弹性需求下公交网络系统票价结构的优化

对具有弹性需求的城市公交网络系统票价的合理设定问题进行了研究分析.考虑到公交收费结构的变化会影响乘客的出行需求量和乘客对路径选择行为,将这一问题描述为一个两级数学规划问题.上一级问题是寻求收益最大的优化问题,下一级问题是估计乘客在网络上的流量分布的具有弹性需求的随机用户平衡分配模型.鉴于两级规划问题的非凸性,提出基于灵敏度分析的启发式算法.最后,给出一个仿真算例说明提出的模型和算法的合理性.     

Stochastic Generalized Gradient Methods for Training Nonconvex Nonsmooth Neural Networks

The paper observes a similarity between the stochastic optimal control of discrete dynamical systems and the learning multilayer neural networks. It focuses on contemporary deep networks with nonconvex nonsmooth loss and activation functions. The machine learning problems are treated as nonconvex nonsmooth stochastic optimization problems. As a model of nonsmooth nonconvex dependences, the so-called generalized-differentiable functions are used. The backpropagation method for calculating stochastic generalized gradients of the learning quality functional for such systems is substantiated basing on Hamilton–Pontryagin formalism. Stochastic generalized gradient learning algorithms are extended for training nonconvex nonsmooth neural networks. The performance of a stochastic generalized gradient algorithm is illustrated by the linear multiclass classification problem.

     

基于lP范数的非凸低秩张量最小化

在低秩矩阵、张量最小化问题中,凸函数容易求得最优解,而非凸函数可以得到更低秩的局部解.文中基于非凸替换函数的低秩张量恢复问题,提出基于l_p范数的非凸张量模型.采用迭代加权核范数算法求解模型,实现低秩张量最小化.在合成数据和真实图像上的大量实验验证文中方法的恢复性能.     

Optimal design of continuous time irrational filter with a set of fractional order gammatone components via norm relaxed sequential quadratic programming approach

This paper proposes a continuous time irrational filter structure via a set of the fractional order Gammatone components instead of via a set of integer order Gammatone components. The filter design problem is formulated as a nonsmooth and nonconvex infinite constrained optimization problem. The nonsmooth function is approximated by a smooth operator. The domain of the constraint functions is sampled into a set of finite discrete points so the infinite constrained optimization problem is approximated by a finite constrained optimization problem. To find a near globally optimal solution, the norm relaxed sequential quadratic programming approach is applied to find the locally optimal solutions of this nonconvex optimization problem. The current or the previous locally optimal solutions are kicked out by adding the random vectors to them. The locally optimal solutions with the lower objective functional values are retained and the locally optimal solutions with the higher objective functional values are discarded. By iterating the above procedures, a near globally optimal solution is found. The designed filter is applied to perform the denoising. It is found that the signal to noise ratio of the designed filter is higher than those of the filters designed by the conventional gradient descent approach and the genetic algorithm method, while the required computational power of our proposed method is lower than those of the conventional gradient descent approach and the genetic algorithm method. Also, the signal to noise ratio of the filter with the fractional order Gammatone components is higher than those of the filter with the integer order Gammatone components and the conventional rational infinite impulse response filters.     

一种基于混沌粒子群优化的OFDM系统资源分配算法

针对无线多用户正交频分复用（OFDM）系统中功率分配问题,提出一种基于效用函数最大化框架的资源分配算法.在实际网络环境中,此类最优化算法为非凸的,利用经典最优化方法很难解决.为此,将智能优化中的粒子群方法应用到非凸优化算法设计中,并针对粒子群优化容易陷入局部极值点的问题,将Logistic混沌搜索嵌入PSO算法中,提出混沌粒子群算法.与同类算法相比,所提出算法不仅有效解决了非凸性问题,而且可以使系统具有更好的性能.     

