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STABILITY AND MARGINAL VALUES OF A convex programming problem

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SIBERIAN MATHEMATICAL JOURNAL 1978年第3期19卷 343-352页

作者： ASTAFEV, NN

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The complexity of a special convex programming problem connected with nonlinear optimization

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Optimization 1993年第3期27卷 229-233页

作者： Nenakhov, E.I. Primary, M.E. Institute of Cybernetics Prosp. Akademika Glushkova 40 252207 Kiev Ukrain Ukraine Temple University Philadelphia United States

In this paper, an algorithm for solving a special convex programming problem (CPP) is proposed. We consider a CPP with an objective function whose values and gradients are not easy to calculate. Algorithm for infinite... 详细信息

关键词： circumscribed and inscribed ellipsoid methods computational cost convex programming problem

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On a convex programming problem of Rozanov

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Applied Mathematics and Optimization 1974年第2期1卷 189-192页

作者： Dantzig, George B. IIASA and Department of Operations Research Stanford University Stanford Calif. United States

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On a Novel Solution Methodology for Intuitionistic Fuzzy Quadratic programming problems with Application in Textile Industry

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2025年 1-12页

作者： Kaur, Shubhpreet Mahajan, Sumati Punjab Engn Coll Dept Math Chandigarh India

This paper deals with a class of quadratic programming problems having intuitionistic fuzzy parameters and bounded constraints. Such problems are designed to handle uncertain parameters in quadratic programming and provide a better representation of many real-life situations. This study presents the utilization of (alpha,u)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha ,u)$$\end{document} and (beta,v)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\beta ,v)$$\end{document} cuts and a new solution methodology is suggested to obtain the lower and upper bounds of the objective function in the problem. Using the bounds obtained, we construct the membership and non-membership functions of the optimal values graphically. By expressing the optimal value through membership and non-membership functions instead of a crisp value, this method offers a more detailed and nuanced view of the data, which can lead to better-informed decision-making. Moreover, it has been found that the proposed method yields more efficient solutions, requiring less computational work. We illustrate the solution procedure of the proposed technique by applying it to a real-life problem in textile industry.

关键词： Quadratic programming Intuitionistic fuzzy theory Duality convex programming problem Bounded constraints

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Duality Theorems for a Class of Nonconvex programming problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1973年第3期11卷 305-308页

作者： Rani, O. Kaul, R. N. Univ Delhi Fac Math Delhi 7 India

The object of this paper is to prove duality theorems for quasiconvex programming problems. The principal tool used is the transformation introduced by Manas for reducing a nonconvex programming problem to a convex programming problem. Duality in the case of linear, quadratic, and linear-fractional programming is a particular case of this general case.

关键词： programming problem convex programming Duality Theorem convex programming problem Principal Tool

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A method of lexicogeaphic search for solutions of discrete convex programming problems

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Ukrainian Mathematical Journal 1974年第2期26卷 226-229页

作者： Chervak, Yu.Yu. Uzhgorod State University

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Task offloading, load balancing, and resource allocation in MEC networks

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IET COMMUNICATIONS 2020年第9期14卷 1451-1458页

作者： Li, S. L. Du, J. B. Zhai, D. S. Chu, X. L. Yu, F. R. Tianyuan Ruixin Commun Technol Co Ltd Xian 710071 Peoples R China Xian Univ Posts & Telecommun Xian 710121 Peoples R China Northwestern Polytech Univ Sch Elect & Informat Xian 710071 Peoples R China Univ Sheffield Dept Elect & Elect Engn Mappin St Sheffield S1 3JD S Yorkshire England Carleton Univ Dept Syst & Comp Engn Ottawa ON Canada

To prolong the time duration of smart mobile devices (SMDs) or enable low-latency tasks, mobile edge computing (MEC) has emerged as a promising paradigm by offloading tasks to nearby MEC servers (MECSs). In this study the authors propose an optimisation problem to minimise the weighted sum of the total delay and energy consumption of all SMDs in a multi-MECS-multi-SMD network via multi-dimensional optimisation on offloading strategy making, load balancing, computation resource allocation and transmit power control. Since the problem is NP-hard, the authors decompose it into three subproblems to solve. First, they propose a low complexity heuristic algorithm to obtain the offloading strategies while guaranteeing load balancing between the multiple MECSs. Then they solve computation resource allocation subproblem using Lagrange dual decomposition. Finally, employing fractional programming, the authors transform the transmit power control subproblem into a convex programming problem where the closed-form solution is obtained. The proposed simulation results verify the convergence of the proposed iterative algorithms, and demonstrate that the proposed joint optimisation could achieve good performance in both delay and energy reduction.

