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An unconstrained convex programming view of linear programming

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Abstract

The major interest of this paper is to show that, at least in theory, a pair of primal and dual “ɛ-optimal solutions” to a general linear program in Karmarkar's standard form can be obtained by solving an unconstrained convex program. Hence unconstrained convex optimization methods are suggested to be carefully reviewed for this purpose.

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References

  1. Dantzig GB (1963) Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey

    Google Scholar 

  2. Dennis J (1983) Numerical Methods for Unconstrained Optimizations and Nonlinear Equations. Prentice Hall, Englewood Cliffs, NJ

    Google Scholar 

  3. Erlander S (1981) Entropy in Linear Programs. Math Prog 21:137–151

    Google Scholar 

  4. Eriksson J (1981) Algorithms for Entropy and Mathematical Programming. PhD Thesis, Linköping University, Linköping, Sweden

    Google Scholar 

  5. Eriksson JR (1985) An Iterative Primal-Dual Algorithm for Linear Programming. Report LitH-MAT-R-1985-10. Department of Mathematics, Linköping University, Sweden

    Google Scholar 

  6. Fang SC, Rajasekera JR (1989) Quadratically Constrained Minimum Cross-Entropy Analysis. Math Prog 44:85–96

    Google Scholar 

  7. Fang SC (1990) A New Unconstrained Convex Programming Approach to Linear Programming. OR Report No 243. North Carolina State University, Raleigh, NC (February, 1990)

    Google Scholar 

  8. Fiacco AV, McCormick GP (1968) Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York

    Google Scholar 

  9. Goldfarb D, Todd MJ (1988) Linear Programming. Cornell University, School of OR and IE, Technical Report No 777, February (revised in November)

  10. Giasu S (1977) Information with Applications. McGraw-Hill, New Jersey

    Google Scholar 

  11. Gill PE, Murray W, Saunders M, Tomlin TA, Wright MH (1986) On Projected Newton Barriers for Linear Programming and An Equivalence to Karmarkar's Projective Method. Math Prog 36:183–209

    Google Scholar 

  12. Karmarkar N (1984) A New Polynomial Time Algorithm for Linear Programming. Combinatorica 4:373–395

    Google Scholar 

  13. Peterson EL (1970) Symmetric Duality for Generalized Unconstrained Geometric Programming. SIAM J Appl Math 19:487

    Google Scholar 

  14. Peterson EL (1976) Geometrical Programming. SIAM Rev 19:1

    Google Scholar 

  15. Rockafellar RT (1970) Convex Analysis. Princeton University Press, Princeton, NJ

    Google Scholar 

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Authors and Affiliations

  1. Graduate Program in Operations Research & Department of Industrial Engineering, North Carolina State University, P.O.Box 7913, 27695, Raleigh, NC

    S. -C. Fang

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  1. S. -C. Fang
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Fang, S.C. An unconstrained convex programming view of linear programming. ZOR - Methods and Models of Operations Research 36, 149–161 (1992). https://doi.org/10.1007/BF01417214

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  • DOI: https://doi.org/10.1007/BF01417214

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