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A general double-proximal gradient algorithm for d.c. programming

MATHEMATIcAL programming 2019年第1-2期178卷 301-326页

作者： Banert, Sebastian Bot, Radu Ioan KTH Royal Inst Technol Dept Math Lindstedtsvagen 25 S-10044 Stockholm Sweden Univ Vienna Fac Math Oskar Morgenstern Pl 1 A-1090 Vienna Austria

The possibilities of exploiting the special structure of d.c. programs, which consist of optimising the difference of convex functions, are currently more or less limited to variants of the dcA proposed by Pham dinh Tao and Le Thi Hoai An in 1997. These assume that either the convex or the concave part, or both, are evaluated by one of their subgradients. In this paper we propose an algorithm which allows the evaluation of both the concave and the convex part by their proximal points. Additionally, we allow a smooth part, which is evaluated via its gradient. In the spirit of primal-dual splitting algorithms, the concave part might be the composition of a concave function with a linear operator, which are, however, evaluated separately. For this algorithm we show that every cluster point is a solution of the optimisation problem. Furthermore, we show the connection to the Toland dual problem and prove a descent property for the objective function values of a primal-dual formulation of the problem. convergence of the iterates is shown if this objective function satisfies the Kurdyka-Lojasiewicz property. In the last part, we apply the algorithm to an image processing model.

关键词： d.c. programming Toland dual Proximal-gradient algorithm Kurdyka-Lojasiewicz property convergence analysis

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Optimization of cooperative Beamforming for Sc-FdMA Multi-User Multi-Relay Networks by Tractable d.c. programming

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IEEE TRANSAcTIONS ON SIGNAL PROcESSING 2013年第2期61卷 467-479页

作者： Ha Hoang Kha Hoang duong Tuan Nguyen, Ha H. Pham, Tung T. Univ Technol Sydney Fac Engn & Informat Technol Sydney NSW 2007 Australia Univ Saskatchewan Dept Elect & Comp Engn Saskatoon SK Canada

This paper addresses the optimal cooperative beamforming design for multi-user multi-relay wireless networks in which the single-carrier frequency division multiple access (Sc-FdMA) technique is employed at the terminals. The problem of interest is to find the beamforming weights across relays to maximize the minimum signal-to-interference-plus-noise ratio (SINR) among source users subject to individual power constraints at each relay. Such a beamforming design is shown to be a hard non-convex optimization problem and therefore it is mathematically challenging to find the optimal solution. By exploring its partial convex structures, we recast the design problem as minimization of a d.c. (difference of two convex) objective function subject to convex constraints and develop an effective iterative algorithm of low complexity to solve it. Simulation results show that our optimal cooperative beamforming scheme realizes the inherent diversity order of the relay network and it performs significantly better than the equal-power beamforming weights.

关键词： cooperative beamforming d.c. programming frequency-domain equalization maximin optimization power allocation Sc-FdMA wireless relay networks

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Optimizing radial basis functions by d.c. programming and its use in direct search for global derivative-free optimization

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TOP 2012年第1期20卷 190-214页

作者： Le Thi, H. A. Vaz, A. I. F. Vicente, L. N. Univ Minho Dept Prod & Syst P-4710057 Braga Portugal Paul Verlaine Univ Lab Theoret & Appl Comp Sci LITA EA 3097 F-57045 Metz France

In this paper, we address the global optimization of functions subject to bound and linear constraints without using derivatives of the objective function. We investigate the use of derivative-free models based on radial basis functions (RBFs) in the search step of direct-search methods of directional type. We also study the application of algorithms based on difference of convex (d.c.) functions programming to solve the resulting subproblems which consist of the minimization of the RBF models subject to simple bounds on the variables. Extensive numerical results are reported with a test set of bound and linearly constrained problems.

关键词： Global optimization derivative-free optimization direct-search methods Search step Radial basis functions d.c. programming dcA

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d.c. programming for cooperative Beamforming in Sc-FdMA Multi-User Multi-Relay Networks

D.C. Programming for Cooperative Beamforming in SC-FDMA Mult...

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IEEE Global communications conference

作者： Ha H. Kha H. d. Tuan Ha H. Nguyen Tung T. Pham Faculty of Engineering and Information Technology University of Technology Department of Electrical and Computer Engineering University of Saskatchewan

ISBN: (纸本)9781467309202

We are concerned with a cooperative beamforming design for multi-user multi-relay wireless networks in which the single-carrier frequency division multiple access (Sc-FdMA) technique is employed at the terminals. The problem of interest is to find the beamforming weights across relays to maximize the minimum signal-to-interference-plus-noise ratio (SINR) among users subject to individual power constraints at each relay. Such a beamforming design is shown to be a hard nonconvex program and therefore it is mathematically challenging to find the optimal solution. By exploring its partial convex structures, we recast the design problem as minimization of a d.c. (difference of two convex) objective function subject to convex constraints and develop an effective iterative algorithm of low complexity to solve it. Simulation results show that our optimal cooperative beamforming scheme realizes the inherent diversity order of the relay network and it performs significantly better than the equal-power beamforming weights.

