DR B.D. CRAVEN

Department of Mathematics & Statistics,
University of Melbourne

List of Research Papers and Books

Books

Mathematical Programming and Control Theory (Chapman & Hall, London,
1978).

Functions of Several Variables (Chapman & Hall, London, 1981).

Lebesgue Measure and Integral (Pitman, Boston, 1982).

Fractional Programming (Heldermann Verlag, Berlin, 1988).

Control and Optimization (Chapman & Hall, London, 1995)

Optimization in Economics and Finance :
Sone Advances in Non-Linear, Dynamic, Multi-Criteria and Stochastic Models
(with Sardar M. N. Islam) (Springer, Dordrect, 2005)

Operations Research Methods : Related Production, Distribution, and
Inventory Management Applioations
(with Sardar M. N. Islam (Icfai University Press,
Hyderabad, 2006).

Research publications (other than mathematical):

An analysis of the stress/strain curve for paper, APPITA 15 (2), 59-67
(1961).

Stress relaxation and work hardening in paper, APPITA 16 (2), 57-70
(1962).

A systematic rheological classification, (with O. Delatycki and P.U.A.
Grossman). Proceeding of Fifth International Congress on Rheology, Kyoto
1969, pages 397-406 (University of Tokyo Press, 1969).

Research papers in Mathematics

1. A generalisation of the transportation methods of linear
programming, Operational Research Quarterly 14 (2), 157-166, (1963).

2. Some results for the bulk service queue, Australian Journal of
Statistics 5 (2), 49-56 (1963).

3. Asymptotic transient behaviour of the bulk service queue, Journal of
the Australian Mathematical Society 3 (4), 501-512 (1963).

4. A note on Green's theorem, Journal of the Australian Mathematical
Society 4 (3), 289- 292 (1964).

5. On digital distribution in some integer sequences, Journal of the
Australian Mathematical Society 5 (3), 325-330 (1965).

6. Serial dependence of a Markov process, Journal of the Australian
Mathematical Society 5 (3), 325-330 (1965).

7. A model for transit delays. Operations Research 14 (1), 174-177
(1966).

8. On the Gauss-Green theorem, Journal of the Australian Mathematical
Society 8 (3), 285- 296 (1968).

9. Complex symmetric matrices, Journal of the Australian Mathematical
Society 10, 341- 354 (1969).

10. Asymptotic correlation in a queue. Journal of Applied Probability 6,
573-583 (1969).

11. The Stone-Weierstrass theorem and completeness of orthogonal
systems, Notices of the American Mathematical Society 16 (5), Abstract
667-165, (Aug. 1969).

12. Stone's theorem and completeness of orthogonal systems, Journal of
the Australian Mathematical Society 12 (2), 211-223 (1971).

13. A generalization of Lagrange multipliers, Bulletin of the Australian
Mathematical Soceity 3, 353-362 (1970).

14. Two properties of Bochner integrals, Bulletin of the Australian
Mathematical Society 3, 363-368 (1970).

15. Linear mappings between topological vector spaces, Journal of the
Australian Mathematical Society 14, 105-118 (1972).

16. On converse duality in nonlinear programming (with B. Mond),
Operations Research 19 (1971), 1075-1078.

17. On duality in complex linear programming (with B. Mond), Journal of
the Australian Mathematical Society 16 (1973), 172-175.

18. Converse and symmetric duality in complex nonlinear programming
(with B. Mond), Journal of Mathematical Analysis and Applications 37
(1972), 617-626.

19. Nonlinear programming in locally convex spaces, Journal of
Optimization Theory and Applications 10 (4) (1972), 197-210.

20. Transposition theorems for cone-convex functions (with B. Mond),
S.I.A.M. Journal on Applied Mathematics 24 (4), (1973), 603-612.

21. A note on mathematical programming with fractional objective
functions (with B. Mond) Naval Research Logistics Quarterly 20 (3),
(1973), 577-581.

22. Linear constraints in the Kuhn-Tucker theorem (with B. Mond).
(unpublished).
23. The dual of a fractional linear program (with B. Mond),
Journal of Mathematical Analysis and Applications 42 (1973), 517-512.
Erratum, ibid, 55 (1976), 807.