关键词： resource allocation convex programming power control computational complexity iterative methods mobile computing task offloading load balancing MEC networks smart mobile devices SMDs low-latency tasks mobile edge computing nearby MEC servers optimisation problem weighted sum energy consumption multiMECS-multiSMD network multidimensional optimisation low complexity heuristic algorithm offloading strategies computation resource allocation subproblem transmit power control subproblem convex programming problem joint optimisation energy reduction

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Queue-aware energy minimisation through sparse beamforming in C-RAN

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IET COMMUNICATIONS 2018年第5期12卷 559-565页

作者： Ouyang, Weiping Teng, Yinglei Song, Mei Zhao, Wanxin Beijing Univ Posts & Telecommun Beijing Key Lab Space Ground Interconnect & Conve Beijing Peoples R China

This paper considers the queue-aware optimal energy minimisation sparse beamforming design (QESB) in a downlink cloud radio access network (C-RAN) system where multi-RRH communicates with multi-user through a central computing cloud via digital front-haul links. The problem is formulated as the joint optimisation problem of the transmission energy consumption, system queue length and front-haul cost with sparse beamforming design. As we know, the beamforming design adaptive to both QSI and CSI is challenging because of the high complexity. Apart from previous works that take queue length as constraints, in this paper we directly minimise the queue length state involved joint optimisation problem with SINR constraints. A smooth function is proposed to approximate the l(0)-norm function which is discrete and non-convex. To overcome the challenge due to the non-convexity of the optimisation problem, the semidefinite relaxation (SDR) technology is utilised to convert the primitive problem into the difference of convex (DC) programming problem, and convex and concave procedure (CCP) algorithm is used to induce the sparsity of the beamforming control. The simulation results show that the scheme proposed by this paper can obtain a good tradeoff between system energy consumption, queue length and front-haul cost with SINR constraints in C-RAN system.

关键词： queueing theory telecommunication power management energy consumption array signal processing radio access networks telecommunication computing minimisation multi-access systems radio links wireless channels radiofrequency interference approximation theory concave programming relaxation theory convex programming cloud computing C-RAN queue-aware optimal energy minimisation sparse beamforming design downlink cloud radio access network system multiremote radio head central computing cloud digital front-haul links total network cost minimisation joint optimisation problem transmission energy consumption system queue length front-haul cost queue state information channel state information queue length state minimisation signal-to-interference-and-noise-ratio constraints SINR constraints l(0)-norm function approximation optimisation problem nonconvexity semidefinite relaxation technology convex programming problem concave procedure algorithm system energy consumption

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convex sub-differential sum rule via convex semi-closed functions with applications in convex programming

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APPLIED MATHEMATICS LETTERS 2011年第8期24卷 1289-1294页

作者： Alimohammady, Mohsen Cho, Yeol Je Dadashi, Vahid Roohi, Mehdi Gyeongsang Natl Univ Dept Math Educ Chinju 660701 South Korea Gyeongsang Natl Univ RINS Chinju 660701 South Korea Univ Mazandaran Fac Basic Sci Dept Math Babol Sar Iran Islamic Azad Univ Sari Branch Sari Iran

This paper deals with some basic notions of convex analysis and convex optimization via convex semi-closed functions. A decoupling-type result and also a sandwich theorem are proved. As a consequence of the sandwich theorem, we get a convex sub-differential sum rule and two separation results. Finally, the derived convex sub-differential sum rule is applied to solving the convex programming problem. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Decoupling lemma Sandwich theorem convex sub-differential sum rule convex programming problem convex semi-closed function

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Numerical Algorithm for Minimizing a convex Function on the Intersection of a Smooth Surface and a convex Compact Set

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2019年第7期59卷 1098-1104页

作者： Chernyaev, Yu. A. Kazan Natl Res Tech Univ Kazan 420111 Tatarstan Russia

A numerical algorithm for minimizing a convex function on the set-theoretic intersection of a smooth surface and a convex compact set in finite-dimensional Euclidean space is proposed. The idea behind the algorithm is to reduce the original problem to a sequence of convex programming problems. Necessary extremum conditions are studied, and the convergence of the algorithm is analyzed.

关键词： smooth surface convex compact set convex programming problem projection onto a nonconvex set necessary conditions for a local minimum convergence of an algorithm

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