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Energy-efficient resource allocation in future wireless networks by sequential fractional programming

DIGITAL SIGNAL PROCESSING 2017年 60卷 324-337页

作者： Zappone, A. Jorswieck, E. A. Univ Cassino & Southern Lazio Cassino Italy Tech Univ Dresden Commun Lab Dresden Germany

This overview paper discusses the framework of sequential fractional programming for energy efficiency maximization in future 5G networks. One of the main features of future systems will be the presence of severe multi-user interference and the need of improved energy efficiency compared to present systems. However, present approaches to energy efficiency maximization, which are based on the theory of fractional programming, result in an exponential complexity in interference-limited networks. In this context, the work shows how to extend available fractional programming approaches to obtain radio resource allocations enjoying strong optimality properties, while at the same time requiring an affordable complexity to be computed. The resulting framework is termed sequential fractional programming, and several examples of its applications to leading 5G candidate technologies are discussed in detail. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Energy efficiency Resource allocation fractional programming 5G networks Massive MIMO Heterogeneous networks Multi-hop communications

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On nonlinear multiple objective fractional programming involving semilocally type-I univex functions

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OPTIMIZATION LETTERS 2009年第2期3卷 171-185页

作者： Mishra, S. K. Rautela, J. S. Govind Ballabh Pant Univ Agr & Technol Dept Math Stat & Comp Sci Coll Basic Sci & Humanities Pantnagar 263145 Uttar Pradesh India Kumaun Univ Dept Math Naini Tal 263002 India

The aim of this paper is to obtain sufficient optimality conditions for a nonlinear multiple objective fractional programming problem involving semilocally type-I univex and related functions. Furthermore, a general dual is formulated and duality results are proved under the assumptions of generalized semilocally type-I univex and related functions. Our results generalize several known results in the literature.

关键词： fractional programming Duality Sufficient optimality Convexity Type-I univexity

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Risk-based electric power system planning for climate change mitigation through multi-stage joint-probabilistic left-hand-side chance-constrained fractional programming: A Canadian case study

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RENEWABLE & SUSTAINABLE ENERGY REVIEWS 2018年第Part1期82卷 1056-1067页

作者： Wang, Lin Huang, Gordon Wang, Xiuquan Zhu, Hua Univ Regina Environm Syst Engn Program Fac Engn & Appl Sci Regina SK S4S 0A2 Canada Univ Regina Inst Energy Environm & Sustainabil Res UR BNU Regina SK S4S 0A2 Canada Beijing Normal Univ UR BNU Inst Energy Environm & Sustainabil Res Beijing 100875 Peoples R China Univ Louisiana Lafayette Sch Geosci Lafayette LA 70503 USA Saskatchewan Minist Environm Climate Change Branch Regina SK S4S 0A2 Canada

Climate change mitigation by reducing greenhouse gas emissions is one of the major challenges for existing electric power systems. This study presents a multi-stage joint-probabilistic left-hand-side chance-constrained fractional programming (MJCFP) approach to help tackle various uncertainties involved in typical electric power systems and thus facilitate risk-based management for climate change mitigation. The MJCFP approach is capable of solving ratio optimization problems associated with left-hand-side random information by integrating multi-stage programming method, joint-probabilistic chance-constrained programming, fractional programming into a general framework. It can balance dual-objectives of two aspects reflecting system optimal ratio and analyze many of possible scenarios due to various end-user demand situations during different periods. The MJCFP approach is implemented and applied to the provincial electric power system of Saskatchewan, Canada to demonstrate its effectiveness in dealing with the tradeoff between economic development and climate change mitigation. Potential solutions under various risk levels are obtained to help identify appropriate strategies to meet different power demands and emission targets to the maximum extent. The results indicate that the MJCFP approach is effective for regional electric power system planning in support of long-term climate change mitigation policies;it can also generate more alternatives through risk-based management, which allows in-depth analysis of the interrelationships among system efficiency, system profit and system-failure risk.