24. Irreducible and cone-monotone matrices (with B. Mond).
(unpublished).

25. Continuous nonlinear fractional programming (with B. Mond).
(unpublished).

26. On fractional programming and equivalence (with B. Mond), Naval
Research Logistics Quarterly 22 (1975), 408-410.

27. The spectal density of a Markov process, Journal of Applied
Probability 10 (3), (1973), 520-527.

28. Nonlinear fractional programming (with B. Mond), Bulletin of the
Australian Mathematical Society 12 (1975), 391-397. (Presented at
Twentieth International Meeting of the Institute of Management Sciences,
Tel Aviv, 1973).

29. Perturbed Markov processes, Stochastic Models 19(2) (2003), 269-285.

30. A Fritz John theorem in complex space (with B. Mond), Bulletin of
the Australian Mathematical Society 8 (1973), 215-220.

31. Real and complex Fritz John theorems (with B. Mond), Journal of
Mathematical Analysis and Applications 44 (1973), 773-778.

32. Converse duality in Banach space, J. Optim. Theor. Appl. 16 (1975),
229-236.

33. Lagrangean conditions for optimization in Banach spaces. Presented
at the International Congress of Mathematicians (Vancounver, Aug. 1974).
University of Melbourne, School of Mathematical Sciences, Research
Report No. 6 (1976).

34. On differentiable functions, Nanta Mathematica 9 (1975), 23-27.

35. Asymptotic rate of a Markov process, Adv. Apple. Prob. 6 (1974),
732-746. And: Manchester-Sheffield School of Probability and Statistics,
Research Report 139/BDC3 (Aug. 1973).

36. The number of customers in a busy period (with D.N. Shanbhag).
Manchester-Sheffield School of Probability and Statistics, Research
Report 140/BDC & DNS 2 (Dec. 1973).

37. Asymptotic behaviour of a dam of infinite depth (with D.N.
Shanbhag). Manchester- Sheffield School of Probability and Statistics,
Research Report 146/BDC & DNS 2 (Dec. 1973).

38. A Fubini theorem for Lebesgue-Stieltjes integrals. (unpuhblished).

39. On constrained maxima and minima, Australian Math. Soc. (Gazette 6
(2) (1979), 46- 50.

40. Nonlinear integer fractional programming (with B. Mond).
(unpublished).

41. A class of nondifferentiable complex programming problems (with B.
Mond), Mathematische Operationsforschung und Statistik 6 (1975),
581-591.

42. Kuhn-Tucker conditions in Banach space, University of Melbourne,
School of Mathematical Sciences, Research Report No. 28 (1974).

43. A generalized Motzkin alternative theorem, University of Melbourne,
School of Mathematical Sciences, Research Report No. 13 (1975).

44. Duality for homogeneous fractional programming (with B. Mond). CCERO
18 (4) (1976), 413-414.

45. Duality in homogeneous programming, University of Melbourne, School
of Mathematical Sciences, Research Report No. 15 (1974).

46. Mathematical programming and Pontryagin's minimum principles,
University of Melbourne, School of Mathematical Sciences, Research
Report No. 3 (1974).

47. Generalizations of Farkas's theorem (with J.J. Koliha), S.I.A.M.
Journal on Mathematical Analysis 8 (6) (1977), 983-997.

48. Complementarity for arbitrary cones (with B. Mond), Zeitschrift fur
Operations Research 21 (1977), 143-150.

49. Sufficient Fritz John optimality conditions (with B. Mond), Bull.
Aust. Math. Soc. 13 (1975), 411-419.

50. Lagrangean conditions for quasidifferentiable optimization (with B.
Mond), University of Melbourne, School of Mathematical Sciences,
Research Report No. 7 (1976), Survey of Mathematical Programming, Vol. I
pages 177-192 (North-Holland, (1979). (Proc. of IX International
Symposium on Mathematical Programming, Budapest, Aug. 1976).

51. Sufficient Fritz John optimality conditions for nondifferentiable
convex programming (with B. Mond), University of Melbourne, School of
Mathematical Sciences, Research Report No. 14 (1976). J. Aust. Math.
Soc. Series B, 19 (1976), 462-468.

52. Alternative theorems with convex cones, University of Melbourne,
School of Mathematical Sciences, Research Report No. 15 (1976).

53. Sufficient optimality conditions for complex programming (with B.
Mond), Naval Res. Log. Quart. 25 (1) (1979), 153-155.

54. Lagrangean conditions and quasiduality, Bull. Austral. Math.
Soc. 16 (1977), 325-339.

55. A note on duality in homogeneous fractional programming (with B.
Mond), Naval Research Logistics Quarterly 25(1) (1979), 153-155.