An Alternating Augmented Lagrangian method for constrained nonconvex optimization

ABSTRACT

We consider the problem of minimizing a smooth nonconvex function over a structured convex feasible set, that is, defined by two sets of constraints that are easy to treat when considered separately. In order to exploit the structure of the problem, we define an equivalent formulation by duplicating the variables and we consider the augmented Lagrangian of this latter formulation. Following the idea of the Alternating Direction Method of Multipliers (ADMM), we propose an algorithm where a two-blocks decomposition method is embedded within an augmented Lagrangian framework. The peculiarities of the proposed algorithm are the following: (1) the computation of the exact solution of a possibly nonconvex subproblem is not required; (2) the penalty parameter is iteratively updated once an approximated stationary point of the augmented Lagrangian is determined. Global convergence results are stated under mild assumptions and without requiring convexity of the objective function. Although the primary aim of the paper is theoretical, we perform numerical experiments on a nonconvex problem arising in machine learning, and the obtained results show the practical advantages of the proposed approach with respect to classical ADMM.     

A heuristic method for simultaneous tower and pattern-free field optimization on solar power systems

A heuristic method for optimizing a solar power tower system is proposed, in which both heliostat field (heliostat locations and number) and the tower (tower height and receiver size) are simultaneously considered.Maximizing the thermal energy collected per unit cost leads to a difficult optimization problem due to its characteristics: it has a nonconvex black-box objective function with computationally expensive evaluation and nonconvex constraints.The proposed method sequentially optimizes the field layout for a given tower configuration and then, the tower design is optimized for the previously obtained field layout. A greedy-based heuristic algorithm is presented to address the heliostat location problem. This algorithm follows a pattern-free method. The only constraints to be considered are the field region and the nonconvex constraints (which allow heliostats to not collide).The absence of a geometrical pattern to design the field and the simultaneous optimization of the field and the tower designs make this approach different from the existing ones. Our method is compared against other proposals in the literature of heliostat field optimization.     

Nonconvex dynamic spectrum allocation for cognitive radio networks via particle swarm optimization and simulated annealing

Dynamic spectrum access is a promising technique designed to meet the challenge of rapidly growing demands for broadband access in cognitive radio networks. By utilizing the allocated spectrum, cognitive radio devices can provide high throughput and low latency communications. This paper introduces an efficient dynamic spectrum allocation algorithm in cognitive radio networks based on the network utility maximization framework. The objective function in this optimization problem is always nonconvex, which makes the problem difficult to solve. Prior works on network resource optimization always transformed the nonconvex optimization problem into a convex one under some strict assumptions, which do not meet the actual networks. We solve the nonconvex optimization problem directly using an improved particle swarm optimization (PSO) method. Simulated annealing (SA), combined with PSO to form the PSOSA algorithm, overcomes the inherent defects and disadvantages of these two individual components. Simulations show that the proposed solution achieves significant throughput compared with existing approaches, and it is efficient in solving the nonconvex optimization problem.     

基于粒子群的CDMA功率和速率联合控制算法

提出了基于效用函数的CDMA网络下行链路的功率和速率联合控制最优化算法.在这类算法中,效用函数为非凸函数,经典的最优化理论很难解决这类问题.将粒子群优化方法应用于算法的非凸性设计,并通过仿真算例证明了该算法能有效解决非凸优化问题,且可保证系统的公平性.     

Convergence of alternating direction method for minimizing sum of two nonconvex functions with linear constraints

The efficiency of the classic alternating direction method of multipliers has been exhibited by various applications for large-scale separable optimization problems, both for convex objective functions and for nonconvex objective functions. While there are a lot of convergence analysis for the convex case, the nonconvex case is still an open problem and the research for this case is in its infancy. In this paper, we give a partial answer on this problem. Specially, under the assumption that the associated function satisfies the Kurdyka–?ojasiewicz inequality, we prove that the iterative sequence generated by the alternating direction method converges to a critical point of the problem, provided that the penalty parameter is greater than 2L, where L is the Lipschitz constant of the gradient of one of the involved functions. Under some further conditions on the problem's data, we also analyse the convergence rate of the algorithm.     

