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dc programming and dca for enhancing physical layer security via relay beamforming strategies

OPTIMIZATION LETTERS 2021年第7期15卷 2377-2405页

作者： Tran, Thi Thuy Pham Thi, Hoai An Pham Dinh, Tao Nguyen, Nhu Tuan FPT Univ Hoa Lac High Tech Pk Hanoi Vietnam LGIPM Univ Lorraine Comp Sci & Applicat Dept F-57073 Metz France Univ Normandie INSA Rouen Math Lab F-76801 St Etienne Du Rouvray France Vietnam Informat Secur Journal 105 Nguyen Chi Thanh Hanoi Vietnam

Beside of cryptography-the primary traditional methods for ensuring information security and confidentiality, the appearance of the physical layer security approach plays an important role for not only enabling the data transmission confidentially without relying on higher-layer encryption, but also enhancing confidentiality of the secret key distribution in cryptography. Many techniques are employed in physical layers to improve secure transmission including cooperative relaying and beamforming technique. In this paper, we consider the secrecy rate maximization problems using two techniques mentioned above with two different relaying protocols: Amplify-and-Forward and Decode-and-Forward. The optimization problems with the aim of maximizing secrecy rate subject to total and individual relay power constraints are formulated as nonconvex problems, which can be reformulated as dc (difference of two convex functions) programs and thus can be solved by dc Algorithms (dca). The special structure of feasible set is exploited which results to an efficient dc decomposition in the sense that it leads to convex subproblems that can be explicitly solved. The numerical results show that the proposed dca schemes are better than the existing methods in terms of both runtime and secrecy rate.

关键词： Amplify-and-forward Decode-and-forward Relay beamforming Physical layer security dc programming and dca

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dc programming and dca for enhancing physical layer security via cooperative jamming

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COMPUTERS & OPERATIONS RESEARCH 2017年 87卷 235-244页

作者： Thi Thuy Tran Hoai An Le Thi Tao Pham Dinh Ton Duc Thang Univ Dept Management Sci & Technol Dev Ho Chi Minh City Vietnam Ton Duc Thang Univ Fac Math & Stat Ho Chi Minh City Vietnam Univ Lorraine Lab Theoret & Appl Comp Sci EA 3097 F-57045 Metz 01 France Univ Normandie Lab Math INSA Rouen F-76801 St Etienne Du Rouvray France

The explosive development of computational tools these days is threatening security of cryptographic algorithms, which are regarded as primary traditional methods for ensuring information security. The physical layer security approach is introduced as a method for both improving confidentiality of the secret key distribution in cryptography and enabling the data transmission without relaying on higher-layer encryption. In this paper, the cooperative jamming paradigm - one of the techniques used in the physical layer is studied and the resulting power allocation problem with the aim of maximizing the sum of secrecy rates subject to power constraints is formulated as a nonconvex optimization problem. The objective function is a so-called dc (Difference of Convex functions) function, and some constraints are coupling. We propose a new dc formulation and develop an efficient dca (dc Algorithm) to deal with this nonconvex program. The dca introduces the elegant concept of approximating the original non convex program by a sequence of convex ones: at each iteration of dca requires solution of a convex subproblem. The main advantage of the proposed approach is that it leads to strongly convex quadratic subproblems with separate variables in the objective function, which can be tackled by both distributed and centralized methods. One of the major contributions of the paper is to develop a highly efficient distributed algorithm to solve the convex subproblem. We adopt the dual decomposition method that results in computing iteratively the projection of points onto a very simple structural set which can be determined by an inexpensive procedure. The numerical results show the efficiency and the superiority of the new dca based algorithm compared with existing approaches. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Physical layer security Cooperative jamming Resource allocation dc programming and dca

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dc programming and dca for a Novel Resource Allocation Problem in Emerging Area of Cooperative Physical Layer Security 1

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3rd International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA)

作者： Thi Thuy Tran Hoai An Le Thi Tao Pham Dinh Univ Lorraine UFR MIM Lab Theoret & Appl Comp Sci LITA F-57045 Metz France Univ Normandie INSA Rouen Math Lab F-76801 St Etienne France

ISBN: (数字)9783319179964

ISBN: (纸本)9783319179964;9783319179957

In this paper, we consider the problem of resource allocation in emerging area of cooperative physical layer security, whose objective function is of the difference of two convex functions, called dc function, and whose some constraints are coupling. We propose a novel dc decomposition for the objective function and use dca (dc algorithms) to solve this problem. The main advantage of the proposed dc decomposition is that it leads to strongly convex quadratic sub-problems that can be easily solved by both distributed and centralized methods. The numerical results show the efficiency of this dc decomposition compared with the one proposed in ([2]). The dc decomposition technique in this article may be applied for a wide range of multiuser dc problems in communication systems, signal processing and networking.