56. Non-differentiable Pontryagin principle, University of Melbourne,
School of Mathematical Sciences, Research Report No. 20 (1977).

57. On duality for fractional programming (with B. Mond), ZAMM 59 (6)
(1979), 278-279.

58. Complete characterizations of optimality for convex programming in
Banach spaces (with S. Zlobec), Applicable Analysis 11 (1980), 66-78.

59. A duality theorem for a nondifferentiable nonlinear fractional
programming problem (with B. Mond), Bull. Austral. Math. Soc. 20 (1979),
379-406.

60. Strong vector minimization and duality. University of Melbourne,
School of Mathematical Sciences, Research Report 16 (1978); ZAMM 60
(1980) 1-5.

61. Multi-criteria optimization. University of Melbourne, Mathematics
Research Report 37 (1978).

62. Augmented restricted Lagrangians in convex programming (with S.
Zlobec) Tech. Report TWISK 62, National Research Laboratory for Math.
Sciences, Pretoria, South Africa, Jan. 1979.

63. On a computational algorithm for time-lag optimal control problems
with restricted phase coordinates (with K.L. Teo), J. Austral. Math.
Soc., Series B, 21 (1980), 385-397.

64. Linear programming with matrix variables (with B. Mond), Linear
Algebra and Appl. 38 (1981), 73-80.

65. Optimization with multiple objectives, Proc. 4th. Annual Conf. of
O.R. Soc. of New Zealand, May 1978, (vol. 1 - Theory, pp. 11-18).

66. Duality and sensitivity for some fractional progress (presented at
Appl. Math. Conference, Leura, Australia, Feb. 1979).

67. Stabilization and determination of the set of minimal binding
constraints in convex programming (with S. Zlobec), Optimization 12 (2)
(1981), 203-220. (and Melbourne University Mathematics Research Report
34 (1979), A method for stabilization of convex programs, with selected
applications).

68. Lagrangian conditions, vector minimization and local duality,
University of Melbourne, School of Mathematical Sciences, Research
Report No. 37, (1980).

69. Implicit function theorems and Lagrange multipliers, Numerical
Functional Analysis and Optimization 2 (1980), 477-486.

70. Vector-valued optimization, pages 661-687 of "Generalized Concavity
in Optimization and Economics", S. Schaible and W.T. Ziemba (eds.),
Academic Press, 1981.

71. Duality for generalized convex fractional programs, pages 473-489 of
"Generalized Concavity in Optimization and Economics", S. Schaible and
W.T. Ziemba (eds.), Academic Press, 1981.

72. On fractional programming duality with generalized convexity (with
B. Mond). (unpublished).

73. Modified duality for mixed-integer programs (with B. Mond), Utilitas
Mathematica 21C (1982), 235-248.

74. Perturbed minimization, with constraints adjoined or deleted,
Optimization 14 (1983), 23-26.

75. Generalized implicit function theorems when the derivative has no
bounded inverse (with M.Z. Nashed), Nonlinear Analysis, Theory, Methods
and Applications 6 (1982), 375- 387.

76. Alternative theorems, ZAMM 62 (12) (1982), 699-705. (And University
of Melbourne, School of Mathematical Sciences, Research Report No. 10,
1982).

77. Invex functions and constrained local minima, Bull. Austral. Math.
Soc. 25 (1981), 37- 46.

78. Linearity and weak convergence on the boundary of numerical range
(with K.C. Das), J. Austral. Math. Soc. Series A, 35 (1983), 221-226.

79. On a complementarity problems associated with nondifferentiable
programming (with B. Mond and J. Parida). University of Melbourne,
School of Mathematical Sciences, Research Report No. 25, (1981). J.
Austral. Math. Soc. Series B. 25 (1984), 419-430.

80. On a programming problem with an Lp norm in the objective function
(with J. Parida and T.R. Gulati), University of Melbourne, School of
Mathematical Sciences, Research Report No. 27, (1981). Utilitas Math. 23
(1984), 339-352.

81. On duality for some nonlinear fractional programs (with T.R.
Gulati). (unpublished).

82. Zero duality gap for infintely constrained problems (with D.F.
Karney), (under revision).

83. On minimization subject to cone constraints (with B.M. Glover and S.
Zlobec), Numberical Funct. Anal. Optim. 6 (1983), 363-378. ( University
of Melbourne, School of Mathematical Sciences, Research Report No. 18,
(1982).).