A strip-splitting-based optimal algorithm for decomposing a query window into maximal quadtree blocks

Decomposing a query window into maximal quadtree blocks is a fundamental problem in quadtree-based spatial database. Recently, Proietti presented the first optimal algorithm for solving this problem. Given a query window of size n/sub 1//spl times/n/sub 2/, Proietti's algorithm takes O(n/sub 1/) time, where n/sub 1/=max(n/sub 1/, n/sub 2/). Based on a strip-splitting approach, we present a new optimal algorithm for solving the same problem. Experimental results reveal that our proposed algorithm is quite competitive with Proietti's algorithm.     

A matrix-free line-search algorithm for nonconvex optimization

In this paper, we have developed a new algorithm for solving nonconvex large-scale problems. The new algorithm performs explicit matrix modifications adaptively, mimicing the implicit modifications used by trust-region methods. Thus, it shares the equivalent theoretical strength of trust-region approaches, without needing to accommodate an explicit step-size constraint. We show that the algorithm is well suited for solving very large-scale nonconvex problems whenever Hessian-vector products are available. The numerical results on the CUTEr problems demonstrate the effectiveness of this approach in the context of a line-search method for large-scale unconstrained nonconvex optimization. Moreover, applications in deep-learning problems further illustrate the usefulness of this algorithm. It does not share any of the prohibitive traits of popular matrix-free algorithms such as truncated conjugate gradient (CG) due to the difficult nature of deep-learning problems. Thus the proposed algorithm serves to bridge the gap between the needs of data-mining community and existing state-of-the-art approaches embraced foremost by the optimization community. Moreover, the proposed approach can be realized with minimal modification to the CG algorithm itself with negligible storage and computational overhead.     

Analysis of steel bolted connections by means of a nonsmooth optimization procedure

A nonsmooth optimization procedure is herein proposed for the investigation of the bearing resistance of steel bolted connections. Taking into account the presence of nonlinear effects such as e.g. plasticity and interface interaction, and describing the resistance in bearing strength by means of a nonmonotone multi-valued reaction-displacement law obtained by experimental testing, the problem is formulated as a hemivariational inequality one. The latter is equivalent to a substationarity problem of the potential energy of the connection under investigation. This problem can be effectively treated numerically by applying an appropriately chosen nonconvex, nonsmooth optimization algorithm and in particular, the NSOLIB optimization algorithm based on the proximal bundle method has been applied. Two numerical examples whose results are compared to experimental testing results demonstrate the effectiveness of the proposed method.     

信赖域共轭梯度法求解二次规划逆问题

为了有效地求解二次规划逆问题,提出了一种求解其对偶问题的子问题的光滑化信赖域共轭梯度法。该方法采用增广拉格朗日法求解其对偶问题,引入光滑函数将对偶问题的子问题转换成连续的无约束优化问题,将信赖域法与共轭梯度法结合,设计出求解二次规划逆问题的算法流程。数值实验结果表明,该方法可行且有效,与牛顿法相比,更适合求解大规模问题。     

Minimizing the multimodal functions with Ant Colony Optimization approach

The ant colony optimization (ACO) algorithms, which are inspired by the behaviour of ants to find solutions to combinatorial optimization problem, are multi-agent systems. This paper presents the ACO-based algorithm that is used to find the global minimum of a nonconvex function. The algorithm is based on that each ant searches only around the best solution of the previous iteration. This algorithm was tested on some standard test functions, and successful results were obtained. Its performance was compared with the other algorithms, and was observed to be better.     

