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Visualizing network communities with a semi-definite programming method

INFORMATION SCIENCES 2015年 321卷 1-13页

作者： Li, Wenye School of Public Administration Macao Polytechnic Institute Rua de Luís Gonzaga Gomes Macao

The existence of community structures is commonly believed in complex networked systems and has gained significant research attention in recent years. The automatic detection of network communities poses a non-trivial challenge due to the inherent computational requirements. In this paper, we investigate the problem from a different perspective and propose a novel model to visualize networks with the objective of exposing their community structures based on the idea of modularity maximization. The model is relaxed by a simple convex positive semi-definite program, which can be optimized efficiently. Compared with other visualization approaches, through empirical evaluation our method is able to highlight network communities and the adversary vertices therein effectively. Thereby, it provides a useful tool in the family of community detection algorithms and in the family of graph layout methods. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Graph layout Network modularity semi-definite programming

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Worst-case topology optimization of self-weight loaded structures using semi-definite programming

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2015年第5期52卷 915-928页

作者： Holmberg, Erik Thore, Carl-Johan Klarbring, Anders Linkoping Univ Inst Technol Dept Management & Engn Div Solid Mech SE-58183 Linkoping Sweden

The paper concerns worst-case compliance optimization by finding the structural topology with minimum compliance for the loading due to the worst possible acceleration of the structure and attached non-structural masses. A main novelty of the paper is that it is shown how this min-max problem can be formulated as a non-linear semi-definite programming (SDP) problem involving a small-size constraint matrix and how this problem is solved numerically. Our SDP formulation is an extension of an eigenvalue problem seen previously in the literature;however, multiple eigenvalues naturally arise which makes the eigenvalue problem non-smooth, whereas the SDP problem presented in this paper provides a computationally tractable problem. Optimized designs, where the uncertain loading is due to acceleration of applied masses and the weight of the structure itself, are shown in two and three dimensions and we show that these designs satisfy optimality conditions that are also presented.

关键词： Topology optimization semi-definite programming Worst-case compliance Self-weight Robust optimization

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SDhaP: haplotype assembly for diploids and polyploids via semi-definite programming

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BMC GENOMICS 2015年第1期16卷 1-16页

作者： Das, Shreepriya Vikalo, Haris Univ Texas Austin Dept ECE Austin TX 78712 USA

Background: The goal of haplotype assembly is to infer haplotypes of an individual from a mixture of sequenced chromosome fragments. Limited lengths of paired-end sequencing reads and inserts render haplotype assembly computationally challenging;in fact, most of the problem formulations are known to be NP-hard. Dimensions (and, therefore, difficulty) of the haplotype assembly problems keep increasing as the sequencing technology advances and the length of reads and inserts grow. The computational challenges are even more pronounced in the case of polyploid haplotypes, whose assembly is considerably more difficult than in the case of diploids. Fast, accurate, and scalable methods for haplotype assembly of diploid and polyploid organisms are needed. Results: We develop a novel framework for diploid/polyploid haplotype assembly from high-throughput sequencing data. The method formulates the haplotype assembly problem as a semi-definite program and exploits its special structure - namely, the low rank of the underlying solution - to solve it rapidly and with high accuracy. The developed framework is applicable to both diploid and polyploid species. The code for SDhaP is freely available at https://***/projects/sdhap. Conclusion: Extensive benchmarking tests on both real and simulated data show that the proposed algorithms outperform several well-known haplotype assembly methods in terms of either accuracy or speed or both. Useful recommendations for coverages needed to achieve near-optimal solutions are also provided.

关键词： Haplotype assembly semi-definite programming Diploid Polyploid

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semi-definite programming Based Waveform Design for Spectrum Sensing

Semi-Definite Programming Based Waveform Design for Spectrum...

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2nd International Conference on Frontiers of Mechanical Engineering and Materials Engineering (MEME 2013)

作者： Wu Xuan-li Sun Lu-kuan Zhao Wan-jun Harbin Inst Technol Sch Elect & Informat Engn Harbin 150006 Peoples R China

ISBN: (纸本)9783037859247

In order to solve the problem of spectrum shortages, dynamic spectrum access based cognitive radio technology was proposed, and the technology of spectrum sensing is the foundation of cognitive radio. In this paper, a semi-definite programming based waveform design algorithm is proposed for spectrum sensing. Considering the energy concentration property of Chirp signal, the Chirp signal is adopted as the basic function, which makes the composite waveform perform like impulse function in fractional Fourier transform domain. Simulation results show that the NESP (Normalized Effective Signal Power) of the designed waveform using the proposed algorithm can be over 70%, and the designed waveform also retains good energy concentration property in fractional domain.

