Linear Algebra and Complex Variables (Institute Core-Course)(Instructor).
  • ECO261/261A : Mathematical Economics.
  • Introduced and taught a new interdisciplinary course titled: Multiobjective Optimization: Theory, Methods and Applications,  jointly with Professor Kalyanmoy Deb of the Department of Mechanical Engineering at the Indian Institute of Technology, Kanpur.
  • Developed and taught a new course titled: Foundations of Mathematical Finance (MTH 512) in the Spring-Semester 2007 and 2013.
  • Developed and taught a new course titled: Advanced Quantitative Finance (MTH 659) in the Spring-Semester of 2008.
  • Developed a  graduate course titled: Mathematical Analysis for Economists (ECO760A/ECO 760) .

STUDENTS

Ph. D SUPERVISION

Dr. Suvendu Pattanaik


Thesis title

Optimization with Generalized Differentiaition and Extremal Principal.
Received Phd in May 2009

Dr. Charitha Churchill


Thesis title

Gap Functions and Error Bounds for Vector Variational Inequalities and Equilibrium Problems.
Received Ph.d in  May 2010.

Dr. Arnab Sur


Thesis title

A Study on Stationarity Concepts for a class of SMPCC problems, 
Receieved Phd in June 2014.