关键词： Resource allocation physical layer dc programming and dca

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dc programming and dca for Enhancing Physical Layer Security via Relay Beamforming Strategies 8th

DC Programming and DCA for Enhancing Physical Layer Security...

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8th Asian Conference on Intelligent Information and Database Systems (ACIIDS)

作者： Tran Thi Thuy Nguyen Nhu Tuan Le Thi Hoai An Gely, Alain FPT Univ Hoa Lac High Tech Pk Hanoi Vietnam Acad Cryptog Tech Dept Cryptog Hanoi Vietnam Univ Lorraine Lab Theoret & Appl Comp Sci LITA UFR MIM F-57045 Metz France

ISBN: (纸本)9783662493908;9783662493892

Beside of cryptography - the primary traditional methods for ensuring information security and confidentiality, the appearance of the physical layer security approach plays an important role for not only enabling the data transmission confidentially without relying on higher-layer encryption, but also enhancing confidentiality of the secret key distribution in cryptography itself. In this paper, we mention a technique used in physical layer security, this is relay beamforming strategy with Decode-and-Forward relaying technique. The optimization problems with the aim of maximizing the sum of secrecy rates subject to individual relay power constraints are formulated as a nonconvex problem. These problems can be rewritten as dc (difference of two convex functions) programs. We apply the standard dca scheme to find solution to this problem. The main benefit of the proposed method is that it provides an optimal value for the system secrecy rate while the previous existing methods only give its upper bound.

关键词： Decode-and-forward Relay beamforming Physical layer security dc programming and dca

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dc programming and dca for Enhancing Physical Layer Security in Amplify-and-Forward Relay Beamforming Networks Based on the SNR Approach 5th

DC Programming and DCA for Enhancing Physical Layer Security...

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5th International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA)

作者： Nguyen Nhu Tuan Dang Vu Son Acad Cryptog Tech Hanoi Vietnam

ISBN: (纸本)9783319619118;9783319619101

Physical layer security is an alternative approach to guarantee secure communication besides the traditional cryptography method. In the physical layer security literature, most of the studies are centered around the secrecy capacity, but a new approach based on signal-to-noise ratios (SNR) was proposed in recent years. In that approach, they considered the transmission of a confidential message over a wireless channel with the help of multiple cooperating relays in the Amplify-and-Forward cooperative scheme based on an SNR approach with the predefined threshold. The optimization problem with the aim of maximizing the received SNR at a legitimate receiver subjects to the conditions that the received SNR at each eavesdropper is below the target threshold, and the condition about relay power are formulated as a nonconvex problem. This problem was solved by Semi-definite Relaxation method. In this paper, we propose the well known method based on dc programming and dca to solve this hard problem. The numerical results show that our proposed method give the better results compared with its obtained by the existing ones.

关键词： dc programming and dca Amplify-and-Forward Physical layer security

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Solving the minimum M-dominating set problem by a continuous optimization approach based on dc programming and dca

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2012年第4期24卷 397-412页

作者： Schleich, Julien Hoai An Le Thi Bouvry, Pascal Univ Paul Verlaine Metz LITA F-57045 Metz France Univ Luxembourg SnT Interdisciplinary Ctr Luxembourg Luxembourg Univ Luxembourg FSTC CSC Luxembourg Luxembourg

We propose a new optimization approach based on dc (Difference of Convex functions) programming and dca (dc Algorithm) to the so-called Minimum M-Dominating Set problem in graphs. This problem is beforehand re-casted as a polyhedral dc program with the help of exact penalty in dc programming. The related dca is original and computer efficient because it consists of solving a few linear programs and converges after a finite number of iterations to an integer solution while working in a continuous domain. Numerical simulations show the efficiency and robustness of dca and its superiority with respect to standard methods.

关键词： dc programming and dca Exact penalty Minimum dominating set

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Recent Advances in dc programming and dca

Recent Advances in DC Programming and DCA

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Workshop on Optimization & Machine Learning (OPML)

作者： Tao Pham Dinh Hoai An Le Thi Natl Inst Appl Sci Rouen Math Lab F-76801 St Etienne France Univ Lorraine Lab Theoret & Appl Comp Sci LITA UFR MIM F-57045 Metz France

ISBN: (纸本)9783642544552;9783642544545

Difference of Convex functions (dc) programming and dc Algorithm (dca) constitute the backbone of Nonconvex programming and Global Optimization. The paper is devoted to the State of the Art with recent advances of dc programming and dca to meet the growing need for nonconvex optimization and global optimization, both in terms of mathematical modeling as in terms of efficient scalable solution methods. After a brief summary of these theoretical and algorithmic tools, we outline the main results on convergence of dca in dc programming with subanalytic data, exact penalty techniques with/without error bounds in dc programming including mixed integer dc programming, dca for general dc programs, and dc programming involving the l(0)-norm via its approximation and penalization.