关键词： Electric power system planning Climate change mitigation Risk-based management Multi-stage Joint-probabilistic programming fractional programming

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A neurodynamic optimization approach to supervised feature selection via fractional programming

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NEURAL NETWORKS 2021年 136卷 194-206页

作者： Wang, Yadi Li, Xiaoping Wang, Jun Henan Univ Henan Key Lab Big Data Anal & Proc Kaifeng 475004 Peoples R China Henan Univ Inst Data & Knowledge Engn Sch Comp & Informat Engn Kaifeng 475004 Peoples R China Southeast Univ Sch Comp Sci & Engn Nanjing 211189 Peoples R China Southeast Univ Minist Educ Key Lab Comp Network & Informat Integrat Nanjing 211189 Peoples R China City Univ Hong Kong Dept Comp Sci Kowloon Hong Kong Peoples R China City Univ Hong Kong Sch Data Sci Kowloon Hong Kong Peoples R China

Feature selection is an important issue in machine learning and data mining. Most existing feature selection methods are greedy in nature thus are prone to sub-optimality. Though some global feature selection methods based on unsupervised redundancy minimization can potentiate clustering performance improvements, their efficacy for classification may be limited. In this paper, a neurodynamics-based holistic feature selection approach is proposed via feature redundancy minimization and relevance maximization. An information-theoretic similarity coefficient matrix is defined based on multi-information and entropy to measure feature redundancy with respect to class labels. Supervised feature selection is formulated as a fractional programming problem based on the similarity coefficients. A neurodynamic approach based on two one-layer recurrent neural networks is developed for solving the formulated feature selection problem. Experimental results with eight benchmark datasets are discussed to demonstrate the global convergence of the neural networks and superiority of the proposed neurodynamic approach to several existing feature selection methods in terms of classification accuracy, precision, recall, and F-measure. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Feature selection Information-theoretic measures fractional programming Neurodynamic optimization

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On the posynomial fractional programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2002年第1期143卷 42-52页

作者： Chang, CT Natl Changhua Univ Educ Dept Informat Management Changhua 50058 Taiwan

The posynomial fractional programming (PFP) problem arises from the summation minimization of several quotient terms, which are composed of posynomial terms appearing in the objective function subject to given posynomial constraints. This paper proposes an approximate approach to solving a PFP problem. A linear programming relaxation is derived for the problem based on piecewise linearization techniques, which first convert a posynomial term into the sum of absolute terms;these absolute terms are then linearized by some linearization techniques. The proposed approach could reach a solution as close as possible to a global optimum. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： fractional programming goal programming piecewise linear function posynomial

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A fractional programming approach for retail category price optimization

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JOURNAL OF GLOBAL OPTIMIZATION 2010年第2期48卷 263-277页

作者： Subramanian, Shivaram Sherali, Hanif D. Retail Analyt Fdn Cambridge MA 02141 USA Virginia Polytech Inst & State Univ Grado Dept Ind & Syst Engn 0118 Blacksburg VA 24061 USA

We present a new mixed-integer programming (MIP) approach to study certain retail category pricing problems that arise in practice. The motivation for this research arises from the need to design innovative analytic retail optimization techniques at Oracle Corporation to not only predict the empirical effect of price changes on the overall sales and revenue of a category, but also to prescribe optimal dynamic pricing recommendations across a category or demand group. A multinomial logit nonlinear optimization model is developed, which is recast as a discrete, nonlinear fractional program (DNFP). The DNFP model employs a bi-level, predictive modeling framework to manage the empirical effects of price elasticity and competition on sales and revenue, and to maximize the gross-margin of the demand group, while satisfying certain practical side-constraints. This model is then transformed by using the Reformulation-Linearization Technique in tandem with a sequential bound-tightening scheme to recover an MIP formulation having a relatively tight underlying linear programming relaxation, which can be effectively solved by any commercial optimization software package. We present sample computational results using randomly generated instances of DNFP having different constraint settings and price range restrictions that are representative of common business requirements, and analyze the empirical effects of certain key modeling parameters. Our results indicate that the proposed retail price optimization methodology can be effectively deployed within practical retail category management applications for solving DNFP instances that typically occur in practice.

