Hiroshima Mathematical Journal

Semi-infinite programs and conditional Gauss variational problems

Maretsugu Yamasaki

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 1, Number 2 (1971), 177-226.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206137972

Digital Object Identifier
doi:10.32917/hmj/1206137972

Mathematical Reviews number (MathSciNet)
MR0371396

Zentralblatt MATH identifier
0275.49017

Subjects
Primary: 90C05: Linear programming

Citation

Yamasaki, Maretsugu. Semi-infinite programs and conditional Gauss variational problems. Hiroshima Math. J. 1 (1971), no. 2, 177--226. doi:10.32917/hmj/1206137972. https://projecteuclid.org/euclid.hmj/1206137972


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References

  • [1] N. Bourbaki: Espaces vectoriels topologiques, Chap. I-II,Paris, 1953.
  • [2] N. Bourbaki: Espaces vectoriels topologiques, Chap. Ill-V, Paris, 1955.
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  • [4] A. Charnes, W. W. Cooper and K.O. Kortanek: Duality in semi-infinite programs and some works of Haar and Caratheodory, Management Sci., 9 (1963), 209-228.
  • [5] R.J. Dufin and L. A. Karlovitz: An infinite linear program with a duality gap, ibid., 12 (1965), 122-134.
  • [6] R.J. Duffin: An orthogonality theorem for Dines related to moment problems and linear programming, J. Combinatorial Theory, 2 (1967), 1-26.
  • [7] K. Isii: Inequalities of the types of Chebyshev and Cramer-Rao and mathematical programming, Ann. Inst. Statist. Math., 16 (1964), 277-293.
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  • [9] M. Ohtsuka: On potentials in locally compact spaces, J. Sci. Hiroshima Univ. Ser. A-I Math., 25 (1961), 135-352.
  • [10] M. Ohtsuka: Applications du theoreme de dualite en theorie du potentiel, Sem. Theorie du Potentiel, 1966/67.
  • [11] E.L. Peterson: An economic interpretation of duality in linear programming, J. Math. Anal. Appl., 30 (1970), 172-196.
  • [12] B.N. Pshenichniy: Linear optimal control problems, SIAM J. Control 4 (1966), 577-593.
  • [13] R.T. Rockafellar: Duality and stability in extremum problems involving convex functions, Pacific J. Math., 21 (1967), 167-187.
  • [14] R. Van Slyke and R. Wets: A duality theory for abstract mathematical programs with applications to optimal control theory, J. Math. Anal. Appl., 22 (1968), 679-706.
  • [15] M. Yamasaki: Remarks on the conditional Gauss variational problem, J. Sci. Hiroshima Univ. Ser. A-I Math., 31 (1967), 67-74.
  • [16] M. Yamasaki: Duality theorems in mathematical programmings and their applications, ibid., 32 (1968), 331-356.
  • [17] M. Yamasaki: Some generalizations of duality theorems in mathematical programming problems, Math. J. Okayama Univ., 14 (1969), 69-81.
  • [18] M. Yamasaki: Monotone limits in linear programming problems, J. Sci. Hiroshima Univ. Ser. A-I Math., 34 (1970), 249-258.

Corrections

  • See Correction: Maretsugu Yamasaki. Corrections to: "Semi-infinite programs and conditional Gauss variational problems". Hiroshima Math. J., Volume 2, Number 2, (1972), 547--547.