关键词： dc programming and dca rate convergence of dca with subanalytic data exact penalty and error-bounds in dc programming dca for general dc programs exact penalty in mixed integer dc programming approximation and penalization of the l(0)-norm

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A novel dictionary learning method for sparse representation with nonconvex regularizations

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NEUROCOMPUTING 2020年 417卷 128-141页

作者： Tan, Benying Li, Yujie Zhao, Haoli Li, Xiang Ding, Shuxue Guilin Univ Elect Technol Sch Artificial Intelligence Guilin Peoples R China Univ Aizu Grad Sch Comp Sci & Engn Aizu Wakamatsu Fukushima Japan Guilin Univ Elect Technol Sch Artificial Intelligence Guangxi Key Lab Wireless Broadband Commun & Signa Guilin 541004 Peoples R China Natl Inst Adv Ind Sci & Technol Tsukuba Ibaraki 3058560 Japan Sun Yat Sen Univ Sch Data & Comp Sci Guangzhou Guangdong Peoples R China

In dictionary learning, sparse regularization is used to promote sparsity and has played a major role in the developing of dictionary learning algorithms. l(1)-norm is of the most popular sparse regularization due to its convexity and the related tractable convex optimization problems. However, l(1)-norm leads to biased solutions and provides inferior performance on certain applications compared with nonconvex sparse regularizations. In this work, we propose a generalized minimax-concave (GMC) sparse regularization, which is nonconvex, to promote sparsity to design dictionary learning model. Applying the alternate optimization scheme, we use the forward-backward splitting (FBS) algorithm to solve the sparse coding problem. As the improvement, we incorporate Nesterov's acceleration technique and adaptive threshold scheme into the FBS algorithm to improve the convergence efficiency and performance. In the dictionary update step, we apply the difference of convex functions (dc) programming and the dc algorithm (dca) to address the dictionary update. Two dictionary update algorithms are designed;one updates the dictionary atoms one by one, and the other one updates the dictionary atoms simultaneously. The presented dictionary learning algorithms perform robustly in dictionary recovery. Numerical experiments are designed to verify the performance of proposed algorithms and to compare with the state-of-the-art algorithms. (C) 2020 Published by Elsevier B.V.

关键词： Dictionary learning Nonconvex GMC regularization dc programming and dca Forward-backward splitting algorithm

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Markov chain stochastic dca and applications in deep learning with PDEs regularization

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NEURAL NETWORKS 2024年 170卷 149-166页

作者： Luu, Hoang Phuc Hau Le, Hoai Minh Le Thi, Hoai An Univ Lorraine LGIPM F-57000 Metz France Inst Univ France IUF Paris France

This paper addresses a large class of nonsmooth nonconvex stochastic dc (difference-of-convex functions) programs where endogenous uncertainty is involved and i.i.d. (independent and identically distributed) samples are not available. Instead, we assume that it is only possible to access Markov chains whose sequences of distributions converge to the target distributions. This setting is legitimate as Markovian noise arises in many contexts including Bayesian inference, reinforcement learning, and stochastic optimization in high-dimensional or combinatorial spaces. We then design a stochastic algorithm named Markov chain stochastic dca (MCSdca) based on dca (dc algorithm) -a well-known method for nonconvex optimization. We establish the convergence analysis in both asymptotic and nonasymptotic senses. The MCSdca is then applied to deep learning via PDEs (partial differential equations) regularization, where two realizations of MCSdca are constructed, namely MCSdca-odLD and MCSdca-udLD, based on overdamped and underdamped Langevin dynamics, respectively. Numerical experiments on time series prediction and image classification problems with a variety of neural network topologies show the merits of the proposed methods.

关键词： dc programming and dca Markov chain Monte Carlo Deep learning Partial differential equations

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A dc programming approach for planning a multisensor multizone search for a target

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COMPUTERS & OPERATIONS RESEARCH 2014年第Jan.期41卷 231-239页

作者： Hoai An Le Thi Duc Manh Nguyen Tao Pham Dinh Univ Lorraine UFR MIM Lab Theoret & Appl Comp Sci F-57045 Metz France Natl Inst Appl Sci Rouen Math Lab F-76801 St Etienne France

In this paper, we consider a well-known problem in the general area of search theory: planning a multisensor in multizone search so as to maximize the probability of detection of a target under a given resource effort to be shared. We propose a new optimization model that is a nonlinear mixed 0-1 programming problem. This problem is then reformulated as a dc (Difference of Convex) functions program via an exact penalty technique. dc programming and dca (dc algorithm) have been investigated for solving the resulting dc program. Numerical experiments demonstrate the efficiency and the superiority of the proposed algorithm in comparison with the existing method. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Search theory Hierarchical optimization Combinatorial optimization dc programming and dca Nonlinear mixed 0-1 programming Exact penalty

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