A nonlinear variational Neumann's type problem

In this work I consider a nonlinear Neumann's problem involving a maximal monotone operator. The existence of a H²-solution was proved in ([4]). Here I prove a weak existence theorem, the uniqueness of a weak continuous solution, the continuous dependence on the data and I state a priori estimate. At the end by applying the finite element method, I obtain approximate solutions, by means of a perturbed variational problem and an estimate of the discretization error. An algorithm is explained.     

Robot reachability problem: A nonlinear optimization approach

The reachability of a robot manipulator to a target is defined as its ability to move its joints and links in free space in order for its hand to reach the given target. This paper presents a way of testing the reachability of a robot to given target. The target could be a three dimensional object represented by a cuboid, a line or merely a point.The reachability test problem is transformed into a nonlinear optimization problem, which is solved by using the Tunneling Algorithm [1–3].The paradigm of the Tunneling Algorithm is described in detail. Several examples of testing the reachability of two robots to given targets are presented and the results are compared with that of the existing RGRG algorithm [5]. The results of comparisons show that the Tunneling Algorithm is better than the RGRG algorithm. It can always obtain the correct answers of testing, and it is effective and suitable to solve the reachability test problem.This project is partially supported by a grant from Martin Marietta (ORNL) 19x-55902V. Also this project is partially funded by ONR grant N00014-94-1-0343.     

A stochastic production planning problem with nonlinear cost

Most production planning models are deterministic and often assume a linear relation between production volume and production cost. In this paper, we investigate a production planning problem in a steel production process considering the energy consumption cost which is a nonlinear function of the production quantity. Due to the uncertain environment, the production demands are stochastic. Taking a scenario-based approach to express the stochastic demands according to the knowledge of planners on the demand distributions, we formulate the stochastic production planning problem as a mixed integer nonlinear programming (MINLP) model.Approximated with the piecewise linear functions, the MINLP model is transformed into a mixed integer linear programming model. The approximation error can be improved by adjusting the linearization ranges repeatedly. Based on the piecewise linearization, a stepwise Lagrangian relaxation (SLR) heuristic for the problem is proposed where variable splitting is introduced during Lagrangian relaxation (LR). After decomposition, one subproblem is solved by linear programming and the other is solved by an effective polynomial time algorithm. The SLR heuristic is tested on a large set of problem instances and the results show that the algorithm generates solutions very close to optimums in an acceptable time. The impact of demand uncertainty on the solution is studied by a computational discussion on scenario generation.     

A neural-network method for the nonlinear servomechanism problem

The solution of the nonlinear servomechanism problem relies on the solvability of a set of mixed nonlinear partial differential and algebraic equations known as the regulator equations. Due to the nonlinear nature, it is difficult to obtain the exact solution of the regulator equations. This paper proposes to solve the regulator equations based on a class of recurrent neural network, which has the features of a cellular neural network. This research not only represents a novel application of the neural networks to numerical mathematics, but also leads to an effective approach to approximately solving the nonlinear servomechanism problem. The resulting design method is illustrated by application to the well-known ball and beam system.     

A distribution-free newsvendor problem with nonlinear holding cost

In this paper, we analyse a single-period newsvendor model to determine the optimal order quantity where the customers’ balking occurs.This scenario occurs when the customers are opposed to buy a product for various reasons, such as decreasing quality of product, product is not as good as fresh when it reaches under a threshold level, etc. The model is investigated by assuming that the holding cost function depends on order quantity and the inventory level at which customer balking occurs depends on holding cost. The model allows partial backlogging and permits part of the backlogged shortages to turn into lost sales. We develop the model without taking any specific distributional form of demand, only assuming the mean and the variance of the distribution of demand. Finally, we illustrate the model by numerical examples and compare our distribution-free model with the specific distributional form of demand.     

The nonlinear lamb problem

The two-dimensional problem of finite amplitude wave propagation in a nonlinear half-space excited by a normal and tangential time-dependent line loads is considered. A numerical scheme is developed and applied. The reliability of the numerical procedure is examined in some special cases by comparison with the corresponding analytical solutions which can be deduced for those cases. Vertical and horizontal displacements in the nonlinear half-space are presented and compared with the behavior of those obtained in the corresponding linear problem. It is noted that the symmetry of the horizontal displacements and the antisymmetry of the vertical displacements which are present in the linear halfspace for the case of tangential loading are completely destroyed in the nonlinear problem and that significant vertical displacements are obtained at stations beneath the load.     

