基于半定规划多用户检测问题的二次规划法

半定规划是解决极大似然多用户检测问题的一种重要方法,但当问题规模较大时,误码率较高。基于多用户检测问题的半定规划松弛模型,给出了一个二次规划松弛模型。该模型能得到比半定规划模型更好的界。根据这个模型,运用分枝定界方法,可以求得多用户检测问题的次优解。这种方法改善了用户多时半定规划方法误码率高的状况,是解决多用户检测问题的有效方法。仿真实验证实了这一点。     

A branch-and-cut approach to portfolio selection with marginal risk control in a linear conic programming framework

Marginal risk represents the risk contribution of an individual asset to the risk of the entire portfolio In this paper, we investigate the portfolio selection problem with direct marginal risk control in a linear conic programming framework. ＇The optimization model involved is a nonconvex quadratically constrained quadratic programming （QCQP） problem. We first transform the QCQP problem into a linear conic programming problem, and then approximate the problem by semidefinite programming （SDP） relaxation problems over some subrectangles. In order to improve the lower bounds obtained from the SDP relaxation problems, linear and quadratic polar cuts are introduced for designing a branch-and-cut algorithm, that may yield an e -optimal global solution （with respect to feasibility and optimality） in a finite number of iterations. By exploring the special structure of the SDP relaxation problems, an adaptive branch-and-cut rule is employed to speed up the computation. The proposed algorithm is tested and compared with a known method in the literature for portfolio selection problems with hundreds of assets and tens of marginal risk control constraints.     

ERBF network with immune clustering

Based on immune clustering and evolutionary programming(EP), a hybrid algorithm to train the RBF network is proposed. An immune fuzzy C-means clustering algorithm (IFCM) is used to adaptively specify the amount and initial positions of the RBF centers according to input data set; then the RBF network is trained with EP that tends to global optima. The application of the hybrid algorithm in multiuser detection problem demonstrates that the RBF network trained with the algorithm has simple network structure with good generalization ability.     

A SUPERLINEAR CONVERGENT FEASIBLE METHOD FOR NONLINEAR PROGRAMMING WITH NONLINEAR CONSTRAINTS

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Orthogonal genetic algorithm for solving quadratic bilevel programming problems

A quadratic bilevel programming problem is transformed  into a single level complementarity slackness problem by applying  Karush-Kuhn-Tucker (KKT) conditions. To cope with the complementarity  constraints, a binary encoding scheme is adopted for  KKT multipliers, and then the complementarity slackness problem  is simplified to successive quadratic programming problems,  which can be solved by many algorithms available. Based on 0−1  binary encoding, an orthogonal genetic algorithm, in which the orthogonal  experimental design with both two-level orthogonal array  and factor analysis is used as crossover operator, is proposed.  Numerical experiments on 10 benchmark examples show that the  orthogonal genetic algorithm can find global optimal solutions of  quadratic bilevel programming problems with high accuracy in a  small number of iterations.     

Efficient multiuser detector based on box-constrained deregularization and its FPGA design

Multiuser detection can be described as a quadratic optimization problem with binary constraint.Many techniques are available to find approximate solution to this problem.These techniques can be characterized in terms of complexity and detection performance.The "efficient frontier" of known techniques include the decision-feedback,branch-and-bound and probabilistic data association detectors.The presented iterative multiuser detection technique is based on joint deregularized and box-constrained solution to quadratic optimization with iterations similar to that used in the nonstationary Tikhonov iterated algorithm.The deregularization maximizes the energy of the solution,this is opposite to the Tikhonov regularization where the energy is minimized.However,combined with box-constraints,the deregularization forces the solution to be close to the binary set.We further exploit the boxconstrained dichotomous coordinate descent (DCD) algorithm and adapt it to the nonstationary iterative Tikhonov regularization to present an efficient detector.As a result,the worst-case and average complexity are reduced down to 2.8 and 2.5 floating point operation per second,respectively.The development improves the "efficient frontier" in multiuser detection,which is illustrated by simulation results.Finally,a field programmable gate array (FPGA) design of the detector is presented.The detection performance obtained from the fixed-point FPGA implementation shows a good match to the floating-point implementation.     

