The dual parameterization approach to optimal least square FIRfilter design subject to maximum error constraints

This paper is concerned with the design of linear-phase finite impulse response (FIR) digital filters for which the weighted least square error is minimized, subject to maximum error constraints. The design problem is formulated as a semi-infinite quadratic optimization problem. Using a newly developed dual parameterization method in conjunction with the Caratheodory's dimensional theorem, an equivalent dual finite dimensional optimization problem is obtained. The connection between the primal and the dual problems is established. A computational procedure is devised for solving the dual finite dimensional optimization problem. The optimal solution to the primal problem can then be readily obtained from the dual optimal solution. For illustration, examples are solved using the proposed computational procedure     

A Globally Optimal Bilinear Programming Approach to the Design of Approximate Hilbert Pairs of Orthonormal Wavelet Bases

It is understood that the Hilbert transform pairs of orthonormal wavelet bases can only be realized approximately by the scaling filters of conjugate quadrature filter (CQF) banks. In this paper, the approximate FIR realization of the Hilbert transform pairs is formulated as an optimization problem in the sense of the lp (p=1, 2, or infinite) norm minimization on the approximate error of the magnitude and phase conditions of the scaling filters. The orthogonality and regularity conditions of the CQF bank pairs are taken as the constraints of such an optimization problem. Whereafter the branch and bound technique is employed to obtain the globally optimal solution of the resulting bilinear program optimization problem. Since the orthogonality and regularity conditions are explicitly taken as the constraints of our optimization problem, the attained solution is an approximate Hilbert transform pair satisfying these conditions exactly. Some orthogonal wavelet bases designed herein demonstrate that our design scheme is superior to those that have been reported in the literature. Moreover, the designed orthogonal wavelet bases show that minimizing the l ₁ norm of the approximate error should be advocated for obtaining better approximated Hilbert pairs.     

Capacity Planning of DiffServ Networks with Best-Effort and Expedited Forwarding Traffic

For networks providing a specific level of service guarantees, capacity planning is an imperative part of network management. Accurate dimensioning is especially important in DiffServ networks, where no per-flow signaling or control exists. In this paper, we address the problem of capacity planning for DiffServ networks with only Expedited Forwarding (EF) and best effort (BE) traffic classes. The problem is formulated as an optimization problem, where the total link cost is minimized, subject to the performance constraints of both EF and BE classes. The edge to edge EF demand pairs and the BE demands on each link are given. The variables to be determined are the non-bifurcated routing of EF traffic, and the discrete link capacities. We show that Lagrangian relaxation and subgradient optimization methods can be used to effectively solve the problem. Computational results show that the solution quality is verifiably good while the running time remains reasonable on practical-sized networks. This represents the first work for capacity planning of multi-class IP networks with non-linear performance constraints and discrete link capacity constraints.     

用于资源动态预留的航天测控资源配置优化算法

针对航天测控资源配置优化问题这类约束条件繁杂且数量众多的组合优化问题,提出了可用于资源动态预留的航天测控资源配置优化算法。具体来讲,考虑测控设备和航天器执行任务的唯一性约束以及时间窗口冲突约束,建立了基于原子型任务调度的0-1整数规划模型;设计了能将实际需求和求解算法进行解耦的求解框架,并基于最大化利用测控资源的思想获得了可回溯的并行最佳优先搜索算法。仿真结果表明,所提算法达到了能在国内东部、西部、南部和北部四大测控区域中更加均衡地动态预留出更多、更重要测控设备的资源配置优化效果。     

一种多约束稀布线阵的天线综合方法

 针对有阵元间距上、下限约束与口径约束的稀布直线阵列综合问题,提出了一种基于向量映射的改进遗传算法.该方法将遗传变量与阵元间距按照特定的关系进行映射,从而使阵元间距的强约束优化问题转换为仅含遗传变量上、下限约束的优化问题,从根本上避免了遗传操作中的不可行解.通过抑制天线峰值旁瓣电平(PSLL)的稀布阵仿真,验证了该方法的有效性和稳健性,且能获得比现有方法更高的优化效率.     

