In this paper, the concept of second order generalized alpha-type I univexity is introduced. Based on the new definitions, we derive weak, strong and strict converse duality results for two second order duals of a min...
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In this paper, the concept of second order generalized alpha-type I univexity is introduced. Based on the new definitions, we derive weak, strong and strict converse duality results for two second order duals of a minmax fractional programming problem.
Given a self-concordant barrier function for a convex set J, we determine a self-concordant barrier function for the conic hull (J) over tilde of J. As our main result, we derive an ''optimal'' barrier...
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Given a self-concordant barrier function for a convex set J, we determine a self-concordant barrier function for the conic hull (J) over tilde of J. As our main result, we derive an ''optimal'' barrier for (J) over tilde based on the barrier function for J. Important applications of this result include the conic reformulation of a convex problem, and the solution of fractional programs by interior-point methods. The problem of minimizing a convex-concave fraction over some convex set can be solved by applying an interior-point method directly to the original nonconvex problem, or by applying an interior-point method to an equivalent convex reformulation of the original problem. Our main result allows to analyze the second approach showing that the rate of convergence is of the same order in both cases.
Parametric analysis in linear fractional programming is significantly more complicated in case of an unbounded feasible region. We propose procedures which are based on a modified version of Martos' algorithm or a...
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Parametric analysis in linear fractional programming is significantly more complicated in case of an unbounded feasible region. We propose procedures which are based on a modified version of Martos' algorithm or a modification of Charnes-Cooper's algorithm, applying each to problems where either the objective function or the right-hand side is parametrized.
In the real world, some problems can be modelled by linear fractional programming with uncertain data as an interval. Therefore, some methods have been proposed for solving interval linear fractional programming (ILFP...
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In the real world, some problems can be modelled by linear fractional programming with uncertain data as an interval. Therefore, some methods have been proposed for solving interval linear fractional programming (ILFP) problems. In this research, we propose two new methods for solving ILFP problems. In each method, we use two sub-models to obtain the range of the objective function. In the first method, we introduce two sub-models in which the objective functions are non-linear and the two sub-models have the largest and smallest feasible regions;therefore, the optimal value range of the objective function has been obtained. In the second method, two sub-models have been proposed in which the objective functions are linear and the optimal value of the objective function lies in the range obtained from the first method. We use our approaches to maximize the ratio of the facilities optimal allocation to the non-return fund in a bank.
Strong Lagrangian duality holds for the quadratic programming with a two-sided quadratic constraint. In this paper, we show that the two-sided quadratic constrained quadratic fractional programming, if well scaled, al...
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Strong Lagrangian duality holds for the quadratic programming with a two-sided quadratic constraint. In this paper, we show that the two-sided quadratic constrained quadratic fractional programming, if well scaled, also has zero Lagrangian duality gap. However, this is not always true without scaling. For a special case, the identical regularized total least squares problem, we establish the necessary and sufficient condition under which the Lagrangian duality gap is positive.
With the exponential growth of wireless users and their traffic demands, it is greatly increasing for the demand of the scarce spectrum resources in the communication networks. In order to enhance the performance of t...
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With the exponential growth of wireless users and their traffic demands, it is greatly increasing for the demand of the scarce spectrum resources in the communication networks. In order to enhance the performance of the wireless networks such as end-to-end delay, energy efficiency and throughput, the device-to-device (D2D) communication has been attracted more attention because the two devices in close proximity can communicate directly without traversing the central base station. However, most of users are very sensitive to the battery. Therefore, we aim to maximize the energy efficiency of wireless communication system in the context of underlaying device-to-device communication in this paper, We focus on the formulated power control and resource allocation problem which is non-convex in the fractional form. We reduce it from the power allocation of all users to the joint power and subchannel allocation of D2D users. Then, we tackle it by an iterative approximation algorithm leveraging to the properties of fractional programming. There are two studied cases for the subchannel allocation. One can be solved by the penalty function approach, and the other can be solved by the dual decomposition as well as sub-gradient method. Accordingly, we propose a dual-based algorithm in general. Numerical simulations demonstrate that the proposed algorithms outperform the conventional algorithm in terms of the energy efficiency.