A genetic algorithm for interval nonlinear integer programming problem

In this paper, we formulate an optimal design of system reliability problem as a nonlinear integer programming problem with interval coefficients, transform it into a single objective nonlinear integer programming problem without interval coefficients, and solve it directly with keeping nonlinearity of the objective function by using Genetic Algorithms (GA). Also, we demonstrate the efficiency of this method with incomplete Fault Detecting and Switching (FDS) for allocating redundant units.     

A CNN-based computational algorithm for nonlinear image diffusion problem

Multimedia Tools and Applications - In the past, several partial differential equations (PDEs) based methods have been widely studied in image denoising. While solving these methods numerically,...     

A nonlinear control law for a stochastic infinite time problem

The expectation of a particular class of nonquadratic performance criterion involving even powers of the state variables up to sixth order is minimized, over an infinite horizon, subject to a linear stochastic system. The process noise is composed of both additive white noise and state dependent white noise processes. The resulting controller is composed of a linear and cubic function of the state. Furthermore, this controller depends upon the noise variances of both the additive and state dependent noise processes. For partially observable systems with no state dependent noise, similar results as the completely observable system are implied by the separation theorem. For state dependent noise alone, a stochastic Lyapunov function is obtained from which simple probability bounds for the trajectory to exit from a given region of the state space are determined.     

A test problem for numerical schemes for nonlinear hyperbolic equations

In this note we solve a model problem to test the applicability of numerical schemes for hyperbolic partial differential equations with shock-containing solutions. This test problem was used successfully in [1]in order to compare analytic and numerical solutions. The construction is made possible by considering the development of a jump discontinuity in the solution of scalar quasilinear equations with piecewise smooth data. This is a simple generalization of a discussion by Lax [2].     

A remark on the problem of semiglobal nonlinear output regulation

This paper shows how the method for semiglobal stabilization by output feedback, based on high-gain observer and saturation, and the method for structurally stable regulation, based on system immersion, can be effectively coupled in order to solve problems of robust output regulation in the presence of parameter uncertainties ranging over compact sets     

A monotone Newton multisplitting method for the nonlinear complementarity problem with a nonlinear source term

In this paper, we develop a Newton multisplitting method for the nonlinear complementarity problem with a nonlinear source term in which the multisplitting method is used as secondary iterations to approximate the solutions for the resulting linearized subproblems. We prove the monotone convergence theorem for the proposed method under proper conditions.     

A neural network approach for solving nonlinear bilevel programming problem

A neural network model is presented for solving nonlinear bilevel programming problem, which is a NP-hard problem. The proposed neural network is proved to be Lyapunov stable and capable of generating approximal optimal solution to the nonlinear bilevel programming problem. The asymptotic properties of the neural network are analyzed and the condition for asymptotic stability, solution feasibility and solution optimality are derived. The transient behavior of the neural network is simulated and the validity of the network is verified with numerical examples.     

A computational study of a nonlinear minsum facility location problem

A discrete location problem with nonlinear objective is addressed. A set of p plants is to be open to serve a given set of clients. Together with the locations, the number p of facilities is also a decision variable. The objective is to minimize the total cost, represented as the transportation cost between clients and plants, plus an increasing nonlinear function of p.     

用于求解井下最短逃生路径问题的离散萤火虫算法

针对煤矿井下避灾路线最短路径求解问题,提出了一种新的离散萤火虫算法。该算法通过采用转移概率方法初始化萤火虫个体,并提出一种新的有效编码和解码方式,重新定义萤火虫的空间距离、最大荧光亮度和相对荧光亮度等,使得萤火虫个体的状态可表示为一条从起点到目标点的有效路径。为增加解的多样性及防止计算结果陷入局部最优解,以一定概率对萤火虫代表的路径执行扰动操作,经过多次迭代计算后,可得到所要求解的最短路径。实验结果表明,该算法在种群规模较小、迭代次数较少的情况下可以收敛到最优解,具有较强的收敛性和灵活性,可用于求解任何实际的最短路径问题。