Publications

I. Monographs, Handbooks, Edited Books and Special Issues

  1. Gao, D.Y., Duality Principles in Nonconvex Systems: Theory, Methods and Applications. Kluwer Academic Publishers, Boston/Dordrecht/London, 2000, xviii+454pp.
  2. Gao, D.Y., R.W. Ogden and G. Stavroulakis, Nonsmooth and Nonconvex Mechanics:  Modelling, Analysis and Numerical Methods.  Kluwer Academic Publishers, Boston/Dordrecht/London, 2001, xliv+471pp.
  3. Gao, D.Y. and R.W. Ogden, Advances in Mechanics and Mathematics, AMMA2002, Kluwer Academic Publishers, Boston/Dordrecht/London. 2002, xvii+302 pp.
  4. Gao, D.Y., Proceedings of IUTAM Symposium on Duality, Complementarity and Symmetry in Nonlinear Mechanics, Kluwer Academic Publishers, Boston/Dordrecht/London, 434pp.
  5. Gao, D.Y. and R.W. Ogden, Advances in Mechanics and Mathematics, AMMA 2003, Kluwer Academic Publishers, Boston/Dordrecht/London, 324pp.
  6. Gao, D.Y. and K.L. Teo, Duality in Global Optimization and Control. Special issue of Journal of Global Optimization. 2004.
  7. Gao, D.Y. and Sherali, H.D., Complementarity and Duality in Global Optimization. Special issue of Journal of Global Optimization. 2008.
  8. Gao, D.Y. and Sherali, H., Advances in Applied Mathematics and Global Optimization, Springer, 2009.
  9. Gao, D.Y., Handbook of Duality in Engineering Science (three volumes), in preparation to be published by Springer.
  10. Gao, D.Y. and Batra, R., Handbook of Computational Mechanics and Methods (two volumes), to be published by Springer.

II. Articles in Encyclopedia

  1. Gao, D.Y., Duality-Mathematics, Wiley Encyclopedia of Electronical and Electronical Engineering, 6, 1999, 68-77. Second edition, 2007.
  2. Gao, D.Y., Mono-Duality in Convex Optimization, in  Encyclopedia of Optimization, C. A. Floudas and P.M. Pardalos (eds). Kluwer Academic Publishers, 2001. Vol. 1, pp. 482-485.
  3. Gao, D.Y., Bi-Duality in Nonconvex Optimization, in  Encyclopedia of Optimization, C. A. Floudas and P.M. Pardalos (eds). Kluwer Academic Publishers, 2001. Vol. 1, pp. 477-482.
  4. Gao, D.Y., Tri-duality in Global Optimization, in Encyclopedia of Optimization, C. A. Floudas and P.M. Pardalos (eds). Kluwer Academic Publishers, 2001. Vol. 1, pp. 485-491.

III  Papers to appear

  1. Gao, D.Y. and Sherali, H.D. (2009). Canonical duality: Connection between nonconvex mechanics and global optimization, in Advances in Applied mathematics and Global Optimization, 249-316, Springer.
  2. Gao, D.Y., Ruan, N., and Sherali, H.D., Solutions and optimality criteria for nonconvex constrained global optimization problems, to appear in Journal of Global Optimization.
  3. Feng, Z.S. and Gao, D.Y. (2009). Traveling wave solutions to a reaction-diffusion equation, to appear in ZAMP
  4. Fang, S.-C., Gao, D.Y., Shue, R.L., and Xin, W.X. (2009).  Global optimization for a class of fractional programming problems, to appear in Journal of Global Optimization
  5. Ruan, N., Gao, D.Y., Jiao, Y. (2009). Canonical dual least square method for solving general nonlinear systems of quadratic equations, Comput Optim Appl, DOI 10.1007/s10589-008-9222-5
  6. Gao, D.Y. and Sherali, H.D. (2009). Preface to Advances in Applied Mathematics and Global Optimization, a special volume dedicated to Professor G. Strang for his 70th Birthday, Springer, 2009.
  7. Ruan, N., Gao, D.Y. (2009) Solutions to quadratic minimization problems with box and  integer  constraints, to appear in J. Global Optimization
  8. Zhang, X, Zhu Jinhao, and Gao, D.Y. (2009). Solution to nonconvex quadratic programming with both inequality and box constraints, to appear in Optimization and Engineering.
  9. Liu, J., Gao, D.Y., and Gao, Y (2009). Canonical duality for solving nonconvex and nonsmooth optimization problem, to appear in Optimization and Engineering.

