Journal of the Operations Research Society of China ›› 2018, Vol. 6 ›› Issue (4): 611-626.doi: https://doi.org/10.1007/s40305-018-0206-6

Special Issue: Continuous Optimization

• Continuous Optimization • Previous Articles    

Interval-Valued Programming Problem with Infinite Constraints

Promila Kumar1 · Bharti Sharma2 · Jyoti Dagar2   

  1. 1 Department of Mathematics, Gargi College, University of Delhi, New Delhi, India
    2 University of Delhi, New Delhi, India
  • Online:2018-12-30 Published:2018-12-30
  • Supported by:

    Bharti Sharma was supported by Council of Scientific and Industrial Research, Senior Research Fellowship, India (No. 09/045(1350)/2014-EMR-1). Jyoti Dagar was supported by University Grant Commission Non-NET research fellowship, India (No. Non-NET/139/Ext-136/2014).

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Abstract:

In this paper, we explore a class of interval-valued programming problem where constraints are interval-valued and infinite. Necessary optimality conditions are derived. Notion of generalized invexity is utilized to establish sufficient optimality conditions. Further, two duals, namely Wolfe and Mond–Weir, are proposed for which duality results are proved.

Key words: LU-optimal solution ·, Interval valued ·, Semi-infinite ·, Generalized invexity ·, Duality

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