Self-organizing maps by difference of convex functions optimization

We offer an efficient approach based on difference of convex functions (DC) optimization for self-organizing maps (SOM). We consider SOM as an optimization problem with a nonsmooth, nonconvex energy function and investigated DC programming and DC algorithm (DCA), an innovative approach in nonconvex optimization framework to effectively solve this problem. Furthermore an appropriate training version of this algorithm is proposed. The numerical results on many real-world datasets show the efficiency of the proposed DCA based algorithms on both quality of solutions and topographic maps.     

On convex transformability and the solution of nonconvex problems via the dual of Falk

In structural optimization, most successful sequential approximate optimization (SAO) algorithms solve a sequence of strictly convex subproblems using the dual of Falk. Previously, we have shown that, under certain conditions, a nonconvex nonlinear (sub)problem may also be solved using the Falk dual. In particular, we have demonstrated this for two nonconvex examples of approximate subproblems that arise in popular and important structural optimization problems. The first is used in the SAO solution of the weight minimization problem, while the topology optimization problem that results from volumetric penalization gives rise to the other. In both cases, the nonconvex subproblems arise naturally in the consideration of the physical problems, so it seems counter productive to discard them in favor of using standard, but less well-suited, strictly convex approximations. Though we have not required that strictly convex transformations exist for these problems in order that they may be solved via a dual approach, we have noted that both of these examples can indeed be transformed into strictly convex forms. In this paper we present both the nonconvex weight minimization problem and the nonconvex topology optimization problem with volumetric penalization as instructive numerical examples to help motivate the use of nonconvex approximations as subproblems in SAO. We then explore the link between convex transformability and the salient criteria which make nonconvex problems amenable to solution via the Falk dual, and we assess the effect of the transformation on the dual problem. However, we consider only a restricted class of problems, namely separable problems that are at least C ¹ continuous, and a restricted class of transformations: those in which the functions that represent the mapping are each continuous, monotonic and univariate.     

基于增补小波变换和PCNN的NSCT域图像融合算法

针对传统NSCT图像融合算法存在的不足,提出一种基于增补小波变换和PCNN的NSCT域图像融合算法。首先对源图像进行NSCT分解,生成一系列低频和高频分量。对低频分量利用二维小波分解,生成一个低频和三个方向分量,对低频分量利用局部区域能量加权方法融合,三个方向分量利用改进的高斯加权SML方法融合;对NSCT分解的高频分量,分为对最高层和其它层的融合,最高层利用改进的高斯加权SML方法融合,其余层利用边缘梯度信息激励PCNN方法融合。最后对NSCT进行逆变换得到融合图像。实验结果证实了所提算法的有效性。     

Heuristic Kalman Algorithm for Solving Optimization Problems

The main objective of this paper is to present a new optimization approach, which we call heuristic Kalman algorithm (HKA). We propose it as a viable approach for solving continuous nonconvex optimization problems. The principle of the proposed approach is to consider explicitly the optimization problem as a measurement process designed to produce an estimate of the optimum. A specific procedure, based on the Kalman method, was developed to improve the quality of the estimate obtained through the measurement process. The efficiency of HKA is evaluated in detail through several nonconvex test problems, both in the unconstrained and constrained cases. The results are then compared to those obtained via other metaheuristics. These various numerical experiments show that the HKA has very interesting potentialities for solving nonconvex optimization problems, notably concerning the computation time and the success ratio.      

基于有效维度特征的手背静脉识别算法

针对手背静脉识别过程中采集的图像出现干扰信息的问题,提出了一种基于有效维度特征的识别算法。首先,该算法对采集的图像进行自适应中值滤波去噪;其次,对图像进行分块处理,并基于混合高斯模型与梯度信息对子图像提取特征;然后,依据子图像间特征相似性,提出了判断子图像是否为干扰信息的方法;最后,融合所有真实静脉区域的特征,形成特征向量,并采用基于稀疏表示的算法对多种有效维度下的特征向量进行匹配。实验表明,该算法具有较高的准确识别率,即使采集的手背静脉图像存在部分遮挡,算法依然能够获得较好的识别效果。