New approach to training support vector machine

1.INTRODUCTIONThe support vector machine(SVM)[1]has been suc-cessful as a high-performance classifier in several do-mains including pattern recognition,data mining,and bioinformatics.It has strong theoretical founda-tions and good generalization capability.Ali mitationof the SVMdesign algorithm,particularly for largedata sets,is the need to solve a quadratic program-ming(QP)probleminvolving a densen×nmatrix,wherenis the number of points in the data set.Since QProutines have highcompl…     

Stabilizing model predictive control scheme for piecewise affine systems with maximal positively invariant terminal set

An efficient algorithm is proposed for computing the solution to the constrained finite time optimal control (CFTOC) problem for discrete-time piecewise affine (PWA) systems with a quadratic performance index. The maximal positively invariant terminal set, which is feasible and invariant with respect to a feedback control law, is computed as terminal target set and an associated Lyapunov function is chosen as terminal cost. The combination of these two components guarantees constraint satisfaction and closed-loop stability for all time. The proposed algorithm combines a dynamic programming strategy with a multi-parametric quadratic programming solver and basic polyhedral manipulation. A numerical example shows that a larger stabilizable set of states can be obtained by the proposed algorithm than precious work.     

Automatic differentiation for reduced sequential quadratic programming

In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD） is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.     

线性一二次双层规划问题

本文利用对偶理论和Kuhn-Tucker条件来研究线性一二次双层规划问题, 给出一些二层规划解的最优性条件和一个求解二层规划解的算法。这些最优性条件丰富了非线性多层规划的理论, 而其求解算法为求解实际问题提供了有力的工具。一些数值试验结果将在本文未给出, 这些结果表明算法对于小规模问题的求解是相当有效的。     

自融资均值方差投资组合模型的旋转算法

将自融资投资组合问题用一个以极小化方差风险为目标的凸二次规划表示,用线性不等式组的一种旋转算法解其库恩塔克条件的线性部分并使互补松弛条件得以满足.     

SENSITIVITY ANALYSIS IN BILEVEL LINEAR PROGRAMMING

1.IntroductionMultilevelprogrammingmodelsdescribesdecisionmakingsituationswhereahierarchyexists.Inabilevelsystem,thedecisionofthehigherlevel(leader)mayaffectthechoiceofstrategyavailabletothelowerlevel(follower)whoattemptstooptimizehisobjectivefunction.Inthissystem,theleaderalsoconsidersthefollower'sresponsewhichisbasedonoptimizingthefollower'sobjectivefunction,forinstance,see[1].Asanextensionandavariationofmathematicalprogramming,multilevelprogrammingwasfirstintroducedbyCandlerandTownsley[2].…     

A LOGARITHMIC BARRIER NEWTON METHOD FOR SEMIDEFINITE PROGRAMMING

1.IntroductionInrecentyears,muchattentionhasbeenfocusedonthesemidefiniteprogramming(SDP)problem.OnereasonisthatSDPhasveryimportantapplicationsinmanyareas,suchascombinationaloptimization,systemandcontroltheory,eigenvalueoptimizationetc.[1'2'3]Anotherreason…     

基于正则信道求逆预编码的MIMO功率分配方案研究

提出一种多用户MIMO系统中基于正则信道求逆预编码并具有QoS保障的功率分配方案:结合信道状态信息和用户QoS需求,分析得出约束条件的可行性判断依据;利用连续几何规划算法将非凸优化问题近似为凸优化问题,并辅以内点法求解最优功率分配方案;最终综合得出一套基于滑动窗口机制的功率分配框架。仿真结果表明,与现有算法相比,该方案能在有效保障用户最小速率和时延需求的基础上,显著提高系统可达速率。     