IV. Papers in Refereed International Journals

  1. Gao, D.Y. and Ogden, R.W.  (2008). Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation, Quarterly J. Mech. Appl. Math. 61 (4), 497-522.
  2. Gao, D.Y. and Ogden, R.W. (2008) Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem, ZAMP, 59 (2008) 498–517
  3. Gao, D.Y. and Wei-Chi Yang (2008). Complete solutions to minimal distance problem between two nonconvex surfaces, Optimization, Vol. 57(5), 705-714. DOI: 10.1080/02331930802355309.
  4. Gao, D.Y. and Ruan, N. (2008), Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem, Math. Meth. Operations Research, 67 (3), 479-491.
  5. Fang, S.-C., Gao, D.Y., R.-L. Shue, and S.Y. Wu (2008) Canonical Dual Approach for Solving 0-1 Quadratic Programming Problems, J. Industrial and Management Optimization.4 (1), 125-142.
  6. Feng, Z.S. and Gao, D.Y. (2008) A nonconvex dissipative system and its applications,  J. Global Optimization. .40 (4), 637 – 651.
  7. Wang, Z.B., Fang, S.-C., Gao, D.Y., and Xin, W.X. (2008). Global extremal conditions for multi-integer quadratic programming, J. Industrial and Management Optimization, 4(2), 213-226.
  8. Gao, D.Y. and Yu, H.F. (2008). Multi-scale modelling and canonical dual finite element method in phase transitions of solids, Int. J. Solids Struct. 45 3660–3673  
  9. X. Wang, Z. Feng, L. Debnath and D.Y. Gao (2008). Burgers-Korteweg-de Vries equation and it approximation, International Journal of Computer Mathematics, Vol. 85 (6), 853-863. DOI: 10.1080/00207160701411152
  10. Gao, D.Y., Solutions and optimality criteria to box constrained nonconvex minimization problems, J. Industrial and Management Optimization. 3(2):293-304, 2007.
  11. Xuan, Z.C., Feng, Z., and Gao, D.Y. (2007) Computing lower and upper bounds on stress intensity factors in bimaterials, International Journal of Nonlinear Mechanics, 42, 336-341.
  12. Gao, D.Y., Duality in distributed-parameter control of nonconvex and nonconservative dynamical systems with applications, Nonlinear Dynamics and Systems Theory, 6(3), 257-279, 2006.
  13. Gao, D.Y., Complete solutions to a class of polynomial minimization problems, J. Global Optimization, 35, 131-143, 2006.
  14. Gao, D.Y. Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints,  J. Industrial and Management Science, 1:59-69, 2005
  15. Gao, D.Y. Complementary variational principle, algorithm, and complete solutions to phase transitions in solids governed by Landau-Ginzburg equation. Mathematics and Mechanics of Solid, 9:285-305, 2004.
  16. Gao, D.Y., Canonical duality theory and solutions to constrained nonconvex quadratic programming, Journal of Global Optimization, 29:377-399, 2004.
  17. Gao, D.Y., Perfect duality theory and complete set of solutions to a class of global optimization,   Optimization, 52 (4-5), pp. 467-493, 2003.
  18. Gao, D.Y., Complementarity, polarity and triality in nonsmooth, nonconvex and nonconservative Hamiltonian systems, Philosophical Transactions of the Royal Society: Mathematical, Physical and Engineering Sciences, 359, 2347-2367, 2001.
  19. Gao, D.Y., Analytic solution and triality theory for nonconvex and nonsmooth variational problems with applications, Nonlinear Analysis, 42, 7, 2000, 1161-1193.
  20. Gao, D.Y., Canonical dual transformation method and generalized triality theory in nonsmooth global optimization, J. Global Optimization, 17(1/4), 2000, 127-160.
  21.  Gao, D.Y.,   Finite deformation beam models and triality theory in dynamical post-buckling analysis.  Int. J. Non-Linear Mechanics, 35, 2000, 103-131.
  22. Gao, D.Y., General Analytic Solutions and Complementary Variational Principles for Large Deformation Nonsmooth Mechanics. Meccanica 34, 1999, 169-198.
  23. Gao, D.Y.   Pure complementary energy principle and triality theory in finite elasticity. Mech. Res. Comm. 26 (1999), no. 1, 31-37.
  24. Gao, D.Y.  General Analytic Solution for Fully Nonlinear, Nonconvex Variational Problems.  Problems of Nonlinear Analysis in Engineering Systems.  An International Journal of IFNA-ANS, 1(9), 1999.
  25. Gao, D.Y., Duality, triality and complementary extremum principles in nonconvex parametric variational problems with applications,  IMA J. Appl. Math., 61, 1998, 199-235.
  26. Gao, D.Y., Bi-complementarity and duality: A framework in nonlinear equilibria with applications to the contact problems of elastoplastic beam theory, J. Appl. Math. Anal., 221, 1998, 672-697.
  27. Gao, D.Y. and Russell, D.L., An extended beam theory for smart materials applications: II Static formation problems.  Appl. Math. Optim. 38, (1998), no. 1, 69-94.
  28. Cai, D.X. and Gao, D.Y., Shear Control and Analytic Solutions for 2-D Dynamical Smart Beam Theory.  J. Intelligent Material Systems and Structures, 9, 1998, 182-188
  29. Gao, D.Y., Dual extremum principles in finite deformation theory with applications to  post-buckling analysis of extended nonlinear beam theory, Applied Mechanics Reviews, Vol. 50, 11, November 1997, S64-S71.
