具有线性等式和不等式约束的非线性规划的一个算法

§1.引言既约梯度法是求解非线性规划的一类方法.我们目前只看到约束为线性等式或非线性等式的既约梯度法,对于线性不等式或非线性不等式约束的情形还没有相应的既约梯度法.如果通过松驰变量把线性不等式约束化成线性等式的情形处理,则要增加变量的维数,而这是与既约梯度法的思想背道而驰的.在本文中,我们结合既约梯度法与 Ritter在文献[3]中的思想,对具有线性等式和不等式约束的非线性规划问题给出了一种算法,它保留了既约梯度法降低维数的优点,又简化了 Ritter 在[3]中给出的算法.另外,我们还证明了算法的收敛性.

Distance Concentration-Based Artificial Immune Algorithm

The diversity, adaptation and memory of biological immune system attract much attention of researchers. Several optimal algorithms based on immune system have also been proposed up to now. The distance concentra- tion-based artificial immune algorithm (DCAIA) is proposed to overcome defects of the classical artificial immune al- gorithm (CAIA) in this paper. Compared with genetic algorithm (GA) and CAIA, DCAIA is good for solving the prob- lem of precocity,holding the diversity of antibody, and enhancing convergence rate.

Adaptive swarm-based routing in communication networks

Swarm intelligence inspired by the social behavior of ants boasts a number of attractive features, including adaptation, robustness and distributed, decentralized nature, which are well suited for routing in modern communication networks. This paper describes an adaptive swarm-based routing algorithm that increases convergence speed, reduces routing instabilities and oscillations by using a novel variation of reinforcement learning and a technique called momentum.Experiment on the dynamic network showed that adaptive swarm-based routing learns the optimum routing in terms of convergence speed and average packet latency.

Effective prediction of DEA model by neural network

In this paper,a fast neural network model for the forecasting of effective points by DEA model is proposed,which is based on the SPDS training algorithm.The SPDS training algorithm overcomes the drawbacks of slow convergent speed and partially minimum result for BP algorithm.Its training speed is much faster and its forecasting precision is much better than those of BP algorithm.By numeric examples,it is showed that adopting the neural network model in the forecasting of effective points by DEA model is valid.

Global optimization by small-world optimization algorithm based on social relationship network

A fast global convergence algorithm, small-world optimization (SWO), was designed to solve the global optimization problems, which was inspired from small-world theory and six degrees of separation principle in sociology. Firstly, the solution space was organized into a small-world network model based on social relationship network. Secondly, a simple search strategy was adopted to navigate into this network in order to realize the optimization. In SWO, the two operators for searching the short-range contacts and long-range contacts in small-world network were corresponding to the exploitation and exploration, which have been revealed as the common features in many intelligent algorithms. The proposed algorithm was validated via popular benchmark functions and engineering problems. And also the impacts of parameters were studied. The simulation results indicate that because of the small-world theory, it is suitable for heuristic methods to search targets efficiently in this constructed small-world network model. It is not easy for each test mail to fall into a local trap by shifting into two mapping spaces in order to accelerate the convergence speed. Compared with some classical algorithms, SWO is inherited with optimal features and outstanding in convergence speed. Thus, the algorithm can be considered as a good alternative to solve global optimization problems.

Multi-strategy Differential Evolution Algorithm for QoS Multicast Routing

This paper studies the difference algorithm parameters characteristic of the multicast routing problem, and to compare it with genetic algorithms. The algorithm uses the path of individual coding, combined with the differential cross-choice strategy and operations optimization. Finally, we simulated 30 node networks, and compared the performance of genetic algorithm and differential evolution algorithm. Experimental results show that multi-strategy Differential Evolution algorithm converges faster and better global search ability and stability.

Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints

Mathematical programs with complementarity constraints(MPCC) is an important subclass of MPEC.It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem.In this paper,we propose a new smoothing method for MPCC by using the aggregation technique.A new SQP algorithm for solving the MPCC problem is presented.At each iteration,the master direction is computed by solving a quadratic program,and the revised direction for avoiding the Maratos effect is generated by an explicit formula.As the non-degeneracy condition holds and the smoothing parameter tends to zero,the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem,its convergence rate is superlinear.Some preliminary numerical results are reported.

A NEW SOLUTION MODEL OF NONLINEAR DYNAMIC LEAST SQUARE ADJUSTMENT

The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.

A CLASS OF REVISED BROYDEN ALGORITHMS

In this paper, we discuss the convergence of the Broyden algorithms withrevised search direction. Under some inexact line searches, we prove that the algorithms areglobally convergent for continuously differentiable functions and the rate of convergence of thealgorithms is one-step superlinear and n-step second-order for uniformly convex objective functions.

Robust Optimization for the Correlated MIMO Downlink with Imperfect Channel State Information

To reduce the performance deterioration induced by imperfect channel state information(CSI) in correlated multiple input multiple output(MIMO) downlink,the linear transmit/receive filters should be optimized to be robust to imperfect CSI.A sub-optimization algorithm based on minimizing sum MSE conditional on available imperfect CSI estimates subject to a per-user power constraint is proposed.The algorithm adapts the existing MMSE algorithm from uncorrelated single-user MIMO system with perfect CSI to correlated MIMO downlink with imperfect CSI.Simulation shows that the suboptimal algorithm can effectively mitigate the performance loss induced by imperfect CSI and has a good convergence performance.In addition,the effect of spatial correlation on the performance of the proposed algorithm is also simulated.

Convergence and error estimate of cascade algorithms with infinitely supported masks in L_p(R^s)

The cascade algorithm plays an important role in computer graphics and wavelet analysis.In this paper,we first investigate the convergence of cascade algorithms associated with a polynomially decaying mask and a general dilation matrix in L p (R s) (1 p ∞) spaces,and then we give an error estimate of the cascade algorithms associated with truncated masks.It is proved that under some appropriate conditions if the cascade algorithm associated with a polynomially decaying mask converges in the L p-norm,then the cascade algorithms associated with the truncated masks also converge in the L p-norm.Moreover,the error between the two resulting limit functions is estimated in terms of the masks.