Optimal Resource Allocation Scheme in a Multirate Overlapped Optical CDMA System

This paper addresses the problem of resource allocation in a multiservice optical network based on an overlapped code-division-multiple-access system. A joint transmission power and overlapping coefficient (transmission rate) allocation strategy is provided via the solution of a constrained convex quadratic optimization problem. The solution of this problem maximizes the aggregate throughput subject to peak laser transmission power constraints. The optimization problem is solved in a closed form, and the resource allocation strategy is simple to implement in an optical network. Simulation results are presented, showing a total agreement between the derived analytical solution and the one obtained using a numerical search method. In addition, analytical and numerical results show that the proposed resource allocation strategy can offer substantial improvement in the system throughput.     

On the optimality of max–min fairness in resource allocation

In this work, a basic resource allocation (RA) problem is considered, where a fixed capacity must be shared among a set of users. The RA task can be formulated as an optimization problem, with a set of simple constraints and an objective function to be minimized. A fundamental relation between the RA optimization problem and the notion of max–min fairness is established. A sufficient condition on the objective function that ensures the optimal solution is max–min fairness is provided. Notably, some important objective functions like least squares and maximum entropy fall in this case. Finally, an application of max–min fairness for overload protection in 3G networks is considered.     

Global Optimum Design of Uniform FIR Filter Bank With Magnitude Constraints

The optimum design of a uniform finite impulse response filter bank can be formulated as a nonlinear semi-infinite optimization problem. However, this optimization problem is nonconvex with infinitely many inequality constraints. In this paper, we propose a new hybrid approach for solving this highly challenging nonlinear, nonconvex semi-infinite optimization problem. In this approach, a gradient-based method is used in conjunction with a filled function method to determine a global minimum of the problem. This new hybrid approach finds an optimal result independent of the initial guess of the solution. The method is applied to some existing examples. The results obtained are superior to those obtained by other existing methods.      

基于违约解转化法的遗传算法及其性能分析

遗传算法在求解约束优化问题时,面临的关键问题之一就是如何处理约束条件.本文提出了一种基于违约解转化法的遗传算法(CIFGA),也就是遗传算法在处理约束条件时,在每一进化代遗传操作后,把所有违反约束条件的个体逐个转化成满足约束条件的个体,整个遗传群体保持不变,经过一代代的进化,最终求出约束问题的最优解.对于采用二进制编码和实数编码的CIFGA,理论证明了其收敛性.测试试验结果表明:CIFGA有较好的算法性能和解决约束优化问题的能力.     

Robust Tomlinson-Harashima Precoders for Multiuser MISO Downlink with Imperfect CSI

In this paper, we consider robust non-linear precoding for the downlink of a multiuser multiple-input single-output (MISO) communication system in the presence of imperfect channel state information (CSI). The base station (BS) is equipped with multiple transmit antennas and each user terminal is equipped with a single receive antenna. We propose two robust Tomlinson-Harashima precoder (THP) designs. The first design is based on the minimization of the total BS transmit power under constraints on the mean square error (MSE) at the individual user receivers. We show that this problem can be solved by an iterative procedure, where each iteration involves the solution of a pair of convex optimization problems that can be solved efficiently. A robust linear precoder with MSE constraints can be obtained as a special case of this robust THP. The second design is based on the minimization of a stochastic function of the sum MSE under a constraint on the total BS transmit power. We formulate this design problem as an optimization problem that can be solved by the method of alternating optimization, the application of which results in a second-order cone program that can be numerically solved efficiently. Simulation results illustrate the improvement in performance of the proposed precoders compared to other robust linear and non-linear precoders in the literature.     

