Advertisement

Journal of Optimization Theory and Applications

, Volume 86, Issue 3, pp 745–752 | Cite as

Unconstrained convex programming approach to linear programming

  • Z. K. Xu
  • S. C. Fang
Technical Note

Abstract

Recently, Fang proposed approximating a linear program in the Karmarkar standard form by adding an entropic barrier function to the objective function and derived an unconstrained dual concave program. We present in this note a necessary and sufficient condition for the existence of a dual optimal solution to the perturbed problem. In addition, a sharp upper bound of error estimation in this approximation scheme is provided.

Key Words

Convex programs linear programs perturbations duality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bertsekas, D. P.,Constrained Optimization and Lagrange Multiplier Methods, Academic Press, New York, New York, 1982.Google Scholar
  2. 2.
    Mangasarian, O. L.,Least-Norm Linear Programming Solution as an Unconstrained Minimization Problem, Journal of Mathematical Analysis and Applications, Vol. 92, pp. 240–251, 1983.Google Scholar
  3. 3.
    Fang, S. C.,An Unconstrained Convex Programming View of Linear Programming, Zeitschrift für Operations Research—Methods and Models of Operations Research, Vol. 36, pp. 149–161, 1992.Google Scholar
  4. 4.
    Rajasekera, J. R., andFang, S. C.,Deriving an Unconstrained Convex Program for Linear Programming, Journal of Optimization Theory and Applications, Vol. 75, pp. 603–612, 1992.Google Scholar
  5. 5.
    Fang, S. C., andTsao, H. S. J.,Linear Programming with Entropic Perturbation, Zeitschrift für Operations Research—Methods and Models of Operations Research, Vol. 37, pp. 171–186, 1993.Google Scholar
  6. 6.
    Karmarkar, N.,A New Polynomial Time Algorithm for Linear Programming, Combinatorica, Vol. 4, pp. 373–395, 1984.Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Z. K. Xu
    • 1
  • S. C. Fang
    • 2
  1. 1.Department of MathematicsZhejiang Normal UniversityZhejiangChina
  2. 2.Graduate Program in Operations ResearchNorth Carolina State UniversityRaleigh

Personalised recommendations