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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 53, 2004 - Issue 2
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Original Articles

Maximum principle for Volterra integral equations with controlled delay time

Pages 177-187 | Received 06 Mar 2003, Accepted 11 Mar 2004, Published online: 01 Sep 2006

References

References

  • Angell , TS . 1976 . On the optimal control of systems governed by nonlinear volterra equations . J. Opt. Theory Appl. , 19 : 29 – 45 .
  • Bakke , VL . 1974 . A maximum principle for an optimal control problem with integral constraints . J. Opt. Theory Appl. , 13 : 32 – 55 .
  • Benhabib , J and Rustichini , A . 1991 . Vintage capital, investment, and growth . J. Econ. Theory , 55 : 323 – 339 .
  • Boucekkine , R , Germain , M , Licandro , O and Magnus , A . 1998 . Creative destruction, investment volatility and the average age of capital . J. Econ. Theory , 58 : 361 – 384 .
  • Carlson , DA . 1987 . An elementary proof of the maximum principle of optimal control problems governed by a volterra integral equation . J. Opt. Theory Appl. , 54 : 43 – 61 .
  • Connor , MA and Hood , DA . 1973 . Gradient method for systems described by integral equation . IEEE Transac. Automat. Contr. , AC-18 : 175 – 177 .
  • Corduneanu C 1991 Integral Equations and Applications, Cambridge University Press New York
  • Dubovitskii , AYa. and Milyutin , AA . 1965 . Extremum problems in the presence of restrictions . USSR. Comp Math Math Phys , 5 ( 3 ) : 1 – 80 .
  • Dubovitskii AYa. Milyutin AA 1981 Theory of maximum principle Methods of the Theory of Extremum Problems in Economics pp. 6–47 Nauka Press Moscow (in Russian)
  • Gabasov R Kirillova F 1971 The Qualitative Theory of Optimal Processes, Nauka Press Moscow (in Russian)
  • van Hilten , O . 1991 . The optimal lifetime of capital equipment . J. Econ. Theory , 5 : 449 – 454 .
  • Hritonenko , N and Yatsenko , Yu. 1996 . Integral-functional equations for optimal renovation problems . Optimization , 36 : 249 – 261 .
  • Hritonenko N Yatsenko Yu. 1996 Modeling and Optimization of the Lifetime of Technologies, Kluwer Academic Publishers Dordrecht, Boston, London
  • Hritonenko N Yatsenko Yu. 1999 Mathematical Modeling in Economics, Ecology and the Environment, Kluwer Academic Publishers Dordrecht,Boston,London
  • Ioffe AD Tikhomirov VD 1979 Theory of Extremal Problems, North-Holland Amsterdam
  • Medhin , N . 1986 . Optimal processes governed by integral equations . J. Math. An. Appl. , 120 : 1 – 12 .
  • Neustadt L 1976 Optimization (Theory of Necessary Conditions), Princeton University Press Princeton
  • Pontryagin LS Boltianskii VG Gamkrelidze RV Mishchenko EF 1962 The Mathematical Theory of Optimal Processes, Wiley-Interscience New York
  • Pshenichnyi BN 1971 Necessary Conditions for an Extremum, Marcel Dekker New York
  • Rockafellar T 1970 Convex Analysis, Princeton University Press Princeton
  • Rubinov AM 2000 Abstract Convexity and Global Optimization, Kluwer Academic Publishers Dordrecht,Boston,London
  • Shaikhet , LE . 1985 . On the optimal control of integral-functional equations . Prikl. Mat. Mekh. USSR. , 49 : 704 – 712 .
  • Solow , R , Tobin , J , von Weizsacker , C and Yaari , M . 1966 . Neoclassical growth with fixed factor proportions . Rev. Econ. Studies , 33 : 79 – 115 .
  • Vasiliev FP 1981 Solution Methods to Extremal Problems, Nauka Moscow (in Russian)
  • Vinokurov , VR . 1969 . Optimal control of processes described by integral equations, I, II, III. . SIAM J. Control , 7 : 324 – 355 .
  • Warga J 1972 Optimal Control of Differential and Functional Equations, Academic Press New York
  • Yatsenko Yu. 1991 Integral Models of Systems with Controllable Memory, Naukova Dumka Press Kiev (in Russian)
  • Yatsenko , Yu. and Hritonenko , N . 1994 . Optimization in integral model of developing systems . Optimization , 31 : 179 – 192 .

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