Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 18, 1987 - Issue 5
27
Views
14
CrossRef citations to date
0
Altmetric
Original Articles

Reduction and Discrete Approximation in Linear Semi-Infinite Programming

&
Pages 643-658 | Received 01 Aug 1986, Published online: 05 Jul 2007

References

  • Astafjev , N.N. 1982 . Linear Inequalities and Convexity Nauka , Moscow
  • Ben-Tal , A. , Ben-Israel , A. and Rosinger , E. 1979 . “ A Helly-type theorem and semi-infinite programming ” . In Constructive Approaches to Mathematical models , Edited by: Coffman , C.V. and Fix , G.J. 127 – 135 . New York : Academic Press .
  • Borwein , J.M. 1980 . A note on perfect duality and limiting Lagrangeans . Mathematical Programming , 18 : 330 – 337 .
  • Borwein , J.M. 1981 . Direct theorems in semi-infinite convex programming . Mathematical Programming , 21 : 301 – 318 .
  • Brosowski , B. 1982 . Parametric semi-lnfinite Programming , Frankfurt : Peter Lang .
  • Charnes , A. , Cooper , W.W. and Kortanek , K.O. 1962 . Duality, HAAR programs and finite sequence spaces , Vol. 48 , 783 – 786 . USA : Proc. Nat, Acad. Sci .
  • Charnes , A. , Cooper , W.W. and Kortanek , K.O. 1963 . Duality in semi-infinite programs and some works of HAAR and CARATHEODORY . Management Science , 9 : 209 – 228 .
  • Charnes , A. , Cooper , W.W. and kortanek , K.O. 1965 . On representations of semi-infinite programs which have no duality gaps . Management Science , 12 : 113 – 121 .
  • Charnes , A. , Cooper , W.W. and Kortanek , K.O. 1969 . On the theory of semi-infinite Programming and some generalizations of Kuhn-Tucker saddle, point theorems for arbitrary -convex functions . Naval Research Logistic Quarterly , 16 : 41 – 51 .
  • Duffin , R.J. , Jeroslow , R.G. and Karlovitz , L.A. 1983 . “ Duality in semi-infinite linear programming ” . In Semi infinite programming and And applications , Edited by: Fiacco , A.V. 50 – 62 . Berlin , New York : Springer-Verlag . Heidelberg
  • Duffin , R.J. and Karlovitz , L.A. 1965 . An infinite linear program with a duality gap . Management science , 12 : 122 – 134 .
  • Duffin , R.J. , Jeroslow , R.G. and Karlovitz , L.A. 1983 . “ Duality in semi- infinite linear programming ” . In Semi-Infinite Programming and Applications , Edited by: Fiacco , A.V. and Kortanek , K.O. Berlin , New York : Springer-Verlag . Heidelberg
  • Glashoff , K. and Hettich , R. 1980 . “ Duality Theory of Semi-Infinite Programming ” . In Semi-Infinite Programming , 1 – 16 . Berlin , New York : Springer-Verlag . Heidelberg
  • Glashoff , K. and Gustafson , S.A. 1983 . Linear Optimization and Approximation , Berlin , New York : Springer-Verlag . Heidelberg
  • Goberna , M.A. and López , M.A. 1984 . “ Conditions for the closedness of the characteristic 3one associated to an infinite linear system ” . In Infinite-Programming , Edited by: Anderson , E.J. and Philpott , A. 16 – 28 . Berlin , New York : Springer-Verlag . Heidelberg
  • Goberna , M.A. , López , M.A. and Pastor , J. 1981 . FARKAS-MINKOWSKI systems in Semi-infinite Programming . Applied Mathematics and Optimization , 7 : 295 – 308 .
  • Hettich , R. 1983 . “ A Review of Numerical Methods for Semi-Infinite Optimization ” . In Semi-Infinite Programming and Applications , Edited by: Fiacco , A. and Kortanek , K.O. 158 – 178 . Berlin , New York : Springer-Verlag . Heidelberg
  • Hettich , R. and Zencke , P. 1982 . Numerische Methoden der approximation und Semi-[nfiniten Optimierung , Stuttgart : Teubner .
  • Hoffmann , K.H. and Klostermair , A. 1976 . “ A Semi-Infinite Linear Programming Procedure and Applications to Approximation Problems in Optimal Control ” . In Approximation Theory II , 379 – 389 . San Francisco , New York : McGraw-Hill . London
  • Isii , K. 1960 . The Extrema of Probability Determined by Generalized Moments (I). Bounded Random Variables . Ann. Inst. Stat. Math , 12 : 119 – 133 .
  • Jeroslow , R.G. 1981 . A Limiting Lagrangian for Infinitely Constrained Convex Optimization in R n . Journal of Optimization Theory and Applications , 33 : 479 – 495 .
  • Jeroslow , R.G. 1983 . Uniform Duality in Semi-Infinite Convex Optimization . Mathematical Programming , 27 : 144 – 154 .
  • Karlin , S. and Studden , W.J. 1966 . TCHEBYCHEFF Systems:with Applications in Analysis and Statistics , London , New York : Interscience Publishers . Sydney
  • Karney , D.F. 1981 . Duality gaps in Semi-Infinite Linear Programming-an Approximation Problem . Mathematical Programming , 20 : 129 – 143 .
  • Karney , D.F. 1985 . In a semi-infinite program only a countable subset of the constraints is essential . Journal of Approximation Theory , 44 : 69 – 72 .
  • Kortanek , K.O. 1977 . Constructing a Perfect Duality in Infinite Programming . Applied Mathematics and Optimization , 3 : 357 – 372 .
  • Rockafellar , K.T. 1970 . Convex Analysis , Princeton , , NJ : Princeton University Press .
  • Zhu , Y.J. 1966 . Generalizations of Some Fundamental Theorems on linear Inequalities . Acta Mathematica Sinica , 16

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.