作者：
Hu, XianzhiDai, XuchuChinese Acad Sci
Univ Sci & Technol China Sch Informat Sci & Technol Key Lab Wireless Opt Commun Hefei 230026 Peoples R China
This paper investigates the linear precoder design for multiuser multiple-input-multiple-output (MIMO) systems, in which the problem of maximizing weighted sum rate (WSR) subject to per-antenna power constraints (PAPC...
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This paper investigates the linear precoder design for multiuser multiple-input-multiple-output (MIMO) systems, in which the problem of maximizing weighted sum rate (WSR) subject to per-antenna power constraints (PAPC) is considered. This problem is hard to solve due to its nonconvexity and the existence of multiple quadratic constraints. Conventional methods to tackle this problem, such as the iterative weighted minimum mean squared error (WMMSE) algorithm, typically consist of two nested loops and thus suffer from high computational complexity. By leveraging the inherent separability of the PAPC constraint set, we propose a low-complexity single-loop algorithm for solving the WSR maximization problem under PAPC, in which each updating step is done efficiently with closed form. Theoretically, we prove the convergence of the proposed algorithm to stationary solutions. Then we extend the proposed algorithm to the multi-carrier scenario where the power constraints are shared over the subcarriers. Complexity analysis and numerical results show that the proposed single-loop algorithm maintains the same WSR performance as existing methods but dramatically reduces the computational complexity.
Much recent research effort has been directed to the development of efficient algo-rithms for solving minimax problems with theoretical convergence guarantees due to the relevance of these problems to a few emergent a...
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Much recent research effort has been directed to the development of efficient algo-rithms for solving minimax problems with theoretical convergence guarantees due to the relevance of these problems to a few emergent applications. In this paper, we propose a unified single-loop alternating gradient projection (AGP) algorithm for solving smooth nonconvex-(strongly) concave and (strongly) convex-nonconcave minimax problems. AGP employs simple gradient projection steps for updating the primal and dual variables alternatively at each iteration. We show that it can find an epsilon-stationary point of the objective function in O (epsilon(-2)) (resp. O (epsilon(-4))) iterations under nonconvex-strongly concave (resp. nonconvex-concave) setting. Moreover, its gradi-by O (epsilon(-2)) (resp., O (epsilon(-4))) under the strongly convex-nonconcave (resp., convex- ent complexity to obtain an epsilon-stationary point of the objective function is bounded nonconcave) setting. To the best of our knowledge, this is the first time that a simple and unified single-loop algorithm is developed for solving both nonconvex-(strongly) concave and (strongly) convex-nonconcave minimax problems. Moreover, the complexity results for solving the latter (strongly) convex-nonconcave minimax problems have never been obtained before in the literature. Numerical results show the efficiency of the proposed AGP algorithm. Furthermore, we extend the AGP algorithm by presenting a block alternating proximal gradient (BAPG) algorithm for solving more general multi-block nonsmooth nonconvex-(strongly) concave and (strongly) convex-nonconcave minimax problems. We can similarly establish the gradient complexity of the proposed algorithm under these four different settings.
This paper proposes an effective couple method for solving reliability-based multi-objective optimization problems of truss structures with static and dynamic constraints. The proposed coupling method integrates a sin...
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This paper proposes an effective couple method for solving reliability-based multi-objective optimization problems of truss structures with static and dynamic constraints. The proposed coupling method integrates a single-loop deterministic method (SLDM) into the nondominated sorting genetic algorithm II (NSGA-II) algorithm to give the so-called SLDM-NSGA-II. Thanks to the advantage of SLDM, the probabilistic constraints are treated as approximating deterministic constraints. And therefore the reliability-based multi-objective optimization problems can be transformed into the deterministic multi-objective optimization problems of which the computational cost is reduced significantly. In these reliability-based multi-objective optimization problems, the conflicting objective functions are to minimize the weight and the displacements of the truss. The design variables are cross-section areas of the bars and contraints include static and dynamic constraints. For reliability analysis, the effect of uncertainty of parameters such as force, added mass in the nodes, material properties and cross-section areas of the bars are taken into account. The effectiveness and reliability of the proposed method are demonstrated through three benchmark-type truss structures including a 10-bar planar truss, a 72-bar spatial truss and a 200-bar planar truss. Moreover, the influence of parameters on the reliability-based Pareto optimal fronts is also carried out.
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