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<p>There are several classes of decision-making problems that explicitly or implicitly prompt fractional programming problems. Portfolio selection problems, agricultural planning, information transfer, numerical analysis of stochastic processes, and resource allocation problems are just a few examples. The huge number of applications of minimax fractional programming problems inspired us to work on this topic. This paper is concerned with a nondifferentiable minimax fractional programming problem. We study a parametric dual model, corresponding to the primal problem, and derive the sufficient optimality condition for an optimal solution to the considered problem. Further, we obtain the various duality results under (<italic>p, r</italic>)-<italic>ρ</italic>-(<italic>η</italic>, <italic>θ</italic>)-invexity assumptions. Also, we identify a function lying exclusively in the class of (−1, 1)-<italic>ρ</italic>-(<italic>η</italic>, <italic>θ</italic>)-invex functions but not in the class of (1, −1)-invex functions and convex function already existing in the literature. We have given a non-trivial model of nondifferentiable minimax problem and obtained its optimal solution using optimality results derived in this paper.</p>
</abstract>

There are several classes of decision-making problems that explicitly or implicitly prompt fractional programming problems. Portfolio selection problems, agricultural planning, information transfer, numerical analysis of stochastic processes, and resource allocation problems are just a few examples. The huge number of applications of minimax fractional programming problems inspired us to work on this topic. This paper is concerned with a nondifferentiable minimax fractional programming problem. We study a parametric dual model, corresponding to the primal problem, and derive the sufficient optimality condition for an optimal solution to the considered problem. Further, we obtain the various duality results under (p, r)-ρ-(η, θ)-invexity assumptions. Also, we identify a function lying exclusively in the class of (−1, 1)-ρ-(η, θ)-invex functions but not in the class of (1, −1)-invex functions and convex function already existing in the literature. We have given a non-trivial model of nondifferentiable minimax problem and obtained its optimal solution using optimality results derived in this paper.

Sufficient optimality condition and duality of nondifferentiable minimax ratio constraint problems under (<italic>p</italic>, <italic>r</italic>)-<italic>ρ</italic>-(<italic>η</italic>, <italic>θ</italic>)-invexity

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Sufficient optimality condition and duality of nondifferentiable minimax ratio constraint problems under (, )--(, )-invexity

There are several classes of decision-making problems that explicitly or implicitly prompt fractional programming problems. Portfolio selection problems,...

Sufficient optimality condition and duality of nondifferentiable minimax ratio constraint problems under (p, r)-ρ-(η, θ)-invexity

Published Online: Aug 12, 2022

Page range: 71 - 89

Received: Jul 01, 2021

Accepted: Jan 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0005

Keywords
minimax fractional programming, optimality conditions, duality, generalized invexity

© 2022 Navdeep Kailey et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Sufficient optimality condition and duality of nondifferentiable minimax ratio constraint problems under (p, r)-ρ-(η, θ)-invexity

Published Online: Aug 12, 2022

Page range: 71 - 89

Received: Jul 01, 2021

Accepted: Jan 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0005

Keywordsminimax fractional programming, optimality conditions, duality, generalized invexity

© 2022 Navdeep Kailey et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
minimax fractional programming, optimality conditions, duality, generalized invexity