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.     

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 sequential LQG approach to nonlinear tracking problem

A new approach, named the sequential LQG solution for nonlinear and nonstationary systems tracking problem, has been proposed in the article. Proposed method for tracking of a desired reference trajectory uses a state space model of the multivariable nonlinear/nonstationary system. The method involves three steps. The first step is the design of nominal trajectory using the predictive control technique. The second step is the sequential linearization of the nonlinear system around the fixed operating points, chosen in accordance to the plant dynamics changes. The third step involves the choice of the weighting matrices in the classical LQG controller design for the sequence of linearized models. The feasibility of the proposed method has been demonstrated through its application to the control of aircraft, represented by the six-degree-of-freedom model around the prespecified nominal trajectory.     

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.     

A solution of the nonlinear stochastic realization problem

In a recent paper we have constructed a solution of the nonlinear stochastic realization problem. The purpose of this paper is to announce the result to system theorists, as well as to motivate the approach by considering in detail some simple examples.     

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 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.     

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 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 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 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 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.     

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 human-computer interactive design program for a multisolution nonlinear problem

An idea of using a human-computer interactive program for an engineering design dealing with a nonlinear multisolution problem is introduced. The example shown is a program for a design of a drainage open channel. The hydraulics and geometry equations for triangular or trapezoidal ditches are to be satisfied by the ditch parameters, which are the side slopes (S_L and S_R), the depth (d) and the width of the bottom (W_b). The data are the flow rate (Q) and maximum allowable flow velocity. After W_b and one of the slopes for a nonsymmetrical ditch (S_L) are chosen by the designer, the other slope and d may be found as a solution of two nonlinear algebraic equations. Instead of trying to solve these equations, the program displays the two curves in s-d coordinate system. If the curves intersect, the designer types in the coordinates of the point of intersection. Otherwise, new curves for decreased velocity are displayed as the indicated key is pressed. The procedure may be continued until the curves intersect. The final parameters chosen by the designer are checked by the program to verify that the actual flow rate and velocity are within the required limits.     

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].