Publication List of  David Yang Gao

Complete list

MathSciNet for Gao's Papers and Books

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 R.W. Ogden, Advances in Mechanics and Mathematics, III.  Springer, 2005.
  8. Gao, D.Y., Handbook of Duality in Engineering Science (three volumes), in preparation to be published by Springer.
  9. Gao, D.Y. and Sherali, H., Advances in Mechanics and Mathematics, IV, Springer (to appear).
  10. Gao, D.Y. and Sherali, H.D., Complementarity and Duality in Global Optimization. Special issue of Journal of Global Optimization. 2004.

 

II. Articles in Encyclopedia

  1. Gao, D.Y., Duality-Mathematics, Wiley Encyclopedia of Electronical and Electronical Engineering, 6, 1999, 68-77.
  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 

  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. and Sherali, H.D. (2007). Canonical duality: Connection between nonconvex mechanics and global optimization, in Advances in Mechanics and Mathematics, III, 249-316, Springer, 2007.
  3. 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
  4. Gao, D.Y.and Ogden, R.W. (2008) Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation, to appear in Quarterly J. Mech. Appl. Math.
  5. 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 (2008) 3660–3673  
  6. Gao, D.Y. and Sherali, H.D. (2007), Preface to Complementarity, Duality, and Global Optimization, J. Global Optimization.
  7. Gao, D.Y. and Sherali, H.D. (2007). Preface to Advances in Mechanics and Mathematics, III, a special volume dedicated to Professor G. Strang for his 70th Birthday, Springer, 2007.
  8. Gao, D.Y. and Wei-Chi Yang (2008), Complete Solutions to Minimal Distance Problem between Two Nonconvex Surfaces,  to appear in Optimization.
  9. Feng, Z.S. and Gao, D.Y. (2008) A nonconvex dissipative system and its applications,  to appear in J.Global Optimization.
  10. Gao, D.Y. and Ruan, N. (2008) Solutions and optimality criteria for nonconvex quadratic-exponential minimization problem, to appear in Math. Meth. Operations Research, 67 (2008) issue 3.
  11. Wang, Z.B., Fang, S.-C., Gao, D.Y., and Xin, W.X., Global extremal conditions for multi-integer quadratic programming,  J. Industrial and Management Optimization.
  12. 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
  13. Fang, S.-C., Gao, D.Y., Shue, R.L., and Xin, W.X., Global optimization for a class of fractional programming problems, submitted to Journal of Global Optimization
  14. 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
  15. Gao, D.Y., Solutions and optimality criteria to box constrained nonconvex minimization problems, J. Industrial and Management Optimization. 3(2):293-304, 2007.
  16. Xuan, Zhaocheng Feng, Zhao-Sheng, and Gao, D.Y. (2007). FEM Approach for Complementary Bounds of Stress Intensity Factors in Bimaterials, Int. J. Nonlinear-Mechanics. 42 336– 341
  17. X. Wang, Z. Feng, L. Debnath and D.Y. Gao, Burgers-Korteweg-de Vries equation and it approximation, International Journal of Computer Mathematics,
  18. Z. Feng and D.Y. Gao, A nonconvex dissipative system and its applications (II), Journal of Global Optimization
  19. Gao, D.Y. (2007) Understand and control chaos in dynamical systems: Canonical duality approach and triality theory, Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems J. Awrejcewicz  (ed.) Springer.
  20. 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.
  21. Gao, D.Y., Complete solutions to a class of polynomial minimization problems, J. Global Optimization, 35, 131-143, 2006.
  22. Gao, D.Y. Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints,  J. Industrial and Management Science, 1:59-69, 2005
  23. 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.
  24. Gao, D.Y., Canonical duality theory and solutions to constrained nonconvex quadratic programming, Journal of Global Optimization, 29:377-399, 2004.
  25. 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.
  26. Gao, David Y., Complementarity, polarity and triality in nonsmooth, nonconvex and nonconservative Hamiltonian systems,
    Philosophical Transactions of the Royal Society: Mathematical, Physical and Engineering Sciences.
    Vol. 359, 2347-2367, Abstract,  Article in pdf file .
  27. Gao, D.Y., Canonical duality in nonsmooth, concave minimization with inequality constraints, 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.
  28. 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. 