  30. Gao, D.Y., Complementary finite element method for finite deformation nonsmooth  mechanics, J. Eng. Math., 30,  pp. 339-353, 1996.
  31. Gao, D.Y. and Russell, D.L., An extended beam theory for smart materials applications, Part I. Extended beam theory, duality theory and finite element simulations, Appl. Math. Optimization, 34, 3, 1996, 279-298.
  32. Gao, D. Y.,  Stability analysis and extremum principles for rigid-plastic plates with large deflections,  European J. Mech., A/Solids, 15 No 4, 599-615, 1996.
  33. Gao, D.Y., Contact problem of 2-D elastoplastic beam theory and dual variational inequality, Appl. Math. Mech., 17, 3, 953-968, 1996.
  34. Gao, D.Y., Nonlinear elastic beam theory with applications in contact problem and variational approaches, Mech. Research Communication, 23, 1, pp. 11-17, 1996.
  35. Gao, D.Y., Duality theory in nonlinear buckling analysis for von Karman equations, Studies in Appl. Math, 94, 1995: 423-444. MIT
  36. Gao, D.Y. and Yang, W.H., Multi-duality in minimal surface type problems, Studies in Appl. Math., 95, 1995: 127-146. MIT.
  37.  Gao, D.Y.,   Limit analysis of plastic shells subjected to large deflections, European J. Mech., A/Solids, 14, no 3, 1995, 459-472.
  38.  Gao, D.Y., Stability and extremum principles for post yield finite plasticity, Acta Mechanica Sinica, 10 (4), pp. 311-325, 1994.
  39.  Gao, D.Y., Global extremum criteria for nonlinear elasticity, J. Appl. Math. Physics, ( ZAMP) 43 (1992), pp. 924-937.
  40.  Yau, S.T. and Gao, D.Y.,   Obstacle problems for von Kármán equations,  Adv. Appl. Math., 13 (1992), pp. 123-141.
  41.  Gao, D.Y., Extended bounding theorems for nonlinear limit analysis, Int. J. Solids Structures, 27 (1991),pp. 523-531.
  42.  Gao, D.Y., Dynamically loaded rigid-plastic analysis under large deformation, Quart. Appl. Math., 48(1990), 4, pp. 731-739.
  43.  Gao, D.Y., On the extremum potential variational principles for geometrical nonlinear thin elastic shell, Science in China (Scientia Sinica) (A), 33 (1990), 1, pp. 324-331.
  44.  Gao, D.Y.,   On the extremum variational principles for nonlinear elastic plates, Quart. Appl. Math., 48 (1990), pp. 361-370.
  45. Gao, D.Y., Complementary Principles in Nonlinear Elasticity, Science in China (Scientia Sinica) (A) (Chinese Ed.), 33 (1990), 4, pp. 386-394.
  46. Gao, D.Y., Bounding theorem on finite dynamic deformations of plasticity, Mech. Research Commu., 17 (1990), pp. 33-39.
  47. Gao, D.Y. and Onate, E.T., Rate variational extremum principles for finite elastoplasticity, Appl. Math. Mech., 11 (1990), 7, pp. 659-667.
  48. Gao, D.Y. and Strang, G., Geometric nonlinearity: Potential energy, complementary energy, and the gap function, Quart. Appl. Math., 47 (1989), pp. 487-504.
  49. Gao, D.Y. and Strang, G., Dual extremum principles in finite deformation elastoplasitc analysis, Acta Applicandae Mathematicae, 17 (1989), pp. 257-267.
  50. Gao, D.Y. and Wierzbicki, T., Bounding theorem in finite plasticity with hardening effect, Quart. Appl. Math., 47 (1989), pp. 395-403.
  51.  Gao, D.Y., Opposite principles in nonlinear conservative systems, Adv. Appl. Math., 10 (1989), pp. 370-377.
  52. Gao, D.Y. and Cheung, Y.K., On the extremum complementary energy principles for nonlinear elastic shells, Int. J. Solids & Struct., 26 (1989), pp. 683-693.
  53. Gao, D.Y., Panpenalty finite element programming for limit analysis, Computers & Structures, 28 (1988), pp. 749-755.
  54. Gao, D.Y., On the complementary bounding theorems for limit analysis, Int. J. of Solids and Structures, 24 (1988), pp. 545-556.
  55. Gao, D.Y., Inverse variational principles in finite elasticity, Mechanics Research Communication, 15 (1988), pp. 161-167.
  56. Gao, D.Y. and Hwang, K.C., On the complementary variational principles for elasto-plasticity, Scientia Sinica (A), 31 (1988), pp. 1469-1476.
  57. Gao, D.Y., Tao of the complementarity-duality, Excellent paper award in   The First National Congress on Natural Philosophy, Anhui, July 1986.  J. of Hefei University of Technology (Sociology Ed.), 2 (1986).
  58.  Gao, D.Y., Penalty-duality finite element method in the analysis for incompressible medium, J. of Hefei University of Technology, 1 (1985).
  59. Gao, D.Y.,   On the generalized variational principles of limit analysis with arbitrary yield conditions, J. of Hefei University of Technology, 1 (1984), pp. 1-14.
  60.  Gao, D.Y., Extended bounding theorems of limit analysis, Appl. Math. Mech., 4 (1983), pp. 571-584.
  61. Gao, D.Y.,  On the unified theory of variational principles for rigid-perfectly plastic medium and penalty-duality finite element mixed models,  J. of Hefei University of Technology, 4 (1983), pp. 91-97.
  62.  Gao, D.Y., Variational principles of limit analysis in discontinuous plastic field, J. of Hefei University of Technology, 1 (1982), pp. 44-51.