84. A class of nondifferentiable continuous programming problems
(with S. Chandra and I. Husain), J. Math. Anal. Apppl. 107 (1985),
12-138. ( University of Melbourne, School of Mathematical Sciences,
Research Report No.28, (1982). ).

85. On quasidifferentiable optimization, University of Melbourne, School
of Mathematical Sciences, Research Report No. 23, (1982), J. Austral.
Math. Soc. Series A, 41 (1986), 64-78.

86. Duality in nondifferentiable convex programming (with T.R. Gulati).
(unpublished).

87. A strict converse duality theorem in nonlinear programming (with
T.R. Gulati). (unpublished).

88. A strict converse duality theorem in nonlinear programming (with
T.R. Gulati) J. of Information and Optim. Sciences 4 (1983), 301-306.

89. On maximizing a ratio of optimization problems (with B. Mond), CCERO
25 (1983), 29-34.

90. Invex functions and duality (with B.M. Glover). University of
Melbourne, School of Mathematical Sciences, Research Report No. 1
(1983), J. Austral. Math. Soc. Series A, 39 (1985), 1-20.

91. Some concepts in multi-criteria optimization. Report TWISK299 (Apr.
1983), National Research Institute for Math. Sciences, Pretoria, South
Africa.

And: Proceedings of Austral. Soc. Operations Research National
Conference, Melbourne, (1987), 34-43.

92. Generalized functions for applications, J. Austral. Math. Soc.
Series B 26 (1985), 362- 379.

93. Modified Kuhn-Tucker conditions when a minimum is not attained,
Operations Research Letters 3 (1), (1984), 47-52.

94. On the Pontryagin principle for stochastic optimal control (Apr.
1983). Report TWISK 328 (Aug. 1983), National Research Institute for
Maths. Sciences, Pretoria, South Africa (supersedes paper no. 46).

95. On nondifferentiable convex functions (with B.M. Glover),
Optimizations 16 (1) (1985) 3-6.

96. Iterative fitting of a time series model, in "New mathematical
advances in economic dynamics", ed. D.F. Batten and P.O. Lesse, Croon
Helm, London, pages 155-162 (1985).

97. Symmetric dual fractional programming (with S. Chandra and B. Mond),
Zeits fur Operations Research 29 (1985), 59-64.

98. Continuous programming containing arbitrary norms (with S. Chandra
and I. Husain), J. Austral. Math. Soc. Series A 39 (1985), 28-38.

99. Generalized fractional programming duality, a ratio game approach
(with S. Chandra and B. Mond) J. Austral. Math Soc. Series B, 28 (1986),
170-180 (and University of Melbourne, School of Mathematical Sciences,
Research Report No.23 (1983).).

100. Generalized concavity and nondifferentiable mathematical
programming duality (with S. Chandra and B. Mond), La Trobe University
Pure Mathematics Research Report No. 83-16 (Dec. 1983). (See 102 for a
revised version).

101.Nonlinear programming duality and matrix game equivalence (with
S. Chandra and B. Mond), J. Austral. Math. Soc. Series B, 26 (4) (1985),
422-429.

102.Generalized concavity and duality with a square root
term ( with S. Chandra and B. Mond), Optimization 16 (5) (1985),
653-662.

103.Symmetric dual nondifferentiable continuous programming problems
(with S. Chandra and I. Husain), University of Melbourne, School of
Mathematical Sciences, Research Report No. 7 (1983).

104.A class of nondifferentiable control problems (with S. Chandra
and I Husain), University of Melbourne, School of Mathematical Sciences,
Research Report No. 9 (1983). J. Math. Anal. Appl. 56 (1988), 227-243. +

105.Nondifferentiable optimization by smooth approximations,
University of Melbourne, School of Mathematical Sciences, Research
Report No. 32 (1984), Optimization 17 (1986), 3-17.

106.Alternative and duality theorems with weakened convexity (with
V. Jeyakumar), University of Melbourne, School of Mathematical Sciences,
Research Report No. 31 (1984) , Utilitas Mathematica 31 (1987), 149-159.

107.Nonconvex theorems of the alternative and minimization (with V.
Jeyakumar and J. Gwinner), Optimization 18 (1987) 2, 151-163.

