Optimality and duality in continuous-time nonlinear fractional programming

AbstractOptimality conditions via subdifferentiability and generalised Charnes-Cooper transformation are obtained for a continuous-time nonlinear fractional programming problem. Perturbation functions play a key role in the development. A dual problem is presented and certain duality results are obtained.

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Minimax fractional programming with nondiferentiable (G,β)-invexity

Filomat ◽

10.2298/fil1410027l ◽

2014 ◽

Vol 28 (10) ◽

pp. 2027-2035 ◽

Cited By ~ 1

Author(s):

Xiaoling Liu ◽

Dehui Yuan

Keyword(s):

Optimality Conditions ◽

Programming Problem ◽

Fractional Programming ◽

Dual Problem ◽

Necessary Optimality Conditions ◽

Minimax Programming ◽

Fractional Programming Problem ◽

Duality Results ◽

Locally Lipschitz ◽

Minimax Fractional Programming

In this paper, we consider the minimax fractional programming Problem (FP) in which the functions are locally Lipschitz (G,?)-invex. With the help of a useful auxiliary minimax programming problem, we obtain not only G-sufficient but also G-necessary optimality conditions theorems for the Problem (FP). With G-necessary optimality conditions and (G,?)-invexity in the hand, we further construct dual Problem (D) for the primal one (FP) and prove duality results between Problems (FP) and (D). These results extend several known results to a wider class of programs.

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Optimality and duality for a class of nondifferentiable minimax fractional programming problems

Yugoslav journal of operations research ◽

10.2298/yjor0901049b ◽

2009 ◽

Vol 19 (1) ◽

pp. 49-61

Author(s):

Antoan Bătătorescu ◽

Miruna Beldiman ◽

Iulian Antonescu ◽

Roxana Ciumara

Keyword(s):

Optimality Conditions ◽

Fractional Programming ◽

Dual Problem ◽

Sufficient Optimality Conditions ◽

Square Root ◽

Duality Results ◽

Minimax Fractional Programming ◽

Optimality And Duality ◽

Necessary And Sufficient

Necessary and sufficient optimality conditions are established for a class of nondifferentiable minimax fractional programming problems with square root terms. Subsequently, we apply the optimality conditions to formulate a parametric dual problem and we prove some duality results.

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Duality for multiobjective fractional programming problems involving d -type-I n-set functions

Yugoslav journal of operations research ◽

10.2298/yjor0901063s ◽

2009 ◽

Vol 19 (1) ◽

pp. 63-73

Author(s):

I.M. Stancu-Minasian ◽

Gheorghe Dogaru ◽

Mădălina Stancu

Keyword(s):

Programming Problem ◽

Fractional Programming ◽

Generalized Convexity ◽

Type I ◽

Multiobjective Fractional Programming ◽

Fractional Programming Problem ◽

Duality Results ◽

Set Functions ◽

Convexity Assumptions ◽

Nonlinear Fractional Programming

We establish duality results under generalized convexity assumptions for a multiobjective nonlinear fractional programming problem involving d -type-I n -set functions. Our results generalize the results obtained by Preda and Stancu-Minasian [24], [25].

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