关键词： cooperative beamforming Power allocation Sc-FdMA Frequency-domain equalization Wireless relay networks d.c. programming Maximin optimization Frequency domain equalization Beamforming power splitting Relay networks wireless relay networks design problems Frequency division multiaccess Individual Power convexity

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A unifying approach to solve a class of rank-three programs involving linear and quadratic functions

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OPTIMIZATION 2017年第11期66卷 1777-1791页

作者： cambini, Riccardo Sodini, claudio Univ Pisa Dept Econ & Management Pisa Italy

The aim of this paper is two-fold, First, the so-called 'optimal level solutions' method is described in a new unifying framework with the aim to provide an algorithmic scheme able to approach various different classes of problems. Then, the 'optimal level solutions' method is used to solve a class of low-rank programmes involving linear and quadratic functions and having a polyhedral feasible region, In particular, the considered.c.ass of programmes covers, among all, rank-three d.c., multiplicative and fractional programmes. Some optimality conditions are used to improve the performance of the proposed algorithm.

关键词： Fractional programming multiplicative programming d.c. programming optimal level solutions global optimization

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On the effectiveness of Lagrangean cuts in solving a class of low rank d.c. programs

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JOURNAL OF STATISTIcS & MANAGEMENT SYSTEMS 2017年第5期20卷 817-834页

作者： cambini, Riccardo Salvi, Francesca Univ Pisa Dept Econ & Management Via Cosimo Ridolfi 10 I-56124 Pisa Italy

d.c. programs have been widely studied in the recent literature due to their importance in applicative problems. In this paper the results of a computational study related to a branch and red.c. approach for solving a class of d.c. problems are provided, pointing out the concrete effectiveness of the use of Lagrangean cuts as an acceleration device.

关键词： d.c. programming branch and red.c.

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Successive Interference Mitigation in Multiuser MIMO channels

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IEEE TRANSAcTIONS ON cOMMUNIcATIONS 2015年第6期63卷 2185-2199页

作者： che, Enlong Hoang duong Tuan Ho Huu Minh Tam Nguyen, Ha H. Univ Technol Sydney Fac Engn & Informat Technol Sydney NSW 2007 Australia Univ Saskatchewan Dept Elect & Comp Engn Saskatoon SK S7N 5A9 Canada

Motivated by the work of dahrouj and Yu in applying the Han-Kobayashi transmission strategy for mitigating the intercell interference in a multi-cell multi-user multiple-input single-output interference network (MISOIN), this paper considers splitting messages into private and.c.mmon parts in a multi-cell multi-user MIMO IN. Specifically, the covariances of the private messages and.c.mmon messages are designed to optimize either the sum rate or the minimal rate. The common messages and private messages are d.c.ded in sequence using successive d.c.ding. This paper shows how these difficult optimization problems can be adequately solved by means of d.c. (difference of concave functions) optimization over a simple convex set. Numerical and simulation results also reveal the great advantage of our proposed solutions for various types of INs. In particular, the proposed solutions are shown to outperform the algorithm developed by dahrouj and Yu for the simpler case of the MISO IN.

关键词： Multi-user interference networks multi-input multi-output systems interference mitigation nonsmooth optimization d.c. programming

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Joint Optimization of cooperative Beamforming and Relay Assignment in Multi-User Wireless Relay Networks

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IEEE TRANSAcTIONS ON WIRELESS cOMMUNIcATIONS 2014年第10期13卷 5481-5495页

作者： che, Enlong Hoang duong Tuan Nguyen, Ha H. Univ Technol Sydney Fac Engn & Informat Technol Sydney NSW 2007 Australia Univ Saskatchewan Dept Elect & Comp Engn Saskatoon SK S7N 5A9 Canada

This paper considers joint optimization of cooperative beamforming and relay assignment for multi-user multi-relay wireless networks to maximize the minimum of the received signal-to-interference-plus-noise ratios (SINR). Separated.c.ntinuous optimization of beamforming and binary optimization of relay assignment already pose very challenging programs. certainly, their joint optimization, which involves nonconvex objectives and.c.upled.c.nstraints in continuous and binary variables, is among the most challenging optimization problems. Even the conventional relaxation of binary constraints by continuous box constraints is still computationally intractable because the relaxed program is still highly nonconvex. However, it is shown in this paper that the joint programs fit well in the d.c. (difference of two convex functions/sets) optimization framework. Efficient optimization algorithms are then developed for both cases of orthogonal and nonorthogonal transmission by multiple users. Simulation results show that the jointly optimized beamforming and relay assignment not only save transmission bandwidth but can also maintain well the network SINRs.

