نامساوي هاي ماتريسي نامنفي و كاربرد آن ها در بهينه سازي نامحدب كنترل توان

چكيده انگليسي :

Nonnegative matrix inequalities and their application to nonconvex power control optimization Narges Hosseinzadeh n hosseinzadeh@math iut ac ir September 2016 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Mohammad Taghi Jahandideh jahandid@cc iut ac irAdvisor Dr Foroogh Sadat Tabataba fstabataba@cc iut ac ir2011 MSC 15A42 15A48 47N10 49K35 65K05 94A40Keywords nonconvex optimization convex relaxation maximization of convex functions nonnegative matrixtheory spectral radii of irreducible nonnegative matrices wireless networksAbstract Maximizing the sum rates in a multiuser Gaussian channel by power control is a nonconvex NP hard problemthat findes engineering application in code division multiple access CDMA wireless communication network We study the problem of total data throughput maximization using power control in a CDMA network whereinterference is a major source of performance impairment Due to the broadcast nature of the wireless medium the data rates in a wireless network are affected by interference when all the users transmit simultaneously overthe same frequency band using CDMA Power control is used to mitigate the effect of multiuser interference onperformance and maximize the total data rates of all the users The CDMA wireless network can be modeledby an information theoretic interference channel that treats multiuser interference as additive Gaussian noise Awidely studied problem is to find the optimal power allocation that maximizes the sum rates over this multiuserGuassian channel and this requires solving a nonconvex problem This nonconvex problem also findes appli cations in the throughput maximization for digital subscriber line DSL wireline systems The complexity ofan exhaustive search is prohibitively expensive since this optimization problem is NP hard and may even behard to approximate Chiang and Tan formulated the problem as a signomial program and used a successiveconvex approximation method on geometric programming An often used technique to tackle nonconvexity isthe standard Lagrange dual relaxation of the problem in the power domain However the shortcoming of thisapproach is that there can exist a positive duality gap between the global optimal primal and optimal dual valueof the main problem Also finding an optimal primal solution given an optimal dual solution or finding an op timal dual solution given an optimal primal solution is in general difficult We adopt a reformulation relaxationapproach to tackle with the nonconvex power control optimization problem Our reformulation possesses cer tain desirable properties which enable the application of nonnegative matrix theory especially Friedland Karlininequalities to find the global optimal solution and motivate efficient relaxation techniques In particular weutilize the problem structure to develope suitablefast computational procedures for solving and computing usefulbounds to the sum rate mximization problem Furthermore analytical solution to both the sum rate maximiza tion problem and its relaxed problem can also be characterized by the spectra of specially crafted nonnegativematrices So in this thesis we extend and apply several fundamental nonnegative matrix inequalties initiated byFriedland and Karlin in a 1975 paper to solve this nonconvex power control optimization problem Leveragingtools such as the Perron Frobenius theorem in nonnegative matrix theory we 1 show that this problem in thepower domain can be reformulated as an equivalent convex maximization problem over a closed unboundedconvex set in the logarithmic signal to interference noise ratio domain 2 propose two relaxation techniquesthat utilize the reformulation problem structure and convexification by Lagrange dual relaxation to compute pro gressively tight bounds and 3 propose a global optimization algorithm with suboptimality to compute theoptimal power control allocation A byproduct of

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نامساوي هاي ماتريسي نامنفي و كاربرد آن ها در بهينه سازي نامحدب كنترل توان

آزادسازي محدب , بيشينه سازي توابع محدب , نظريه ماتريس هاي نامنفي , شعاع طيفي ماتريس هاي نامنفي تحويل ناپذير , شبكه هاي بي سيم