关键词： semi-definite programming waveform design spectrum sensing cognitive radio fractional Fourier transform

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A second-order Mehrotra-type predictor-corrector algorithm with a new wide neighbourhood for semi-definite programming

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2014年第5期91卷 1082-1096页

作者： Yang, Ximei Liu, Hongwei Zhang, Yinkui Xidian Univ Dept Math Xian Peoples R China Xihua Univ Sch Math & Comp Engn Chengdu Peoples R China

In this paper, we present a new second-order Mehrotra-type predictor-corrector algorithm for semi-definite programming (SDP). The proposed algorithm is based on a new wide neighbourhood. We are particularly concerned with an important inequality. Based on the inequality, the convergence is shown for a specific class of search directions. In particular, the complexity bound is O(root nlog epsilon(-1)) for the Nesterov-Todd search direction and O(nlog epsilon(-1)) for the Helmberg-Kojima-Monteiro search direction. The derived complexity bounds coincide with the currently best known theoretical complexity bounds obtained so far for SDP. We provide some preliminary numerical results as well.

关键词： semi-definite programming Mehrotra-type predictor-corrector algorithm Schatten 1-norm wide neighbourhood complexity bound

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Stochastic dual dynamic programming for optimal power flow problems under uncertainty

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2025年第3期321卷 814-836页

作者： Kiszka, Adriana Wozabal, David Tech Univ Munich TUM Sch Management Arcisstr 21 D-80333 Munich Germany Vrije Univ Amsterdam Sch Business & Econ Boelelaan 1105 NL-1081 HV Amsterdam Netherlands

Planning in the power sector has to take into account the physical laws of alternating current (AC) power flows as well as uncertainty in the data of the problems, both of which greatly complicate optimal decision making. We propose a computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in AC power systems. Our approach uses recent results on dual convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the stochastic dual dynamic programming (SDDP) algorithm for problems with a Markovian structure. We show that the usual SDDP lower bound remains valid and that the algorithm converges to a globally optimal policy of the stochastic AC-OPF problem as long as the SDP relaxations are tight. To test the practical viability of our approach, we set up a case study of a storage siting, sizing, and operations problem. We show that the convex SDP relaxation of the stochastic problem is usually tight and discuss ways to obtain near-optimal physically feasible solutions when this is not the case. The algorithm finds a physically feasible policy with an optimality gap of 3% and yields a significant added value of 27% over a rolling deterministic policy, which leads to overly optimistic policies and underinvestment in flexibility. This suggests that the common industry practice of assuming direct current and deterministic problems should be reevaluated by considering models that incorporate realistic AC flows and stochastic elements in the data as potentially more realistic alternatives.

关键词： Stochastic programming Optimal power flow semi-definite programming Stochastic dual dynamic programming Electricity storage

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Gabor Phase Retrieval via semidefinite programming

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FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2024年 1-67页

作者： Jaming, Philippe Rathmair, Martin Univ Bordeaux CNRS Bordeaux INP IMBUMR 5251 F-33400 Talence France Univ Vienna Fac Math Oskar Morgenstern Pl 1 A-1090 Vienna Austria

We consider the problem of reconstructing a function f is an element of L2(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\in L<^>2({\mathbb R})$$\end{document} given phase-less samples of its Gabor transform, which is defined by Gf(x,y):=214 integral Rf(t)e-pi(t-x)2e-2 pi iytdt,(x,y)is an element of R2.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\mathcal {G}}f(x,y) :=2<^>{\frac{1}{4}} \int _{\mathbb R}f(t) e<^>{-\pi (t-x)<^>2} e<^>{-2\pi i y t}\,\text{ d }t,\quad (x,y)\in {\mathbb R}<^>2. \end{aligned}$$\end{document}More precisely, given sampling positions Omega subset of R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega \subseteq {\mathbb R}<^>2$$\end{document} the task is to reconstruct f (up to global phase) from measurements {|Gf(omega)|:omega is an element of Omega}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{|{\mathcal {G}}f(\omega )|: \,\omega \in \Omega \}$$\end{document}. This non-linear inverse problem is known to suffer from severe ill-posedness. As for any other phase retrieval problem, constructive recovery is a notoriously delicate affair due to the lack of convexity. One of the fundamental insights in this line of research is that the connectivity of the measurements is both necessary and sufficient

关键词： Phase retrieval Phase-less sampling semi-definite programming Matrix completion

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Channel Allocation in Sociability-Assisted Cognitive Radio Networks Using semi-definite programming 9

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9th International Conference on Wireless Algorithms, Systems, and Applications (WASA)