  29. Gao, D.Y. Nonconvex Semi-Linear Problems And Canonical Duality Solutions, Advances in Mechanics and Mathematics, Vol. II, 261-312. Springer.
  30. 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.
  31. 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.
  32. 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.
  33. 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. 
  34. 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.
  35. 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.
  36. 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.
  37. Gao, David 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,  NONCONVEX OPTIMIZATION AND ITS   APPLICATIONS  Volume 55, 2001.
  38. Gao, David Y., Analytic solution and triality theory for nonconvex and nonsmooth variational problems with applications,
    in Nonlinear Analysis, 42, 7, 2000, 1161-1193. pdf file
  39. Gao, David Y., Canonical dual transformation method and generalized traility theory in nonsmooth global optimization,
    in J. Global Optimization, 17, 2000, 97-126.
  40. Gao, David Y., Canonical Dual Control for Nonconvex Distributed-Parameter Systems: Theory and Method,
    in Control of Nonlinear Distributed Parameter Systems, Goong Chen, Irena Lasiecka and Jianxin Zhou (eds). Marcel Dekker, 2001, 85-112. dvi file
  41. Gao, David Y., Nonsmooth and nonconvex dynamics: Duality, polarity and complementary extrema,
    in Nonsmooth/Nonconvex Mechanics: Modeling, Analysis and Numerical Methods, D.Y. Gao, R.W. Ogden and G. E. Stavroulakis (eds), Kluwer Academic Publishers, 2001, 95-140.
  42. Gao, David Y.,Finite deformation beam models and triality theory in dynamical post-buckling analysis
    in Int. J. Non-Linear Mechanics 35, 2000, 103-131. pdf file
  43. Gao, David Y., General Analytic Solutions and Complementary Variational Principles for Large Deformation Nonsmooth Mechanics in Meccanica 34, 1999, 169-198. ps file
  44. Gao, David Y.,Duality-Mathematics in Wiley Encyclopedia of Electronical and Eletronical Engineering6, 1999, 68-77 ps file
  45. Gao, David Y., Pure complementary energy principle and triality theory in finite elasticity.
    Mech. Res. Comm. 26 (1999), no. 1, 31-37 ps file,  html file
  46. Gao, David Y., General Analytic Solution for Fully Nonlinear, Nonconvex Variational Problems
    Problems of nonlinear Analysis in Engineering Systems. An International Journal of IFNA-ANS, No 1(9),1999.
  47. Gao, David Y., Duality, triality and complementary extremum principles in nonconvex parametric variational problems with applications in IMAJ. Appl. Math. 61, 1998, pp. 199-235. pdf file
  48. Cai, Duxing and Gao, David Y. Shear Control and Analytic Solutions for 2-D Dynamical Smart Beam Theory
    J. Intelligent Material Systems and Structures, 9, 1998, 182-188
  49. Gao, David 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. ps file
  50. Gao, David Y. and Russell, David L. An extended beam theory for smart materials applications. II. Static formation problems.
    Appl. Math. Optim. 38 (1998), no. 1, 69--94. pdf file
  51. Gao, David Y., Bi-complementarity and duality: A framework in nonlinear equilibria with applications to contact problem of elastoplastic beam theory,  J. Math. Analy. Appl. 221, 672-697, 1998 pdf file
  52. Gao, David Y., Dual extremum principles in finite deformation theory with applications to post-buckling analysis of extended nonlinear beam theory , Applied Mechanics Reviews, ASME,50, no. 11, Part 2, November 1997, S64-S71. PS file
  53. Gao, David Y. and Russell, D.L., Finitely deformed thick beam theory and dual variational extremum principles in post-buckling analysis,
    in Proceedings of the 14th US Army Symposium on Solid Mechanics,
    Edited by K.R. Iyer and Shun-Chin Chou, Battelle Press, Columbus/Richiand, 497-506.
  54. Gao, David Y., Post-buckling analysis of nonlinear extended beam theory and dual variational principles ,
    Applied Mechanics in Americas Vol. 4, Ed. by L.A. Godoy, M. Rysz and L. Suarez, Proceedings of PACAM V, San Juan, Puerto Rico, Iowa Univ. Press, Aug. 1996
  55. Gao, David Y., Complementarity and dual principles in natural sciences,
    in Selected Philosophical Papers of Tsinghua's Ph.D. , Tsinghua Univ. Press, 1996
  56. Gao, David Y. Contact problems and dual variational inequality of 2-D elastoplastic beam theory ,
    Appl. Math. Mech. (English Eition), 17, 10, pp. 953-968, 1996
  57. Gao, David Y., Complementary finite element method for finite deformation nonsmooth mechanics,
    J. Eng. Math., 1996. AbstractCompressed