关键词： Multinomial logit model Retail category pricing Embedded demand model Reformulation-Linearization Technique (RLT) Mixed-integer programming fractional programming

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A simplex algorithm for piecewise-linear fractional programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第2期178卷 343-358页

作者： Pandey, Pooja Punnen, Abraham P. Simon Fraser Univ Dept Math Surrey BC V3T 5X3 Canada Univ New Brunswick Dept Math Sci St John NB E2L 4L5 Canada

Generalizations of the well-known simplex method for linear programming are available to solve the piecewise linear programming problem and the linear fractional programming problem. In this paper we consider a further generalization of the simplex method to solve piecewise linear fractional programming problems unifying the simplex method for linear programs, piecewise linear programs, and the linear fractional programs. Computational results are presented to obtain further insights into the behavior of the algorithm on random test problems. (c) 2006 Elsevier B.V. All rights reserved.

关键词： fractional programming simplex method piecewise linear functions

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Identification of redundant objective functions in multi-objective stochastic fractional programming problems

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2006年第2期23卷 155-170页

作者： Charles, V. Dutta, D. SDM Inst Management Dev Dept Quantitat Methods & Operat Res Mysore 570011 Karnataka India Natl Inst Technol Dept Math & Humanities Warangal 506004 Andhra Pradesh India

Redundancy in constraints and variables axe usually studied in linear, integer and non-linear programming problems. However, main emphasis has so far been given only to linear programming problems. In this paper, an algorithm that identifies redundant objective functions in multi-objective stochastic fractional programming problems is provided. A solution procedure is also illustrated. This reduces the number of objective functions in cases where redundant objective functions exist.

关键词： stochastic programming fractional programming multi-objective programming redundancy

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Robust Precoding Design for Massive MIMO: An Efficient fractional programming-Based Approach

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IEEE COMMUNICATIONS LETTERS 2022年第12期26卷 2999-3003页

作者： Lin, Tian Zhu, Yu Fudan Univ Sch Informat Sci & Technol Key Lab Informat Sci Electromagnet Waves MoE Shanghai Peoples R China

Due to the effects of channel aging and estimation errors, perfect instantaneous channel state information (CSI) is unavailable at a base station. Therefore, robust precoding under imperfect CSI is important for practical communications. In this letter, we propose an efficient robust precoding design for massive multiple-input multiple-output systems. Based on the fractional programming technique, we transform the original non-convex optimization problem into a much more tractable equivalent problem, which can be iteratively solved by alternating optimization. Since all variables are updated via closed-form optimal solutions, the proposed algorithm is guaranteed to converge to a locally optimal point. Simulation results reveal that the proposed robust precoding algorithm has fast convergence and achieves significant performance improvement over the conventional ones.

关键词： Robust precoding fractional programming alternating minimization massive MIMO

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Deep Unfolded fractional programming-Based Beamforming in RIS-Aided MISO Systems

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IEEE WIRELESS COMMUNICATIONS LETTERS 2024年第2期13卷 515-519页

作者： Xia, Wenchao Jiang, Yajing Zhao, Ben Zhao, Haitao Zhu, Hongbo Nanjing Univ Posts & Telecommun Jiangsu Key Lab Wireless Commun Nanjing 210003 Peoples R China

Reconfigurable intelligent surface (RIS) is a promising solution to programmable wireless channels. However, most existing RIS phase optimization algorithms, relying on iterative processes, suffer from high latency and poor scalability. To address this issue, we propose a low-complexity scheme based on deep unfolding. Specifically, we consider a downlink MISO system aided by a RIS and aim to maximize users' weighted sumrate (WSR). We employ Lagrangian dual transformation to decouple the original non-convex problem into two sub-problems: transmit beamforming optimization and phase shift design. Then, we introduce a block coordinate descent (BCD) method, which still relies on iterative updates and includes complex operations such as matrix inversion, leading to high computational complexity and latency. To achieve fast solutions, we further propose to unfold the BCD method's iterative process into layers of an interpretable neural network (NN) with a few trainable parameters. The NN is trained offline and deployed online for realtime solutions. Finally, numerical results validate the performance of the proposed scheme in terms of comparable WSR and reduced computational complexity.

关键词： RIS beamforming fractional programming deep unfolding

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