a new neural network for solving linear and quadratic programming problems a new neural network for solving linear and quadratic programming problems is presented and is shown to be globally convergent the new neural network improves existing neural networks for solving these problems it avoids the parameter turning problem it is capable of achieving the exact solutions and it uses only simple hardware in which no analog multipliers for variables are required furthermore the network solves both the primal problems and their dual problems simultaneously

a mixed type finite element approximation for radiation problems using fictitious domain method in the finite element approximation of the exterior helmholtz problem we propose an approximation method to implement the dtn mapping formulated as a pseudo differential operator on a computational artificial boundary the method is then combined with the fictitious domain method our method directly gives an approximation matrix for the sesqui linear form for the dtn mapping the eigenvalues of the approximation matrix are simplified to a closed form and can be computed efficiently by using a continued fraction formula solution outside the computational domain and the far field solution can also be computed efficiently by expressing them as operations of pseudo differential operators an inner artificial dtn boundary condition is also implemented by our method we prove the convergence of the solution of our method and compare the performance with the standard finite element approximation based on the fourier series expansion of the dtn operator the efficiency of our method is demonstrated through numerical examples

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

a fictitious domain method with mixed finite elements for elastodynamics we consider in this paper the wave scattering problem by an object with neumann boundary conditions in an anisotropic elastic body to obtain an efficient numerical method permitting the use of regular grids we follow a fictitious domain approach coupled with a first order velocity stress formulation for elastodynamics we first observe that the method does not always converge when the q 1 rm div q 0 finite element is used in particular the method converges for some scattering object geometries but not for others note that the convergence of the q 1 rm div q 0 finite element method was shown in e becache p joly and c tsogka siam j numer anal 39 2002 pp 2109 2132 for the elastodynamic problem in the absence of a scattering object i e without the coupling of the mixed finite elements with the fictitious domain method therefore we propose here a modification of the q 1 rm div q 0 element following the approach in e becache j rodriguez and c tsogka on the convergence of the fictitious domain method for wave equation problems technical report 5802 inria 2006 where the simpler acoustic case was considered to study the numerical properties of the new element we carry out a dispersion analysis several numerical simulations as well as a numerical convergence analysis show that the proposed method provides a good approximate solution

hybrid electric magnetic methods in eddy current problems we discuss a method of approximation of eddy current equations in bounded space that relies on the use of the electric field as primary variable in the conductive parts and of the magnetic field in the air theoretical issues about this hybrid approach are addressed is the problem well posed and one shows that edge elements offer a straightforward way to discretize such formulations the now popular a v method is then shown to come as a variant of this formulation in such a way that it allows the use of standard nodal elements however attention is called on the fact that the numerical convergence of the latter method may be in question

a unified variational formulation for the parabolic elliptic eddy current equations transient excitation currents generate electromagnetic fields which in turn induce electric currents in proximal conductors for slowly varying fields this can be described by the eddy current equations which are obtained by neglecting the dielectric displacement currents in maxwell s equations the eddy current equations are of parabolic elliptic type in insulating regions the field instantaneously adapts to the excitation quasistationary elliptic behavior while in conducting regions this adaptation takes some time due to the induced eddy currents parabolic behavior for fixed conductivity the equations are well studied however little rigorous mathematical results are known for the solution s dependence on the conductivity in particular for the solution s sensitivity with respect to the equation changing from elliptic to parabolic type in this work we derive a new unified variational formulation for the eddy current equations that is uniformly coercive with respect to the conductivity

a review of hopfield neural networks for solving mathematical programming problems the hopfield neural network hnn is one major neural network nn for solving optimization or mathematical programming mp problems the major advantage of hnn is in its structure can be realized on an electronic circuit possibly on a vlsi very large scale integration circuit for an on line solver with a parallel distributed process the structure of hnn utilizes three common methods penalty functions lagrange multipliers and primal and dual methods to construct an energy function when the function reaches a steady state an approximate solution of the problem is obtained under the classes of these methods we further organize hnns by three types of mp problems linear non linear and mixed integer the essentials of each method are also discussed in details some remarks for utilizing hnn and difficulties are then addressed for the benefit of successive investigations finally conclusions are drawn and directions for future study are provided

boundary conditions for the numerical solution of elliptic equations in exterior regions elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the weill posedness of the problem examples of practical applications include the helmholtz equation and laplace s equation computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition at infinity by a boundary condition on a finite artificial surface direct imposition of the condition at infinity along the finite boundary results in large errors a sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain estimates of the error due to the finite boundary are obtained for several cases computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions the examples are based on a finite element formulation but finite difference methods can also be used