Branch-and-bound redundancy optimization for a series system withmultiple-choice constraints

This paper considers a redundancy optimization problem in which multiple-choice and resource constraints are incorporated. The problem is expressed as a nonlinear integer programming problem and is characterized as an NP-hard problem. The purpose of the paper is to develop a SSRP (solution space reduction procedure). Therefore, the problem is analyzed first to characterize some solution properties. An iterative SSRP is then derived using those solution properties. Finally, the iterative SSRP is used to define an efficient B&BP (branch-and-bound procedure) algorithm. Experimental tests show how dramatically the SSRP can work on removing any intermediately-found unnecessary decision variables from further consideration in solution search, and how efficient this B&BP is     

Optimum waveforms subject to both energy and peak–value constraints

For any stable linear system with kernel K(t, τ), we derive a formula for the input waveform W(t) which maximizes |R(T)| the absolute value of the output waveform at a prescribed time instant T, subject to the constraints that |W(t)| ≤ A and ∫-∞^∞[W(t)]²dt ≤ E, where A and E are prescribed positive constants. The input and output are related by the formula R(t) = ∫-∞^∞K(t, τ)W(τ)dτ. Roughly, the optimum W(t) can be found by scaling the system kernel function appropriately and then "clipping" it at the value A. The problem and the solution are closely related to the matched filter problem of radar theory and the "bang-bang" problem of optimal control theory and their solutions. The well-known results of these problems appear as special cases of our solution when A or E, respectively, becomes sufficiently large. Theoretically, this problem is of interest because of the incompatible nature of the constraints. That is, the combination of constraints prevents one from using standard optimization tools. Practically, in addition to its direct application in signal design, our solution can also be used indirectly, since it provides a standard of performance for more realistic situations where additional constraints, such as range resolution in radar, are important. The solution is justified in three different ways, providing a comparison of optimization techniques and an example of the Pontryagin Maximum Principle.     

Computation of 3-D velocity fields from 3-D cine CT images of a human heart

A method of computing the three-dimensional (3-D) velocity field from 3-D cine computer tomographs (CTs) of a beating heart is proposed. Using continuum theory, the authors develop two constraints on the 3-D velocity field generated by a beating heart. With these constraints, the computation of the 3-D velocity field is formulated as an optimization problem and a solution to the optimization problem is developed using the Euler-Lagrange method. The solution is then discretized for computer implementation. The authors present the results for both simulated images and clinical cine CT images of a beating heart.     

基于速率约束的OFDM中继链路能效最优资源分配策略

该文研究解码转发(DF)模式的OFDM中继链路的能效最大化资源分配问题。与现有典型的固定速率最小化发射功率或无约束最大化能效算法不同,该文考虑电路功率消耗的前提下,将问题建模为以最大化系统能效为目标,同时考虑用户最小速率需求、源节点S和中继节点R各自总发射功率约束下的联合子载波配对和最优功率分配问题。证明了速率和功率联合约束条件下中继链路全局能效最优解的唯一性,在此基础上提出一种低复杂度联合最优资源分配策略。仿真结果表明,该文所提方案能够在最小速率和S/R节点最大发射功率约束下自适应分配功率资源,实现系统能效最优,并能够降低链路的中断概率。     

Optimal apportionment of reliability and redundancy in seriessystems under multiple objectives

A multiobjective reliability apportionment problem for a series system with time-dependent reliability is presented. The resulting mathematical programming formulation determines the optimal level of component reliability and the number of redundant components at each stage. The problem is a multiobjective, nonlinear, mixed-integer mathematical programming problem, subject to several design constraints. Sequential unconstrained minimization techniques in conjunction with heuristic algorithms are used to find an optimum solution. A generalization of the problem in view of inherent vagueness in the objective and the constraint functions results in an ill-structured reliability apportionment problem. This multiobjective fuzzy optimization problem is solved using nonlinear programming. The computational procedure is illustrated through a numerical example. The fuzzy optimization techniques can be useful during initial stages of the conceptual design of engineering systems where the design goals and design constraints have not been clearly identified or stated, and for decision making problems in ill-structured situations     

Application of the surrogate constraints algorithm to optimal reliability design of systems

This paper presents a solution method for the reliability optimization problem of series-parallel systems which is formulated as a mixed integer nonlinear programming problem with multiple constraints. In the solution method, the optimal solution is obtained by solving the surrogate dual problem. Surrogate problems with only one constraint which appear in the optimization process are solved by a technique using dynamic programming. Some computational experiences are shown along with the comparison with an existing approach.     

