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., Handbook of Duality in Engineering Science (three volumes), in preparation to be published by Springer.
6. Gao, D.Y. and R.W. Ogden, Advances in Mechanics and Mathematics, AMMA 2003, Kluwer Academic Publishers, Boston/Dordrecht/London, 324pp.
7. Gao, D.Y. and K.L. Teo, Duality in Global Optimization and Control. Special issue of Journal of Global Optimization. 2004.
8. Gao, D.Y. and R.W. Ogden, Advances in Mechanics and Mathematics, III. Springer, 2005.
9. Gao, D.Y. and Sherali, H. Complementarity, Duality, and Global Optimization, A special volume dedicated to Professor G. Strang on the occasion of his 70^th birthday. Springer, 2006.

II. Articles in Encyclopedia

10. Gao, D.Y., Duality-Mathematics, Wiley Encyclopedia of Electronical and Electronical Engineering, 6, 1999, 68-77.
11. 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.
12. 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.
13. 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 in Refereed International Journals

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, Vol. 359, 2347-2367, 2001.
19. Gao, D.Y. and Ogden, R.W., On the complementary-dual-polar variational principles in finite deformation theory: I. Hyperelasticity, Proceedings of the Royal Society of London, Mathematical, Physical and Engineering Sciences, to appear.
20. Gao, D.Y. and Ogden, R.W., On the complementary-dual-polar variational principles in finite deformation theory: II. Differential geometry and Hypersurfaces. Proceedings of the Royal Society of London, Mathematical, Physical and Engineering Sciences, to appear.
21. Gao, D.Y., Analytic solution and triality theory for nonconvex and nonsmooth variational problems with applications, Nonlinear Analysis, 42, 7, 2000, 1161-1193.
22. Gao, D.Y., Canonical dual transformation method and generalized triality theory in nonsmooth global optimization, J. Global Optimization, 17(1/4), 2000, 127-160.
23. Gao, D.Y., Finite deformation beam models and triality theory in dynamical post-buckling analysis. Int. J. Non-Linear Mechanics, 35, 2000, 103-131.
24. Gao, D.Y., General Analytic Solutions and Complementary Variational Principles for Large Deformation Nonsmooth Mechanics. Meccanica 34, 1999, 169-198.
25. Gao, D.Y. Pure complementary energy principle and triality theory in finite elasticity. Mech. Res. Comm. 26 (1999), no. 1, 31-37.
26. 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.
27. Gao, D.Y., Duality, triality and complementary extremum principles in nonconvex parametric variational problems with applications, IMA J. Appl. Math., 61, 1998, 199-235.
28. 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.
29. 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.
30. 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
31. 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.
32. Gao, D.Y., Complementary finite element method for finite deformation nonsmooth mechanics, J. Eng. Math., 30, pp. 339-353, 1996.
33. 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.
34. 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.
35. Gao, D.Y., Contact problem of 2-D elastoplastic beam theory and dual variational inequality, Appl. Math. Mech., 17, 3, 953-968, 1996.
36. Gao, D.Y., Nonlinear elastic beam theory with applications in contact problem and variational approaches, Mech. Research Communication, 23, 1, pp. 11-17, 1996.
37. Gao, D.Y., Duality theory in nonlinear buckling analysis for von Karman equations, Studies in Appl. Math, 94, 1995: 423-444.
38. Gao, D.Y. and Yang, W.H., Multi-duality in minimal surface type problems, Studies in Appl. Math., 95, 1995: 127-146.
39. Gao, D.Y., Limit analysis of plastic shells subjected to large deflections, European J. Mech., A/Solids, 14, no 3, 1995, 459-472.
40. Gao, D.Y., Stability and extremum principles for post yield finite plasticity, Acta Mechanica Sinica, 10 (4), pp. 311-325, 1994.
41. Gao, D.Y., Global extremum criteria for nonlinear elasticity, J. Appl. Math. Physics, ( ZAMP) 43 (1992), pp. 924-937.
42. Yau, S.T. and Gao, D.Y., Obstacle problems for von Kármán equations, Adv. Appl. Math., 13 (1992), pp. 123-141.
43. Gao, D.Y., Extended bounding theorems for nonlinear limit analysis, Int. J. Solids Structures, 27 (1991),pp. 523-531.
44. Gao, D.Y., Dynamically loaded rigid-plastic analysis under large deformation, Quart. Appl. Math., 48(1990), 4, pp. 731-739.
45. 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.
46. Gao, D.Y., On the extremum variational principles for nonlinear elastic plates, Quart. Appl. Math., 48 (1990), pp. 361-370.
47. Gao, D.Y., Complementary Principles in Nonlinear Elasticity, Science in China (Scientia Sinica) (A) (Chinese Ed.), 33 (1990), 4, pp. 386-394.
48. Gao, D.Y., Bounding theorem on finite dynamic deformations of plasticity, Mech. Research Commu., 17 (1990), pp. 33-39.
49. Gao, D.Y. and Onate, E.T., Rate variational extremum principles for finite elastoplasticity, Appl. Math. Mech., 11 (1990), 7, pp. 659-667.
50. Gao, D.Y. and Strang, G., Geometric nonlinearity: Potential energy, complementary energy, and the gap function, Quart. Appl. Math., 47 (1989), pp. 487-504.
51. Gao, D.Y. and Strang, G., Dual extremum principles in finite deformation elastoplasitc analysis, Acta Applicandae Mathematicae, 17 (1989), pp. 257-267.
52. Gao, D.Y. and Wierzbicki, T., Bounding theorem in finite plasticity with hardening effect, Quart. Appl. Math., 47 (1989), pp. 395-403.
53. Gao, D.Y., Opposite principles in nonlinear conservative systems, Adv. Appl. Math., 10 (1989), pp. 370-377.
54. 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.
55. Gao, D.Y., Panpenalty finite element programming for limit analysis, Computers & Structures, 28 (1988), pp. 749-755.
56. Gao, D.Y., On the complementary bounding theorems for limit analysis, Int. J. of Solids and Structures, 24 (1988), pp. 545-556.
57. Gao, D.Y., Inverse variational principles in finite elasticity, Mechanics Research Communication, 15 (1988), pp. 161-167.
58. Gao, D.Y. and Hwang, K.C., On the complementary variational principles for elasto-plasticity, Scientia Sinica (A), 31 (1988), pp. 1469-1476.
59. 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).
60. Gao, D.Y., Penalty-duality finite element method in the analysis for incompressible medium, J. of Hefei University of Technology, 1 (1985).
61. 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.
62. Gao, D.Y., Extended bounding theorems of limit analysis, Appl. Math. Mech., 4 (1983), pp. 571-584.
63. 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.
64. Gao, D.Y., Variational principles of limit analysis in discontinuous plastic field, J. of Hefei University of Technology, 1 (1982), pp. 44-51.