 

V. Book Chapters and Papers in Refereed Proceedings

  1. Gao, D.Y. (2008). Advances in canonical duality theory with applications to global optimization, Proceedings of the Fifth International Conference on Foundations of Computer-Aided Process Operations (FOCAPO 2008), M. Ierapetriou, M. Bassett and S. Pistikopoulos (eds.), Omni Press, pp.73-82.
  2. Gao, D.Y. (2007) Understand and control chaos in dynamical systems: Canonical duality approach and triality theory, Proceedings of 9th Conf. on Dynamical Systems- Theory and Applications,J. Awrejcewicz, P. Olejnik, J. Mrozowski  (ed.) , Lodz, Poland, Dec. 17-20, Vol. 1, 41-64 (ISBN: 978-83-924382-9-8).
  3. Gao, D.Y., Canonical duality in nonsmooth, concave minimization with inequality constraints, to appear in Advances in Nonsmooth Mechanics, a special volume in honor of Professor J.J. Moreau’s 80th birthday, P. Alart and O. Maisonneuve (eds). Springer, 2005, pp305-314.
  4. Gao, D.Y. Multi-scale modeling and duality algorithm in phase transitions of ferroelectric materials, Proceedings of the 3rd International Conference on Computational Modelling and Simulation of Materials, Pietro Vincenzini (eds), 2004. 
  5. Gao, D.Y. Nonconvex Semi-Linear Problems And Canonical Duality Solutions, Advances in Mechanics and Mathematics, Vol. II, 261-312. Springer.
  6. Gao, D.Y., Duality, complementarity, and polarity in nonsmooth/nonconvex dynamics and global optimization. Proceedings of IUTAM Symposium on Complementarity, Duality and Symmetry in Nonlinear Mechanics, D.Y. Gao (eds). Kluwer Academic Publishers, 2003. pp. 21-65.
  7. Gao, D.Y., Nonconvex semi-linear problems and canonical dual solutions. Advances in Mechanics and Mathematics, Vol. II, D.Y. Gao and R.W. Ogden (ed), Kluwer Academic Publishers, 2003. pp. 261-312.
  8. Gao, D.Y., Jie-Fang Li and D. Viehland. Tri-duality theory in phase transformations of ferroelectric crystals with random defects. Proceedings of IUTAM Symposium on Complementarity, Duality and Symmetry in Nonlinear Mechanics. Kluwer Academic Publishers, 2003. pp. 67-84.
  9. David Y. Gao,  Jie-Fang Li and D. Viehland, Triality theory to Landau-Ginzburg equation in imperfect ferroelectrics, Proceedings of the 4th International Conference on Nonlinear Mechanics, W.Z. Chien (ed), Shanghaui University Press, 2002. 
  10. Gao, D.Y., Duality and triality in non-smooth, nonconvex and nonconservative systems: A survey, new phenomena and new results, in Nonsmooth/Nonconvex Mechanics with Applications in Engineering, edited by C. Baniotopoulos. Thessaloniki, Greece. 2002,  pp. 1-14.
  11. Gao, D.Y. and Lin, P., Calculating global minimizers of a nonconvex energy potential, in Recent Advances in Computational Science & Engineering, edited by H.P. Lee and K. kumar, Imperial College Press, 2002, pp. 696-700.
  12. Gao, D.Y., Duality and triality: Unify Mathematical Physics and Global Optimization, Plenary lecture, Proceedings of the 7th Asian Technology Conference in Mathematics, ATCM, Inc., 2002.
  13. Gao, D.Y., Duality in nonconvex finite deformation theory: A survey and unified approach,  in From Convexity to Nonconvexity: A Volume dedicated to the memory of Professor Gaetano Fichera, R. Gilbert, P.D. Panagiotopoulos and P. Pardalos eds. Kluwer Academic Publishers: Dordrecht, 2001, 69-84.
  14. Gao, D.Y., Canonical Dual Control for Nonconvex Distributed-Parameter Systems: Theory and Method. Control of Nonlinear Distributed Parameter Systems, Goong Chen, Irena Lasiecka and Jianxin Zhou (eds). Marcel Dekker, 2000, 85-112.