jump dynamics due to jump datum of compressible viscous navier stokes flows in a bounded plane domain abstract in this paper when the initial density has a jump across an interior curve in a bounded domain we show unique existence piecewise regularity and jump discontinuity dynamics for the density and the velocity vector governed by the navier stokes equations of compressible viscous barotropic flows a critical difficulty is in controlling the gradient of the pressure across the jump curve this is resolved by constructing a vector function associated with the pressure jump value on the convecting curve and extending it to the whole domain

fictitious domain methods for the numerical solution of two dimensional scattering problems fictitious domain methods for the numerical solution of two dimensional scattering problems are considered the original exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a nonreflecting boundary condition on the artificial boundary first order second order and exact nonreflecting boundary conditions are tested on rectangular and circular boundaries the finite element discretizations of the corresponding approximate boundary value problems are performed using locally fitted meshes and the discrete equations are solved with fictitious domain methods a special finite element method using nonmatching meshes is considered this method uses the macro hybrid formulation based on domain decomposition to couple polar and cartesian coordinate systems a special preconditioner based on fictitious domains is introduced for the arising algebraic saddle point system such that the subspace of constraints becomes invariant with respect to the preconditioned iterative procedure the performance of the new method is compared to the fictitious domain methods both with respect to accuracy and computational cost

a novel recurrent neural network with finite time convergence for linear programming in this letter a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems finite time convergence of the proposed neural network is proved by using the lyapunov method compared with the existing neural networks for linear programming the proposed neural network is globally convergent to exact optimal solutions in finite time which is remarkable and rare in the literature of neural networks for optimization some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network

fast direct solution of the helmholtz equation with a perfectly matched layer or an absorbing boundary condition we consider the efficient numerical solution of the helmholtz equation in a rectangular domain with a perfectly matched layer pml or an absorbing boundary condition abc standard bilinear trilinear finite element discretization on an orthogonal mesh leads to a separable system of linear equations for which we describe a cyclic reduction type fast direct solver we present numerical studies to estimate the reflection of waves caused by an absorbing boundary and a pml and we optimize certain parameters of the layer to minimize the reflection copyright 2003 john wiley sons ltd

second order absorbing boundary conditions for the wave equation a solution for the corner problem the treatment of domains with corners in the problem of absorbing boundary conditions for the wave equation is very important from a practical point of view a technical difficulty appears as soon as conditions of order greater than or equal to 2 are considered a solution is proposed for the two dimensional case when second order conditions are used this solution consists of prescribing an adequate corner condition the problem thus obtained is analyzed theoretically and the condition is proved to be optimal the results obtained here are illustrated by numerical simulations some extensions to higher space dimensions and higher order conditions are proposed

a dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits in this paper a recurrent neural network called the dual neural network is proposed for online redundancy resolution of kinematically redundant manipulators physical constraints such as joint limits and joint velocity limits together with the drift free criterion as a secondary task are incorporated into the problem formulation of redundancy resolution compared to other recurrent neural networks the dual neural network is piecewise linear and has much simpler architecture with only one layer of neurons the dual neural network is shown to be globally exponentially convergent to optimal solutions the dual neural network is simulated to control the pa10 robot manipulator with effectiveness demonstrated

navier stokes equations for compressible fluids global existence and qualitative properties of the solutions in the general case we consider the equations which describe the motion of a viscous compressible fluid taking into consideration the case of inflow and or outflow through the boundary by means of some a priori estimates we prove the existence of a global in time solution moreover as a consequence of a stability result we show that there exist a periodic solution and a stationary solution

attractive periodic sets in discrete time recurrent networks with emphasis on fixed point stability and bifurcations in two neuron networks we perform a detailed fixed point analysis of two unit recurrent neural networks with sigmoid shaped transfer functions using geometrical arguments in the space of transfer function derivatives we partition the network state space into distinct regions corresponding to stability types of the fixed points unlike in the previous studies we do not assume any special form of connectivity pattern between the neurons and all free parameters are allowed to vary we also prove that when both neurons have excitatory self connections and the mutual interaction pattern is the same i e the neurons mutually inhibit or excite themselves new attractive fixed points are created through the saddle node bifurcation finally for an n neuron recurrent network we give lower bounds on the rate of convergence of attractive periodic points toward the saturation values of neuron activations as the absolute values of connection weights grow

stability and convergence of fully discrete galerkin fems for the nonlinear thermistor equations in a nonconvex polygon in this paper we establish the unconditional stability and optimal error estimates of a linearized backward euler galerkin finite element method fem for the time dependent nonlinear thermistor equations in a two dimensional nonconvex polygon due to the nonlinearity of the equations and the non smoothness of the solution in a nonconvex polygon the analysis is not straightforward while most previous efforts for problems in nonconvex polygons mainly focused on linear models our theoretical analysis is based on an error splitting proposed in 30 31 together with rigorous regularity analysis of the nonlinear thermistor equations and the corresponding iterated time discrete elliptic system in a nonconvex polygon with the proved regularity we establish the stability in l infty l infty l l and the convergence in l infty l 2 l l2 for the fully discrete finite element solution without any restriction on the time step size the approach used in this paper may also be applied to other nonlinear parabolic systems in nonconvex polygons numerical results confirm our theoretical analysis and show clearly that no time step condition is needed