IV. Book Chapters and Papers in Refereed Proceedings

65. Gao, D.Y. Multi-scale modeling and duality algorithm in phase transitions of ferroelectric materials, Proceedings of the 3^rd International Conference on Computational Modelling and Simulation of Materials, Pietro Vincenzini (eds), 2004.
66. Gao, D.Y. Nonconvex Semi-Linear Problems And Canonical Duality Solutions, Advances in Mechanics and Mathematics, Vol. II, 261-312. Springer.
67. 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.
68. 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.
69. 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.
70. David Y. Gao, Jie-Fang Li and D. Viehland, Triality theory to Landau-Ginzburg equation in imperfect ferroelectrics, Proceedings of the 4^th International Conference on Nonlinear Mechanics, W.Z. Chien (ed), Shanghaui University Press, 2002.
71. 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.
72. 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. 696-7000
73. 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.
74. 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.
75. 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.
76. 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.
77. 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.
78. 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.
79. Gao, D.Y., Complementarity and duality in natural sciences, Philosophical Study in Modern Science and Technology, Tsinghua University Press, 12-25, 1996.
80. 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
81. 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.
82. 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.
83. 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.
84. 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.
85. 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.
86. 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.
87. Gao, D.Y., Dual bounding theorems for plastic limit analysis, Proc. 20th Midwestern Mechanics Conference, Purdue University, 1987.
88. 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.
89. Gao, D.Y., Variational principle with movable boundary for nonlinear elasticity, Proc. 20th Midwestern Mechanics Conference, Purdue University, 1987.
90. 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.
91. 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.

V. Papers to appear

92. Gao, D.Y., Jie-Fang Li and D. Viehland, Complete solutions and triality theory to Landau-Ginzburg equation in imperfect ferroelectrics, submitted to Physics Review.
93. 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 80^th birthday, P. Alart and O. Maisonneuve (eds). Springer, 2004.
94. Gao, D.Y., Complete solutions to a class of polynomial minimization problems, to appear in J. Global Optimization.
95. Gao, D.Y. Complete solutions and optimality criteria for nonconvex quadratic minimization with box constraints, to appear in Mathematical Programming,
96. Gao, D.Y., Duality in distributed-parameter control of nonconvex and nonconservative dynamical systems with applications, to appear in J. Nonlinear Dynamics and Systems Theory.
97. Gao, D.Y. and Yu, H.F., Primal-dual algorithm for solving nonconvex rank-one quadratic minimization problem, to appear in J. Global Optimization
98. Gao, D.Y., Canonical duality theory: Connection between nonconvex mechanics and global optimization, to appear in Complementarity, Duality, and Global Optimization, Gao, D.Y. and Sherali, H. (ed), Springer, 2006.

VI. Book Review, Preface, Recreation Articles

99. 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.
100. 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.
101. 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.
102. Gao, D.Y. and Teo, K.L., Preface for special issue on Duality, J. Global Optimization, 29, 2004.

VII. Dissertations

1. Complementary Theory in Nonsmooth Elasto-plasticity and Pan-penalty Finite Element Methods, 236pp. Ph.D Thesis. Tsinghua University, 1986.
2. Plastic Buckling Analysis and Limit Analysis in Sheet Metal Forming Process, 65pp. M.A. Thesis. Beijing University of Aeronautics and Astronautics, 1982.