Continuous-time multiobjective fractional programming

Abstract

Both parametric and semiparametric necessary and sufficient proper efficiency principles are established for a class of continuous-time multiobjective fractional programming problems. Based on the forms and contents of these proper efficiency results, two parametric and four semiparametric duality models are constructed and, in each case, weak and strong duality theorems are proved. These proper efficiency and duality results contain, as special cases, similar results for continuous-time programming problems with multiple nonfractional, single fractional, and conventional objective functions. These results improve and generalize a number of existing results in the area of continuous-time programming and, moreover, provide continuous-time analogues of various kindred results previously obtained for certain classes of finitedimensional nonlinear programming problems.

Keywords:

• Continuous-time Programming
• Multiple Fractional Objective Functions
• Proper Efficiency Conditions
• Dual Problems
• Duality Theorems