  15. Gao, D.Y., Nonsmooth and nonconvex dynamics: Duality, polarity and complementary extrema, in Nonsmooth/Nonconvex Mechanics, D.Y. Gao, R.W. Ogden and G. E. Stavroulakis (eds), Kluwer Academic Publishers, 2000, 95-140.
  16. Gao, D.Y. Minimax and triality theory in nonsmooth variational problems, in Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods M. Fukushima and L.Q. Qi eds., Kluwer Academic Publishers, 1998, pp. 161-179.
  17. Gao, D.Y. and Russell, D.L., Finitely deformed thick beam theory and dual variational extremum principles in post-buckling analysis, in Proc. of the 14th Army Symposium on Solid Mechanics, Kailasan Iyer and S.C. Chou (eds), 1997. Battelle Press, Columbus/Richiand, 497-506.
  18. Gao, D.Y.,  Post-buckling analysis and anomalous dual variational problems in nonlinear beam theory, Applied Mechanics in Americans, Vol. 4, Proc. of the Fifth Pan American Congress of Applied Mechanics, Ed. by L.A. Godoy, L.E. Suarez, The University of Iowa, Iowa city, Aug. 1996.
  19. Gao, D.Y.,  Complementarity and duality in natural sciences, Philosophical Study in Modern Science and Technology, Tsinghua University Press, 12-25, 1996.
  20. 64. Gao, D.Y. and Russell, D.L.,  Finite deformation extended beam theory and nonlinear buckling analysis,  Contemporary Research in the Mathematics and Mechanics  of Materials, Ed. by R. Batra and M. F. Beatty, CIMNE, Barcelona, Spain. pp. 430-441, 1996
  21. Gao, D.Y.,  2-Dimensional elastoplastic beam theory and limit analysis,  Developments in Theoretical and Applied Mechanics, Vol. XVIII, Ed. by H.B. Wilson, et al, The University of Alabama, 1996, pp. 42-53.
  22.  Gao, D.Y. and Russell, D.L.,   A finite element approach to optimal control of smart beam, Proc. of Int. Conf. Comput. Meth. Struct., Y.K. Cheung ed., Vol. 1,  pp. 135-140, 1994.
  23. Gao, D.Y.,   Dual extremum principles for incremental analysis of  finite plasticity, Developments in Theoretical and Applied Mechanics, Ed. by I.C. Jong and F.A. Akl, Vol. XVII, 1994, pp. 163-174.
  24. Gao, D.Y.,  Upper bound theorems for plastic dynamics of large deformation, Adv. in Applied Mathematics and Mechanics in China, Vol. 3, pp. 171-178, Int. Acad. Publ., Beijing, 1991.
  25.  Gao, D.Y., Opposite principles in nonlinear conservative systems,  Advances in Systems Research and Cybernetics, Edited by George E. Lasker, University of Windsor, Canada, 1989.
  26. Gao, D.Y.,  Convex analysis and mathematical theory of plasticity, Modern Mathematics and Mechanics, Z.H. Guo (ed.) Beijing University Press, 1988, pp. 165-187.
  27. Gao, D.Y., Dual bounding theorems for plastic limit analysis, Proc. 20th Midwestern Mechanics Conference, Purdue University, 1987.
  28. Gao, D.Y. and Hwang, K.C., Panpenalty finite element method for plastic limit analysis,  Proc. National Conf. on Engineering Computational Mechanics, Ed. by W.Z. Qien and Z.Z. Fu, Science Press, 1987.
  29. Gao, D.Y., Variational principle with movable boundary for nonlinear elasticity, Proc. 20th Midwestern Mechanics Conference, Purdue University, 1987.
  30. Gao, D.Y. and Hwang, K.C.,  Panpenalty finite element methods, Computational Mechanics'86,  Theory and Applications Ed. by S. Atluri-Yagawa, Springer-Verlag, 1986, Vol. 1, pp. 191-196.
  31. Gao, D.Y. and Hwang, K.C.,  On the complementary energy variational principle for Hencky plasticity,  Proc. Int. Conf. on Nonlinear Mechanics,  Chien Wei-zang ed., Science Press 1985, 489-494.