作者： Li, Zhen Jing, Tao Huo, Yan Pan, Lili Zhou, Wei Beijing Jiaotong Univ Sch Elect & Informat Engn Beijing Peoples R China Beijing Jiaotong Univ Sch Sci Beijing Peoples R China

ISBN: (纸本)9783319077826;9783319077819

Channel allocation is an important part of cognitive radio(CR), and has received intensive studies in recent years. Previous works of channel allocation haven't taken the social relationship between primary users(PUs) and secondary users(SUs) into consideration. As a result, these allocation schemes ignore the willingness of CR users and may not adapt a personalized environment. Moreover, the traditional channel allocation schemes do not have the capability to protect the network performance from being hurt by some ill-behaved nodes. To tackle this challenge, we first introduce the social relationship into channel allocation and make some definitions about the social attributes. Then, we propose a Sociability-Assisted Channel Allocation Scheme(SACAS) which takes both the social relationship and the channel condition into consideration. Then, we use semi-definite programming(SDP) to obtain the optimal solution of SACAS. The simulation results show the superiority of SACAS over traditional algorithms.

关键词： Sociability-assisted channel allocation semi-definite programming cognitive radio

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Optimality Conditions in DC-Constrained Mathematical programming Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2023年第3期198卷 1191-1225页

作者： Correa, Rafael Lopez, Marco A. Perez-Aros, Pedro Univ OHiggins Rancagua Chile Univ Chile DIM CMM Santiago Chile Univ Alicante Dept Math Alicante 03071 Spain Federat Univ Australia Ctr Informat & Appl Optimizat Ballarat Australia Univ OHiggins Inst Ciencias Ingn Rancagua Chile

This paper provides necessary and sufficient optimality conditions for abstract-constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of certain mappings, in particular their structure as difference of convex functions, and uses techniques of generalized differentiation (subdifferential and coderivative). It turns out that these tools can be used fruitfully out of the scope of Asplund spaces. Applications to infinite, stochastic and semi-definite programming are developed in separate sections.

关键词： DC functions DC-constrained programming Conic programming Infinite programming Stochastic programming semi-definite programming Supremum function

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Quantifying the performance of bidirectional quantum teleportation

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CANADIAN JOURNAL OF PHYSICS 2025年第2期103卷 174-214页

作者： Siddiqui, Aliza U. Wilde, Mark M. Louisiana State Univ Div Comp Sci & Engn Baton Rouge LA 70803 USA Louisiana State Univ Hearne Inst Theoret Phys Dept Phys & Astron Baton Rouge LA 70803 USA Louisiana State Univ Ctr Computat & Technol Baton Rouge LA 70803 USA Univ Colorado Boulder Dept Elect Comp & Energy Engn Boulder CO 80309 USA Stanford Univ Stanford Inst Theoret Phys Stanford CA 94305 USA Cornell Univ Sch Elect & Comp Engn Ithaca NY 14850 USA Cornell Univ Sch Appl & Engn Phys Ithaca NY 14850 USA

Bidirectional teleportation is a fundamental protocol for exchanging quantum information between two parties by means of a shared resource state and local operations and classical communication (LOCC). In this paper, we develop two seemingly different ways of quantifying the simulation error of unideal bidirectional teleportation by means of the normalized diamond distance and the channel infidelity, and we prove that they are equivalent. By relaxing the set of operations allowed from LOCC to those that completely preserve the positivity of the partial transpose, we obtain semi-definite programming lower bounds on the simulation error of unideal bidirectional teleportation. We evaluate these bounds for several key examples: when there is no resource state at all and for isotropic and Werner states, in each case finding an analytical solution. The first aforementioned example establishes a benchmark for classical versus quantum bidirectional teleportation. Another example consists of a resource state resulting from the action of a generalized amplitude damping channel on two Bell states, for which we find an analytical expression for the simulation error that is in agreement with numerical estimates (up to numerical precision). We then evaluate the performance of some schemes for bidirectional teleportation due to (Kiktenko et al., Phys. Rev. A 93, 062305 (2016)) and find that they are suboptimal and do not go beyond the aforementioned classical limit for bidirectional teleportation. We offer a scheme alternative to theirs that is provably optimal. Finally, we generalize the whole development to the setting of bidirectional controlled teleportation, in which there is an additional assisting party who helps with the exchange of quantum information, and we establish semi-definite programming lower bounds on the simulation error for this task. More generally, we provide semi-definite programming lower bounds on the performance of bipartite and multipartite channel simul

关键词： quantum teleportation bidirectional teleportation semi-definite programming diamond distance channel infi-delity bidirectional controlled teleportation

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