108. A note on nondifferentiable symmetric duality, J. Austral. Math.
Soc. Ser. B. 28 (1986), 30-35.

109.Equivalence of a Ky Fan type minimax theorem and Gordan type
alternative theorem, (with V. Jeyakumar), Operations Research Letters 5
(1986), 99-102

110.Weak minimization and duality, (with T. Weir and B. Mond),
Numerical Functional Analysis and Optimization 9 (1987), 181-192.

111.On duality for weakly minimized vector valued optimization
problems (with T. Weir and B. Mond), Optimization 17 (1986) 6, 711-721.

112.On sensitivity analysis for multicriteria optimization (1986),
International Conference on Vector Optimization, Darmstadt, Aug. 1986;
Optimization 19 (1988) , 513-523.

113.Sensitivity in multicriteria optimization, Proc. Int. Conference
on Optimization Techniques and Applications (ICOTA), Singapore, 1987,
790-797.


114.Extensions of Hahn-Banach theorems using convexity (with V.
Jeyakumar) (1988), submitted for publication.

115. Boundary conditions in optimal control, (1988), J. Austral.
Math. Soc. Ser. B. 30 (1989), 790-797.

116.A modified Wolfe dual for weak vector minimization, Numer.
Funct. Anal. Optim. 10 (9&10) (1989), 899-907.

117. A vector variational inequality and optimization over an
efficient set (with G.-Y. Chen) (1988), Z. O. R: Methods and Models of
Operations Research 34 (1990), 1-12.

118.Fractional programming - a survey, Opsearch 25 (1988), 165-176.

119. Nonsmooth multiobjective programming, Numer. Funct. Anal.
Optim. 10 (1&2) (1989), 49-64.

120. Approximate dual and approximate vector variational inequality
for multiobjective optimization (with G.-Y. Chen), (1988), J. Austral.
Math. Soc., Series A, 47 (1989), 418-423.

121. Existence and continuity of solutions for multiobjective
optimization (with G.-Y. Chen) , (1988) ( ? to appear in Journal
of Optimization Theory and Applications).

122. On duality in generalized minimax problems (with B. Mond and
T. Weir), (1988). Asia-Pacific J. of Opns. Res.7(1)(1990), 55-62.

123 Lagrangian conditions for a minimax, Proc. of Conference on
Functional Analysis/Optimization, Austral. Nat. Univ., Canberra (Aug.
1988), 24-33.

124 Aspects of multicriteria optimization, Australian Society of
Operations Research, Conference 1989 , in Recent Prospects in
Mathematical Programming ,Gordon & Breach , Philadelphia, (1991), pages
93-100.

125 Vector valued Lagrangian and multiobjective fractional
programming duality (with S. Chandra and B. Mond) (1989) , Numer.
Funct. Anal. Optim. 11 (3&4)(1990), 235- 254.

126 Multiobjective fractional programming duality : a Lagrangian
approach (with S. Chandra and B. Mond), Optimization 33 (1991), 549-566.

127 Quasimin and quasisaddlepoint for vector optimization , Numer.
Functi. Anal. Optim. 11 (1990), 45-54.

128 An algorithm for minimax, ZOR - Methods and Models of
Operations Research 35 (1991) , 425-434.

129 A nonsmooth version of alternative theorem and nonsmooth
multiobjective programming (with Xiaoiqi Yang) Utilitas Mathematica
40 (1991), 117-128.

130 Necessary optimality conditions with a modified subdifferential
(with Xiaoqi Yang), Optimization 22 (1991), 387-400.

131 Mathematical programming with iterative aggregation (with C. Petr),
Opsearch 28 (1991), 1-17

132.Regularity properties of the optimal value function in nonlinear
programming (with R. Janin), Optimization 28 (1993)1-7.

133.Invexity in multifunction optimization (with P.H. Sach), Numer.
Funct. Anal. Optim. 12 (1991), 383-394.

134.Invex multifunctions and duality (with P.H. Sach), University of
Melbourne, Dept. of Mathematics, Preprint 9-1991; Numer. Funct. Anal.
Optim. 12 (1991), 575-591.

135 A new class of invex multifunctions (with P.H.Sach, N.D.Yen,
T.D.Phuong), in "Nonsmooth Optimization Methods and Applications", F.
Gianessi (ed.), Gordon & Breach, New York (1992), 52-69.

136 Multicriteria sensitivity and shadow costs (with S. Bolintineanu),
Optimization 26 (1992), 115-127.

137 On continuous programming with generalized convexity, Asia-Pacific J
of Oper. Res.10 (1993), 219-231.

138 Convergence of discrete approximations for constrained minimization,
J. Austral. Math. Soc., Series B, 35 (1994), 50-59.