  postscript file(100KB)

  1. Gao, David Y., Post-yield analysis for rigid-plastic plates with large deflections,
    European J. Mech., A/Solids,     15, N. 4, 599-616, 1996. Abstract
  2. Gao, David Y., Nonlinear elastic beam theory with applications in contact problem and variational approaches,
    Mech. Research Communication, Vol 23, No. 1, 1996, pp. 11-17. PS file
  3. Gao, David Y. and Russell, David L., Finite deformation extended beam theory and nonlinear buckling analysis,
    Development in Mechanics and Mathematics of Materials, Ed. by R. Batra and M. F. Beatty, 1996.
  4. Gao, David Y., 2-D elastoplastic beam theory and limit analysis,
    Developments in Theorerical and Applied Mechanics,     XVIII, Ed. by H. B. Wilson et at, 1996, pp. 42-53.
  5. Gao, David 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: 279-298, 1996.
  6. Gao, David Y.,Duality theory in nonlinear buckling analysis for von Karman equations,
    Studies in Appl. Math,     94, 1995: 423-444.
  7. Gao, David Y. and Yang, W.-H., Multi-duality in minimal surface type problems,
    Studies in Appl. Math.,     95, 1995: 127-146.
  8. Gao, David Y., Complementarity and duality: A unified framework in nonlinear equilibrium problems,
    ICAM Report, 95-12-02, pp. 1-20.
  9. Gao, David Y. Limit analysis of plastic shells subjected to large deflections,  European J. Mech., A/Solids, 14, 3, 1995, 459-472.
  10. Gao, David 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.
  11. Gao, David Y., Stability and extremum principles for post yield finite plasticity,
    Acta Mechanica Sinica,     10 (4), pp. 311-325, 1994.
  12. Gao, David Y., Dual extremum principles for incremental analysis of finite plasticity,
    Adv. Theoretical and Applied Mechanics, I.C. Jong (ed.), Vol. 15, 1994.
  13.  Gao, David Y., Global extremum criteria for nonlinear elasticity,
    J. Appl. Math. Physics, ( ZAMP)     43 (1992), pp. 924-937.
  14. Yau, S.-T. and Gao, David Y., Obstacle problems for von K\'{a}rm\'{a}n equations,
    Adv. Appl. Math.,     13 (1992), pp. 123-141.
  15. Gao, David Y., Extended bounding theorems for nonlinear limit analysis,
    Int. J. Solids Structures,     27 (1991),pp. 523-531.
  16. Gao, David Y., Dynamically loaded rigid-plastic analysis under large deformation,
    Quart. Appl. Math.,     48(1990), 4, pp. 731-739.
  17. Gao, David 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.
  18. Gao, David Y., On the extremum variational principles for nonlinear elastic plates,
    Quart. Appl. Math.,     48 (1990), pp. 361-370.
  19. Gao, David Y., Complementary Principles in Nonlinear Elasticity,
    Science in China (Scientia Sinica) (A) (Chinese Ed.),     33 (1990), 4, pp. 386-394.
  20. Gao, David Y., Bounding theorem on finite dynamic deformations of plasticity,
    Mech. Research Commu.,     17 (1990), pp. 33-39.
  21. Gao, David Y. and Onat, E.T., Rate variational extremum principles for finite elastoplasticity,
    Appl. Math. Mech.,     11 (1990), 7, pp. 659-667.
  22. Gao, David Y. and Strang, G., Geometric nonlinearity: Potential energy, complementary energy, and the gap function,
    Quart. Appl. Math.,     47 (1989), pp. 487-504.
  23. Gao, David Y. and Strang, G., Dual extremum principles in finite deformation elastoplasitc analysis,
    Acta Applicandae Mathematicae,     17 (1989), pp. 257-267.
  24. Gao, David Y. and Wierzbicki, T., Bounding theorem in finite plasticity with hardening effect, Quart. Appl. Math., 47 (1989), pp. 395-403.
  25. Gao, David Y., Opposite principles in nonlinear conservative systems,
    Adv. Appl. Math.,     10 (1989), pp. 370-377.
  26. Gao, David Y. and Cheung, Y.K., On the extremum complementary energy principles for nonlinear elastic shells,
    Int. J. Solids \& Struct.,     26 (1989), pp. 683-693.
  27. Gao, David Y., Panpenalty finite element programming for limit analysis,
    Computers \& Structures,     28 (1988), pp. 749-755.
  28. Gao, David Y., On the complementary bounding theorems for limit analysis,
    Int. J. of Solids and Structures,     24 (1988), pp. 545-556.
  29. Gao, David Y., Inverse variational principles in finite elasticity,
    Mechanics Research Communication,     15 (1988), pp. 161-167.
  30. Gao, David Y., Convex analysis and mathematical theory of plasticity,
    in Modern Mathematics and Mechanics, Z.H. Guo (ed.) Beijing University Press, 1988, pp. 165-187.
  31. Gao, David Y. and Hwang, Keh-chih, On the complementary variational principles for elasto-plasticity
    Scientia Sinica (A),     31 (1988), pp. 1469-1476.
  32. Gao, D.Y., Dual bounding theorems for plastic limit analysis
    Proc. 20th Midwestern Mechanics Conference, Purdue University, 1987.
  33. 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.
  34. Gao, D.Y., Variational principle with movable boundary for nonlinear elasticity
    Proc. 20th Midwestern Mechanics Conference, Purdue University, 1987.
  35. 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).
  36. Gao, D.Y. and Hwang, K.C., Panpenalty finite element methods
    Computational Mechanics'86, Theory and Applications Ed. by Atluri-Yagawa, Springer-Verlag, 1986, Vol. 1, pp. 191-196.
  37. 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.
  38. Gao, D.Y., Penalty-duality finite element method in the analysis for incompressible medium
    J. of Hefei University of Technology,     1 (1985).
  39. 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.
  40. Gao, D.Y., Extended bounding theorems of limit analysis
    Appl. Math. Mech.,     4 (1983), pp. 571-584.
  41. Gao, D.Y., On the unified theory of variational principles for rigid-perfectly plastic medium and penalty-du ality finite element mixed models,  J. of Hefei University of Technology, 4 (1983), pp. 91-97.
  42. Gao, D.Y., Variational principles of limit analysis in discontinuous plastic field
    J. of Hefei University of Technology,     1 (1982), pp. 44-51.