Research

 

Research Interests

 

Variational Analysis, Variational Principle, Vector Optimization, Set-Valued Optimization, Generalized Differentiation, Mathematical Programs with Equilibrium Constraints (MPEC), Set-Valued Optimization Problems with Equilibrium Constraints (SOPEC), Bilevel Programming,  Applications to Welfare Economics.

 

Publications

 

17. (with B. Mordukhovich) Extended Pareto Optimality in Multiobjective Problem. To appear in Recent Advances in Vector Optimization (eds. Q.H. Ansari and J.-C. Yao), Springer, Berlin, 2011.

18. (with B. Mordukhovich) Necessary optimality conditions and applications to welfare economics. To appear in J. Pure Appl. Math. (2010).

19. (with C. Tammer) Lagrange necessary conditions for Pareto minimizers in Asplund spaces and applications. To appear in a special issue on Variational Analysis and its Applications of J. Nonlin. Anal. (2011).

20. (with Q. Zhang and R. Zhang) Multistage hierarchical optimization problems with multi-criterion objectives. To appear in J. Global Optim. (2010).

21. (with B. Mordukhovich) Set-valued optimization in welfare economics. Adv. Math. Eco. 13 (2010), 113-153. Abstract

22. (with B. Mordukhovich) Relative Pareto minimizers in multiobjective optimization: existence and optimality conditions. Math. Prog. 122 (2010), 301-347. Abstract   

23. (with Q. Zhang and R. Zhang) Multiobjective hierarchical optimization problems with many followers. In Global Optimization: Theory, Methods & Application I (Ma, C., Yu, L., Zhang, D., Zhou, Z., Eds.) 12 (2009), 23-31. Global-Link Publisher, Hong Kong. Abstract

24. (with B. Mordukhovich) Necessary conditions for super minimizers in constrained multiobjective optimization.  J. Global Optim. 43 (2009), 533 – 552. Abstract   

25. On Fréchet subdifferential sum rule and its applications. WSU Preprint (2008). Abstract

26. Variational Analysis with Applications to Multiobjective Optimization. Ph.D. Dissertation (Advisor: Boris Mordukhovich). Wayne State University, 2008. Abstract

27. (with P. Gupta and B. Mordukhovich) Suboptimality conditions in mathematical programs with equilibrium constraints. Taiwanese J. Math. 12 (2008), 2569-2592. Abstract   

28. (with B. Mordukhovich) Existence of minimizers and necessary conditions for set-valued optimization with equilibrium constraints. Appl. Math. 52 (2007), 453 - 472. Abstract 

29. (with B. Mordukhovich) Variational principles for set-valued mappings with applications to multiobjective optimization. Control Cyber. 36 (2007), 531 - 562. Abstract    

30. (with P. Gupta and B. Mordukhovich) Necessary conditions for multiobjective optimization with equilibrium constraints. J. Optim. Theory and Appl. 135 (2007), 179-203. Abstract    

31. (with P. Q. Khanh) Some algorithms for solving mixed variational inequalityes. Acta Math. Vietnamica 31 (2006), 83-103. Abstract 

32. (with P. Q. Khanh) A projection-type algorithm for pseudo-monotone non-Lipschitzian multivalued variational inequalities. In Nonconvex Optim. Appl. (Hadjisavvas, N., Komlosi, S., Schaible, S. Eds.) 77 (2005), 113-129, Springer, New York. Abstract   

33. (with P. Q. Khanh) Are several recent generalizations of Ekeland's variational principle more general than the original principle? Acta Math. Vietnamica 28 (2003), 345-350. Abstract     

 

Conferences

 

· AMS Joint Annual Mathematics Meeting, special session on Set-Valued Optimization and Variational Problems, January 6 - 9, 2011, New Orleans, Los Angeles.
Invited talk: Lagrange necessary conditions for Pareto minimizers in Asplund spaces and applications.

· Annual UP MAA Meeting, October 8-9, 2010, Northern Michigan University, Marquette, Michigan.
Talk:     Necessary conditions in vector optimization with nonsolid cones in Asplund spaces and application.

· 3rd International Conference on Continuous Optimization ICCOPT 2010, July 24-25, 2010 (winter school) July 26-29, 2010 (conference), Santiago, Chile.
Talk:     Set-valued optimization in welfare economics.