139 Generalized invexity and duality with multifunctions (with P.H. Sach
and N.D. Yen), Numer. Funct. Anal.Optim. 15 (1994), 131-153.

140 A generalized Karush-Kuhn-Tucker optimality condition without
constraint qualification using the approximate subdifferential (with B.
M. Glover and S. D. Flam), Numer. Funct. Anal. Optim. 14 (1993),
333-353.

141 A Fritz John optimality condition using the approximate
subdifferential (with B.M. Glover), J. Optim. Theor. Appl. 14 (1994),
253-265..

142 An approach to optimality conditions for nonsmooth minimax problems
(with D.V. Luu), University of Melbourne, Mathematics Dept., Preprint
Series No. 8 (1993).

143 Constrained minimax for a vector-valued function (with D.V. Luu),
University of Melbourne, Mathematics Dept., Preprint Series No. 11
(1993), Optimization 31 (1994), 199-208.

144 Lagrangian conditions for a nonsmooth vector-valued minimax (with
D.V. Luu), University of Melbourne, Mathematics Dept., Preprint Series
No. 21 (1993); J. Austral. Math. Soc., series A, 65 (1998), 163-175.

145. A method for establishing optimality conditions for a
nonsmooth vector-valued minimax problem (with D.V. Luu), University of
Melbourne, Mathematics Dept., Preprint Series No.23 (1993), and
J. Optim. Theor. Appl. 95 (1997), 295-304.

146 Strengthened invex and perturbations (with D. V. Luu and B. M.
Glover), (1994) Zeitschrift fuer Operations Research (Mathematical
Methods of Operations Research) 43 (1996), 319-336..

147 Relations between invex properties (1994),WSSIAA 5 (1995), 25-34
(World Scientific Publishing Company, Singapore).

148 Small convex-valued subdifferentials in mathematical
programming, Optimization 32(1) (1995), 1-21.

149 Relations between invex concepts, Proceedings of Optimization
Miniconference, University of Ballarat (July 1994), 47-54.

150 Morse theory and relations between smooth and nonsmooth
optimization (with V. Gershkovich and D. Ralph), Proceedings of
Optimization Miniconference, University of Ballarat (July 1994), 39-46.

151 Morse theory and invariant concepts of convexity (with V.
Gershkovich and D Ralph), Optimization 35 (1995), 99-112.

152 On converse duality and invexity (with B. Mond) (1995), Indian J.
of Mathematics 42(3)(2000), 267-272.

153 Jensen-type inequalities for invex functions (with S.S. Dragomir)
(1995). preprint.

154 An approach to vector subdifferentials (with B.M. Glover)(1995),
Optimization 38 (1996), 237-251.

155 On invariant concepts of convexity for vector functions (with V.
Gershkovich and D. Ralph) (1995),University of Melbourne, Mathematics
Research Report 20 (1995).

156 Multicriteria optimal control , Asia-Pacific Journal of
Operational Research 16(1), (1999), 53-62.

157 Optimal control with an elliptic partial differential equation -
to appear (2003)

158 Avoiding a constraint qualification, Optimization 41 (1997),
291-302.

159 Optimization with set-functions described by functions (with D. V.
Luu), Optimization 42 (1997), 39-50.

160 Computing optimal control (with K. de Haas and J.M.Wettenhall),
Dynamics of Coninuous, Discrete and Impulsive Systems, 4 (1998),
601-615.

161. Optimal control and invexity (Feb. 1997, Computers and Mathematics
with Applications35(5), (1998), 17-25.

162. Pontryagin principle for fractional optimal control (1977) -
preprint, University of Pisa).

163. Perturbing convex multiobjective programs (with D V Luu),
Optimization 28 (2000), 391-407.

164. Optimal control for an obstruction problem (1997 - preprint,
University of Pisa), and J. Optim. Theor. Appl. 100 (1999), 435-439.

165. Non-differentiable invex, Proceedings of Conference for
Mathematics and ite Applications 36 (1000), 25-28. (National Symposium
on Functional Analysis, Optimization and Applications, Univ. of
Newcastle, March 1998).

166. Fractional programming with invexity (with B. Mond), (1998), to
appear.

167. Lagrange multipliers for nonconvex optimization, Progress in
Optimization II (Kluwer, 2000), 173-136 (Fifth Miniconference :
Optimization, Perth, June 1998).