 

VI.   Book Review, Preface, and Recreation Articles

  1.  Gao, D.Y. and Sherali, H.D. (2008), Preface to Complementarity, Duality, and Global Optimization, special issue of J. Global Optimization.
  2. Gao, D.Y. and Teo, K.L., Preface for special issue on Duality, J. Global Optimization, 29, 2004.
  3. M. Kamat and David Y. Gao (1999): Book review for Nonconvex Optimization in Mechanics: Algorithms, Heuristics and Engineering Applications by the F.E.M. by E.S. Mistakidis, G.E. Stavroulakis. Kluwer Academic Publishers, Dordrecht, Boston, London. In: Applied Mechanics Reviews, Volume 52, Number 6, Review 6R2, page B58, American Society of Mechanical Engineers, June 1999.
  4. Gao, D.Y. (2002): Canonical Dual Transformation Method: A New Powerful Approach in Global Optimization and Nonconvex Variational Problems, Optimization Research Bridge, Issue 7, September 2002, http://www.ballarat.edu.au/itms/orb/index.html.
  5. Gao, D.Y. (2002): An Intelligent, Energetic and Popular Greek-American Scientist, an interview with Professor Panos Pardalos. Optimization Research Bridge, Issue 8, December, 2002, http://www.ballarat.edu.au/itms/orb/index.html