关键词： cooperative beamforming power allocation relay selection relay assignment wireless relay networks d.c. programming

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Linear Precoder design for doubly correlated Partially coherent Fading MIMO channels

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IEEE TRANSAcTIONS ON WIRELESS cOMMUNIcATIONS 2014年第7期13卷 3621-3635页

作者： Yadav, Animesh Juntti, Markku Lilleberg, Jorma Univ Oulu Dept Commun Engn FI-90014 Oulu Finland Univ Oulu Ctr Wireless Commun FI-90014 Oulu Finland Rice Univ Ctr Multimedia Commun Houston TX 77005 USA Broadcom Corp Oulu 90590 Finland

We consider the single-user multiple-input multiple-output (MIMO) precoder design problem for the doubly spatially correlated partially coherent Rayleigh fading channels with discrete inputs. The objective is to design a linear precoder to adapt to the degradation caused by the imperfect channel estimation at the receiver and the transmit-receive antenna correlation. The system is partially coherent so that the MIMO channel coefficients are estimated at the receiver and its error covariance matrix is fed back to the transmitter. We utilized the cutoff rate (cR) expression, an alternative to the mutual information (MI), and propose to use it as a design criterion to design the linear precoders. A linear precoder is obtained by numerically maximizing the cR with respect to the precoder matrix with a given average power constraint. Furthermore, the precoder matrix is d.c.mposed using singular value d.c.mposition (SVd) into the input shaping matrix, power loading matrix, and beamforming matrix. The beamforming matrix is found to coincide with the eigenvectors of the transmit correlation matrix. The power loading and input shaping matrices are solved numerically using the difference of convex (d.c.) functions programming algorithm and optimization under the unitary constraint, respectively. A 2-block alternating optimization (AO) algorithm is proposed to solve the input shaping matrix and power loading matrix iteratively. Precoders are designed to be used in conjunction with two MIMO transmission schemes: the spatial multiplexing (SM) and space-time (ST) block transmission modes. The frame error rate (FER) and average MI are used as the performance metrics to validate the performance of the newly designed.c.-precoders in comparison with the conventional no-precoding case and.c.toff rate optimized partially coherent constellations (Pccs). Numerical examples show that the performance gains of the designed precoders are significant compared to the cR-Pccs and.c.nventional c

关键词： Linear precoder design multiple-input multiple-output (MIMO) systems partial cSI cutoff rate spatial correlated.c.annels spatial multiplexing (SM) space-time block codes (STBc) unitary space-time codes (USTc) d.c. programming alternating optimization

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Joint Optimization of Source Power Allocation and.c.operative Beamforming for Sc-FdMA Multi-User Multi-Relay Networks

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IEEE TRANSAcTIONS ON cOMMUNIcATIONS 2013年第6期61卷 2248-2259页

作者： Kha, Ha H. Tuan, Hoang d. Nguyen, Ha H. Univ Technol Sydney Fac Engn & Informat Technol Sydney NSW 2007 Australia Univ Technol Sydney Fac Engn & Informat Technol Ctr Hlth Technol Sydney NSW 2007 Australia Univ Saskatchewan Dept Elect & Comp Engn Saskatoon SK Canada

This paper is concerned with design problems of joint source power allocation and relay beamforming in multiuser multi-relay networks that use single-carrier frequency division multiple access (Sc-FdMA) and amplify-and-forward relaying. Examined are the joint programs of (i) maximizing the minimum signal-to-interference-plus-noise ratio (SINR) under various transmitted power constraints, and (ii) minimizing the total transmitted power subject to prescribed SINR thresholds of users. Although these optimization problems are highly non-convex and have large dimensions, by exploiting their partial convexities and making elegant nonlinear variable changes, they are recast as d.c. (difference of two convex) programs. Efficient d.c. iterative procedures are then developed to find the solutions. Simplified joint programs under the two cases of equal source power and equal relay beamforming weights, respectively, are also considered. Branch-and-bound algorithms of deterministic global optimization are then proposed for solving the simplified joint programs. Simulation results confirm the excellent performance and.c.mputational efficiency of all the proposed solutions.

关键词： Wireless relay networks cooperative beamforming power allocation Sc-FdMA joint optimization max-min optimization d.c. programming global optimization

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