· CIMPA-UNESCO-VIETNAM School on Variational Inequalities and Related Problems, May 10-21, 2010, Hanoi, Vietnam.
Talk:     Subdifferential necessary conditions for generalized-order optimal solutions in constrained set-valued optimization.

· Annual UP MAA Meeting, October 2-3, 2009, Michigan Technological University, Houghton, Michigan.
Talk:     Necessary conditions for multiobjective optimization with preferences.

· 2009 Mathematical Programming Symposium, August 23-29, 2009, Chicago, Illinois.
Talk:     Necessary Conditions for optimal solutions in constrained multiopjective optimization. Abstract

· International School of Mathematics “Guido Stampacchia” and 51st Workshop: Variational Analysis and Applications, May 9 – 17, 2009, Sicily, Italy.
Talk:     Some relationships between set-valued optimization and welfare economics theory.

· AMS Fall Central Section Meeting, October 17-19, 2008, Kalamazoo, Michigan.
Talk:     Some applications of Mordukhovich coderivative for set-valued mappings to multiobjective
optimization.

· 5th World Congress of Nonlinear Analysts, special session on Variational Analysis and Its Applications, July 2-9, 2008, Orlando, Florida.
Invited Talk:     Some applications of variational analysis to multiobjective optimization.

· AMS Joint Annual Mathematics Meeting, special section on Global Optimization and Operation Research, January 6-9, 2008,  San Diego, California.
Invited Talk:     Necessary and sufficient conditions for global weak Pareto solutions in constrained multiobjective optimization.

· 9th Midwest Optimization Meeting, October 20, 2007, University of Michigan, Ann Arbor, Michigan.
Invited Talk:     Necessary condition for local super minimizers in constrained multiobjective optimization.

· 2nd International Conference on Continuous Optimization ICCOPT 2007, August 13--16, 2007, McMaster University, Canada.
Invited Talk:     Variational principles for set-valued mappings with applications to multiobjective optimization.

· AMS Sectional Meeting, special section on Optimization, March 16-17, 2007, Miami University, Oxford, Ohio.
Invited Talk:     Necessary and sufficient conditions of global/local weak Pareto optima in set-valued mappings.

· CUD International Spring School on Optimization, March 3-10, 2007, University of Pedagogy, Ho Chi Minh, Vietnam.
Talk:     Necessary and sufficient conditions of global/local minimizers.

· 8th Midwest Optimization Meeting, October 12-14, 2006, Miami University, Oxford, Ohio.
Invited Talk:      Necessary conditions in multiobjective optimization with equilibrium constraints.

· 7th Midwest Optimization Meeting, October 15, 2005, Western Michigan University, Kalamazoo, Michigan.
Talk:     Necessary conditions for Pareto and strong Pareto optimality in multiobjective problems.

· 1st International Conference on Continuous Optimization ICCOPT 2004, July 31-1, 2004 (summer school) August 2-4, 2004 (conference), Rensselaer Polytechnic Institute, Troy, New York.

· 7th International Symposium on Generalized Convexity/ Monotonicity, August 27-31, 2002, Hanoi Institute of Mathematics, Hanoi, Vietnam.
Talk:     On the equivalence of several generalizations of the Ekeland variational principle and the original principle.

· CIUF-CUD Summer School on Optimization and Applied Mathematics, August 4-21,  2002, College of Pedagogy, Nha Trang, Vietnam. Certificate.

· Summer School on Optimization Methods in Technology and Management, August 23-27, 2000, Da Nang University, Da Nang, Vietnam.

· International Workshop on Applied Analysis and Optimization AAO 2000, August 28-31, 2000, Da Nang University, Da Nang Vietnam.
Talk:     On equivalents of generalized Ekeland's variational principle

 

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Department of Mathematics & CS
Hanoi Institute of Mathematics
Department of mathematics (WSU)
Department of Mathematics (FUNDP)
Department of mathematics (HCMC University of Science)

Department of Mathematics (Martin-Luther-University Halle-Wittenberg)
         

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


"What is now proved was once only imagined."         William Blake

 

 

Generalized subdifferential of the absolute value function

Generalized subdifferential of the opposite of the absolute value

"Namely, because the shape of the whole universe is most perfect and, in fact, designed by the wisest creator, nothing in all of the world will occur in which no maximum or minimum rule is somehow shining forth."       Leonhard Euler (1744)  

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