Considering a constrained fractional programming problem, within the present paper we present some necessary and sufficient conditions, which ensure that the optimal objective value of the considered problem is greate...
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Considering a constrained fractional programming problem, within the present paper we present some necessary and sufficient conditions, which ensure that the optimal objective value of the considered problem is greater than or equal to a given real constant. The desired results are obtained using the Fenchel-Lagrange duality approach applied to an optimization problem with convex or difference of convex (DC) objective functions and finitely many convex constraints. These are obtained from the initial fractional programming problem using an idea due to Dinkelbach. We also show that our general results encompass as special cases some recently obtained Farkas-type results. (c) 2006 Elsevier Ltd. All rights reserved.
作者：
Tan, QianZhang, TianyuanChina Agr Univ
Coll Water Resources & Civil Engn 17 Qinghua East Rd Beijing 100083 Peoples R China Sichuan Univ
State Key Lab Hydraul & Mt River Engn Chengdu 610065 Sichuan Peoples R China
Water-use efficiency and uncertainty treatment are foci in the modeling of agricultural water management systems. To address these challenging issues, a robust fractional programming (RFP) method that coupled fraction...
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Water-use efficiency and uncertainty treatment are foci in the modeling of agricultural water management systems. To address these challenging issues, a robust fractional programming (RFP) method that coupled fractional programming with robust optimization was developed in this study to improve agricultural water-use efficiency under uncertainty. RFP improved upon the fractional programming by being able to tackle highly uncertain information without known distributions. It also extended the capability of the robust optimization method in addressing ratio optimal problems. To demonstrate its effectiveness and applicability, RFP was applied to a long-term agricultural water resources management problem in arid north-west China, where water scarcity and low water-use efficiency hindered local development. It generated benefit- and risk-explicit plans for crop pattern adjustments. Vegetables were recommended as the preferred crop. A number of scenarios combining different fluctuation and protection levels were analyzed and interpreted with practical implications. It was observed that higher water-use efficiency could be achieved through reducing parametric uncertainty and risk-aversion levels. Simulation experiments validated that the benefits claimed by the RFP model were sufficiently conservative and could be reliably achieved. The comparisons of RFP results against the baseline operations and those from two other alternatives demonstrated that, RFP could result in higher resource-use efficiency and controllable system-violation risks. The developed approach is also applicable to other optimization problems aiming at enhancing resource-use efficiency under uncertainty.
With the increasing prominence of the global climate change, China's carbon intensity reduction has attracted considerable worldwide concern. This study proposes a fractional programming model to evaluate Chinese ...
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With the increasing prominence of the global climate change, China's carbon intensity reduction has attracted considerable worldwide concern. This study proposes a fractional programming model to evaluate Chinese provincial carbon intensity reduction potential based on data envelopment analysis theory, which is superior to the common directional distance function approach in identifying global optimal solutions and improving the robustness of the estimation. To avoid the biased estimation, a meta-frontier is constructed according to the convergence of provincial carbon intensity, and then the overall potential is decomposed from the perspective of ineffective management, spatial technological gap and intertemporal technological gap. The results show that the carbon intensity of 30 Chinese provinces cannot converge to a common equilibrium and that 5 clubs that converge to different equilibria are clustered. Moreover, different clubs have diversified potentials for carbon intensity reduction, and spatial technological gaps contribute the most potential for clubs 3, 4 and 5. Even worse, the spatial technological gaps have not been significantly narrowed over time. This study provides not only a theoretical tool to investigate carbon intensity reduction potentials but also empirical evidence to guide China's carbon intensity reduction. (C) 2020 Elsevier B.V. All rights reserved.
For a kind of fractional programming problem that the objective functions are the ratio of two DC (difference of convex) functions with finitely many convex constraints, in this paper, its dual problems are constructe...
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For a kind of fractional programming problem that the objective functions are the ratio of two DC (difference of convex) functions with finitely many convex constraints, in this paper, its dual problems are constructed, weak and strong duality assertions are given, and some sufficient and necessary optimality conditions which characterize their optimal Solutions are obtained. Some recently obtained Farkas-type results for fractional programming problems that the objective functions are the ratio of a convex function to a concave function with finitely many convex constraints are the special cases of the general results of this paper. (C) 2008 Elsevier Ltd. All rights reserved.
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