A Simple Approach for Constrained Redundancy Optimization Problem

This paper provides a simple algorithm for the solution of the redundancy optimization problem in the presence of multiple linear constraints. Basicaily, the solution to an r-constraint problem is obtained successively from the solution of r-unconstrained problems. At each step, an active constraint is picked out, then the maximum gradient concept is used to find a closer point. The approach requires minimum effort and time for solution.     

Compensation of Multimode Fiber Dispersion Using Adaptive Optics via Convex Optimization

In this paper, we propose a provably optimal technique for minimizing intersymbol interference (ISI) in multimode fiber (MMF) systems using adaptive optics via convex optimization. We use a spatial light modulator (SLM) to shape the spatial profile of light launched into an MMF. We derive an expression for the system impulse response in terms of the SLM reflectance and the field patterns of the MMF principal modes (PMs). Finding optimal SLM settings to minimize ISI, subject to physical constraints, is posed as an optimization problem. We observe that our problem can be cast as a second-order cone program, which is a convex optimization problem. Its global solution can, therefore, be found with minimal computational complexity, and can be implemented using fast, low-complexity adaptive algorithms. We include simulation results, which show that this technique opens up an eye pattern originally closed due to ISI. We also see that, contrary to what one might expect, the optimal SLM settings do not completely suppress higher order PMs.     

Worst-case performance optimization for robust power control in downlink beamforming

In this paper,¹ we examine the problem of robust power control in a downlink beamforming environment under uncertain channel state information (CSI). We suggest that the method of power control using the lower bounds of signal-to-interference-and-noise ratio (SINR) is too pessimistic and will require significantly higher power in transmission than is necessary in practice. Here, a new robust downlink power control solution based on worst-case performance optimization is developed. Our approach employs the explicit modeling of uncertainties in the downlink channel correlation (DCC) matrices and optimizes the amount of transmission power while guaranteeing the worst-case performance to satisfy the quality of service (QoS) constraints for all users. This optimization problem is non-convex and intractable. In order to arrive at an optimal solution to the problem, we propose an iterative algorithm to find the optimum power allocation and worst-case uncertainty matrices. The iterative algorithm is based on the efficient solving of the worst-case uncertainty matrices once the transmission power is given. This can be done by finding the solutions for two cases: (a) when the uncertainty on the DCC matrices is small, for which a closed-form optimum solution can be obtained and (b) when the uncertainty is substantial, for which the intractable problem is transformed into a convex optimization problem readily solvable by an interior point method. Simulation results show that the proposed robust downlink power control using the approach of worst-case performance optimization converges in a few iterations and reduces the transmission power effectively under imperfect knowledge of the channel condition.     

Optimal Design of All-Pass Variable Fractional-Delay Digital Filters

This paper presents a computational method for the optimal design of all-pass variable fractional-delay (VFD) filters aiming to minimize the squared error of the fractional group delay subject to a low level of squared error in the phase response. The constrained optimization problem thus formulated is converted to an unconstrained least-squares (LS) optimization problem which is highly nonlinear. However, it can be approximated by a linear LS optimization problem which in turn simply requires the solution of a linear system. The proposed method can efficiently minimize the total error energy of the fractional group delay while maintaining constraints on the level of the error energy of the phase response. To make the error distribution as flat as possible, a weighted LS (WLS) design method is also developed. An error weighting function is obtained according to the solution of the previous constrained LS design. The maximum peak error is then further reduced by an iterative updating of the error weighting function. Numerical examples are included in order to compare the performance of the filters designed using the proposed methods with those designed by several existing methods.