### A disjunctive linear fractional max-min problem

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This paper presents a unified approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set $E$, a family $\mathcal{F}$ of feasible subsets of $E$ and a nonnegative real capacity ${\widehat{c}}_{e}$ for all $e\in E$. Moreover, we are given monotone increasing cost functions ${f}_{e}$ for increasing the capacity of the elements $e\in E$ as well as a budget $B$. The task is to determine new capacities ${c}_{e}\ge {\widehat{c}}_{e}$ such that the objective function given by ${max}_{F\in \mathcal{F}}{min}_{e\in F}{c}_{e}$ is maximized under the side constraint...

This paper presents a unified approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set E, a family F of feasible subsets of E and a nonnegative real capacity ĉe for all e ∈ E. Moreover, we are given monotone increasing cost functions fe for increasing the capacity of the elements e ∈ E as well as a budget B. The task is to determine new capacities ce ≥ ĉe such that the objective function given by maxF∈Fmine∈Fce...

The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow...

We analyze the convergence of the prox-regularization algorithms introduced in [1], to solve generalized fractional programs, without assuming that the optimal solutions set of the considered problem is nonempty, and since the objective functions are variable with respect to the iterations in the auxiliary problems generated by Dinkelbach-type algorithms DT1 and DT2, we consider that the regularizing parameter is also variable. On the other hand we study the convergence when the iterates are only...

We analyze the convergence of the prox-regularization algorithms introduced in [1], to solve generalized fractional programs, without assuming that the optimal solutions set of the considered problem is nonempty, and since the objective functions are variable with respect to the iterations in the auxiliary problems generated by Dinkelbach-type algorithms DT1 and DT2, we consider that the regularizing parameter is also variable. On the other hand we study the convergence when the iterates are only ηk-minimizers...

The present article explores the way $\eta $-approximated method is applied to substantiate duality results for the fractional variational problems under invexity. $\eta $-approximated dual pair is engineered and a careful study of the original dual pair has been done to establish the duality results for original problems. Moreover, an appropriate example is constructed based on which we can validate the established dual statements. The paper includes several recent results as special cases.