基于动态规划的雷达微弱目标检测

微弱目标检测和跟踪是雷达信号处理领域中一个急需解决的关键问题,提出了一种将相参积累与基于动态规划的检测前跟踪算法相结合的雷达微弱目标处理方法,在该算法中引入方向加权的思想,减小动态规划的能量扩散范围,并采用两级门限检测方法降低运算量。仿真数据和实际测试数据处理结果表明,此算法对雷达微弱目标的检测性能优于传统方法,可以有效实现低信噪比下目标的检测与跟踪,且其处理速度较传统检测前跟踪方法有一定提高,更利于工程应用。     

用于回归估计的最小二乘广义支持向量机

提出了一种用于回归估计的最小二乘广义支持向量机.这种最小二乘广义支持向量机的核函数同标准的支持向量机相比没有或者只有很少的限制.将这种用于回归估计的最小二乘广义支持向量机表示成标准的二次规划(QP)问题,采用基于矩阵分裂的超松弛法同投影梯度法相结合的算法来解这一QP问题.根据超松弛法的特点,这一算法可以处理大量数据的情形.     

利用进化规划和逐步二次规划实现前馈神经网络的结构优化

用进化规划与逐步二次规划来实现前馈神经网络的结构优化问题 ,并提出了一个相应的学习算法 .针对进化规划与逐步二次规划各自的特点 ,进行了组合 ,使算法不仅具有随机全局搜索能力 ,而且还具有更好的全局收敛能力 ,并与环境有更强的自适应能力 .最后通过仿真和应用实验证实了算法的有效性.     

基于灵敏度分析的系统可靠性稳健分配优化方法

在系统可靠性分配中,考虑单元可靠度的不确定性已是可靠性分配的现实需要.为了提高系统可靠性分配优化的质量,将稳健理论引入可靠性分配中,提出基于单元可靠性灵敏度的系统可靠性稳健分配方法.将单元可靠性灵敏度溶入系统可靠性分配模型之中,建立系统可靠性稳健分配模型.在此基础上,采用粒子群-序列二次规划算法对该模型进行优化设计,该混合算法既保持了粒子群算法全局收敛的特点,又补充了序列二次规划法精确求解的能力,因此该混合算法可以快速获取全局最优解.通过对发动机曲柄连杆机构进行可靠性稳健分配设计,验证了可靠性稳健分配模型的合理性和混合算法的寻优能力.对结果分析表明,所提方法可以较好解决单元可靠度不确定时的可靠性分配问题,混合算法具有较强的全局搜索能力,分配优化结果具有较强的稳健性.     

企业竞争策略选择的建模、算法与仿真

企业选择竞争行为应对潜在竞争威胁是确保企业盈利的要素之一。针对此问题,利用博弈论展开定量研究。首先通过引入两阶段博弈形式化企业竞争战略选择过程,并用二层规划刻画该博弈过程,通过求解该二层二次规划获得两期博弈的均衡解;据此对处于价格竞争市场中的两个企业竞争行为选择过程进行仿真,验证了根据两期博弈进行的企业竞争行为的分类和选择的正确性。     

MU-MIMO单比特ADC系统中软输出检测算法

低精度量化技术能解决毫米波通信射频链高能耗问题而使相关的接收技术受到广泛关注。本文针对应用于单比特量化上行多用户多输入多输出(multiuser multiple input multiple output, MU-MIMO)系统的软输出检测(soft output detection, SOD)算法计算复杂度高的问题，针对软输出检测(soft output detection, SOD)算法计算复杂度高的问题,结合串行干扰消除算法与SOD算法,提出排序多用户单比特串行干扰消除SOD(ordered multiuser one-bit successive interference cancellation SOD, OMuOSIC-SOD)算法,所提算法计算复杂度更低且能动态调整。在基于polar编码的MU-MIMO系统中的仿真结果表明, OMuOSIC-SOD算法随着同时检测的用户数目增加,误帧率(frame error rate, FER)逐渐接近SOD检测算法;在8×32 MIMO中, FER为10^-3时, OMuOSIC-SOD算法每次检测的用户数目每增加2个,得到约0.6 dB的性能增益。综上所述，所提算法可以通过调整每次检测的用户数量来调整检测性能，提升了算法的灵活性。