168. On generic locally convex vector functions (V. Gershkovich, B. D.
Craven, and D. Ralph) , Progress in Optimization, X. Yang et al.
(eds.), (Kluwer, 2000), 135-152.

169. Invexity and ite applications, Encyclopedia of Optimization, Vol.
III (Kluwer, 2001), 82-86.

170. Global invexity and duality in mathematical programming,
Asia-Pacific Journal of Operational Research 19 (2002), 169-175.

171. On nonconvex optimization, Acta Mathematica Vietnamica 26(3),
(20010, 249-256.

172. Perturbations and approximate minimum in constrained
optimization, Taiwanese J. of Math. 5(3),(2001), 603-608,

173. Vector generalized invex, Opsearch 38(4)(2001), 345-351.

174. Computing optimal control on MATLAB - the SCOM package and
economic growth models (with S. M. N.Islam), in Optimization and
Related Topic, A, Rubinov & B. Glover (eds.), Kluwer 2001, pp. 61-70.

175. Computation of non-linear continuous boptimal growth models:
experiments with optimal control algorithms abd computer programs (with
S.M.N. Islam), Economic Modelling 18 (2001), 551-568.

176. Models and meaqsurement of sustainable growth and social welfare
(with S. M. N. Islam), Social Responsibility: Corporate Governance
Issues 17 (2003), 227-255 (Elsevier).

177. Some properties of optimal multifunctions in parametric
multiobjective optimization with set-valued maps (with Mao-Qin LI),
Asia-Pacific Journal of Operational Research, 21(1) (2003, 1-8. .

178. Pontryagin principle with a partial differential equation - a
unified approach, Optimization, Structure & Applications, C.Pearce
(ed.), Kluwer (2003). (to appear)

179. Optimal control of an economic model with a small stochastic term,
Pacific Journal of Optimization 1(1), 2005, 2332-241..

180. Dynamic optimization models in finance: some extensions to the
frameword, models and computation (with S.M.N. Islam), submitted
(2002).

181. Uncertainty and economic growth (with S. M. N. Islam) , submitted
(2002).

182. Measuring sustainable growth and welfare: models, computational
methods, and the SCOM computer paxckage (with S. M. N. Islam),
submitted (2002).

183. Static vector optimization in welfare economics, (with S. M. N. Islam),
Journal of Multi-Criteria Decision Analysis 12 (2003), 273-284.

184. On multiobjective dynamic optimization models for growth,
planning, social welfare and sustainability (with S. M. N. Islam),
Journal of Multicriteria Decision Analysis 12 92003), 273-284. .

185. Some extensions of nonconvex economic modelling : invexity,
quasimax, and new stability conditions (with S. M. N. Islam),
J. Optim. Theor. Appl. 125 (2) (2005)., 315-330

186. Computation of nonlinear continuous optimal growth models -experiments
with optimal control algorithms and computer programs (with S. M. N. Islam), (
Economic Modelling 18 (2001), 557-568.

187. A step to Kurzweil-Henstock - an outline, Mathematica Bohemica 3 (2004), 297-304.

188. Optimal control on an infinite domain, ANZIAM J.. 47(2) (2005), 1-11

189. Transversality conditions for infinite horizon economic and finance models
(with S. M. N. Islam), (submitted) .

190 Characterizing invex and related properties, in Generalized Convexity, Generalized
Monotonicity and Appl.ications, A. Eberhard, N.Hadjisavvas and D. T. Luc (eds.),
Springer, New York (2005), 183-191.

191. Optimization with generalized invexity, Optimization 54(6)(2005), 595-603.

192. Optimization and second derivative for a Lipschitz function, Optimization 55(3)(2006), 263-268.

193. Switching times in bang-bang control (with Chen, Ping), Opsearch 42(1) (2005), 55-68,

194. Perturbed Markov processes, Stochastic Models 15(3)(2003), 269-285,

195 Optimal control of an economic model with a small stochastic term,
Pacific J. of Optimization 1(1) (2005), 233-241.

196. Modelling Inventories in a network, Optimization Letters 1 (2007),401-406.

197. Logistics and supply chain management: a review of some operations research approaches
(with S. M. N. Islam), International Journal of Systems Engineering 2(4) (2007). 445-453.

198. Transversality and well-posed control problems (2007) (submitted).

199. Pontryagin principle in abstract spaces (2007) (submitted)

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