tailieunhanh - Optimality criteria for sum of fractional multiobjective optimization problem with generalized invexity

The sum of a fractional program is a nonconvex optimization problem in the field of fractional programming and it is difficult to solve. The development of research is restricted to single objective sums of fractional problems only. | Turk J Math (2015) 39: 900 – 912 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Optimality criteria for sum of fractional multiobjective optimization problem with generalized invexity Deepak BHATI, Pitam SINGH∗ Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Allahabad, India • Received: Accepted/Published Online: • Printed: Abstract: The sum of a fractional program is a nonconvex optimization problem in the field of fractional programming and it is difficult to solve. The development of research is restricted to single objective sums of fractional problems only. The branch and bound methods/algorithms are developed in the literature for this problem as a single objective problem. The theoretical and algorithmic development for sums of fractional programming problems is restricted to single objective problems. In this paper, some new optimality conditions are proposed for the sum of a fractional multiobjective optimization problem with generalized invexity. The optimality conditions are obtained by using a modified objective approach and equivalency with the original problem is established. Key words: Multiobjective programming, sum of ratio, multiobjective linear fractional programming, optimality and duality, saddle point criteria 1. Introduction Optimization of the ratio of two functions is called a fractional programming (ratio optimization) problem. If collections of fractional objective functions are optimized simultaneously, then the problem is called multiobjective fractional programming. The general fractional programming is defined as: Optimize F (x) = f (x) g(x) subject to x ∈ S = {x ∈ Rn : hl (x) ≤ 0, (1) x ≥ 0, g(x) > 0, l = 1, 2, 3 . . . m}. Fractional programming is classified according to the nature of the functions involved in the ratio. If the ratio functions and constraints are linear,