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Optimality conditions and duality in subdifferentiable multiobjective fractional programming

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Abstract

Fritz John and Kuhn-Tucker necessary and sufficient conditions for a Pareto optimum of a subdifferentiable multiobjective fractional programming problem are derived without recourse to an equivalent convex program or parametric transformation. A dual problem is introduced and, under convexity assumptions, duality theorems are proved. Furthermore, a Lagrange multiplier theorem is established, a vector-valued ratio-type Lagrangian is introduced, and vector-valued saddle-point results are presented.

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Authors and Affiliations

  1. Department of Actuarial and Management Sciences, University of Manitoba, Winnipeg, Manitoba, Canada

    C. R. Bector (Professor)

  2. Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi, India

    S. Chandra (Professor)

  3. Department of Mathematics, Regional Engineering College, Srinagar, Jammu and Kashmir, India

    I. Husain (Lecturer)

Authors
  1. C. R. Bector
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  2. S. Chandra
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  3. I. Husain
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Additional information

Communicated by P. L. Yu

The authors are thankful to the referees and Professor P. L. Yu for their many useful comments and suggestions which have improved the presentation of the paper.

The first author is thankful to the Natural Science and Engineering Research Council of Canada for financial support through Grant No. A-5319. The authors are also thankful to the Dean's Office, Faculty of Management, University of Manitoba, for the financial support provided for the third author's visit to the Faculty.

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Bector, C.R., Chandra, S. & Husain, I. Optimality conditions and duality in subdifferentiable multiobjective fractional programming. J Optim Theory Appl 79, 105–125 (1993). https://doi.org/10.1007/BF00941889

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