a damping preconditioner for time harmonic wave equations in fluid and elastic material a physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering the earlier preconditioners for the helmholtz equation are generalized for elastic materials and three dimensional domains an algebraic multigrid method is used in approximating the inverse of damped operators several numerical experiments demonstrate the behavior of the method in complicated two dimensional and three dimensional domains

error analysis for absorbing boundary conditions an estimate is derived for the error committed by the introduction of artificial boundaries and corresponding artificial boundary conditions when solving wave equations on unbounded domains the estimate has two terms one is proportional to the largest reflection coefficient for the artificial boundary condition the maximum taken only on those rays which appear in the computation the second term is proportional to 1 k wherek is a measure of the average frequency present in the solution

a fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems part 2 neumann boundary conditions we present a fictitious domain decomposition method for the fast solution of acoustic scattering problems characterized by a partially axisymmetric sound hard scatterer we apply this method to the solution of a mock up submarine problem and highlight its computational advantages and intrinsic parallelism a key component of our method is an original idea for addressing a neumann boundary condition in the general framework of a fictitious domain method this idea is applicable to many other linear partial differential equations besides the helmholtz equation copyright 2003 john wiley sons ltd

a parallel fictitious domain method for the three dimensional helmholtz equation the application of a fictitious domain domain embedding method to the three dimensional helmholtz equation with absorbing boundary conditions is considered the finite element discretization is performed by using locally fitted meshes and an algebraic fictitious domain method with a separable preconditioner is used in the iterative solution of the resultant linear systems such a method is based on embedding the original domain into a larger one with a simple geometry with this approach it is possible to realize the gmres iterations in a low dimensional subspace and use the partial solution method to solve the linear systems with the preconditioner an efficient parallel implementation of the iterative algorithm is introduced results of numerical experiments demonstrate good scalability properties on distributed memory parallel computers and the ability to solve high frequency acoustic scattering problems

linear and quadratic programming neural network analysis neural networks for linear and quadratic programming are analyzed the network proposed by m p kennedy and l o chua ieee trans circuits syst vol 35 pp 554 562 may 1988 is justified from the viewpoint of optimization theory and the technique is extended to solve optimization problems such as the least squares problem for quadratic programming the network converges either to an equilibrium or to an exact solution depending on whether the problem has constraints or not the results also suggest an analytical approach to solve the linear system bx b without calculating the matrix inverse the results are directly applicable to optimization problems with c sup 2 convex objective functions and linear constraints the dynamics and applicability of the networks are demonstrated by simulation the distance between the equilibria of the networks and the problem solutions can be controlled by the appropriate choice of a network parameter

a new recurrent neural network for solving convex quadratic programming problems with an application to the k winners take all problem in this paper a new recurrent neural network is proposed for solving convex quadratic programming qp problems compared with existing neural networks the proposed one features global convergence property under weak conditions low structural complexity and no calculation of matrix inverse it serves as a competitive alternative in the neural network family for solving linear or quadratic programming problems in addition it is found that by some variable substitution the proposed network turns out to be an existing model for solving minimax problems in this sense it can be also viewed as a special case of the minimax neural network based on this scheme a k winners take all k wta network with o n complexity is designed which is characterized by simple structure global convergence and capability to deal with some ill cases numerical simulations are provided to validate the theoretical results obtained more importantly the network design method proposed in this paper has great potential to inspire other competitive inventions along the same line

a domain decomposition solver for acoustic scattering by elastic objects in layered media a finite element solution procedure is presented for accurately computing time harmonic acoustic scattering by elastic targets buried in sediment an improved finite element discretization based on trilinear basis functions leading to fourth order phase accuracy is described for sufficiently accurate discretizations 100 million to 1 billion unknowns are required the resulting systems of linear equations are solved iteratively using the gmres method with a domain decomposition preconditioner employing a fast direct solver due to the construction of the discretization and preconditioner iterations can be reduced onto a sparse subspace associated with the interfaces numerical experiments demonstrate capability to evaluate the scattered field with hundreds of wavelengths

the solution of exterior interface problems using a variational method with lagrange multipliers abstract a numerical method is proposed and analyzed for approximately solving a class of exterior interface problems in three dimensions the solution satisfies the helmholtz equation near infinity as well as an outgoing or incoming radiation condition the interface conditions involve jumps in both the function and the normal derivative of the function across a two dimensional surface the former condition is an essential interface condition and is treated using lagrange multipliers the unboundedness of the exterior domain is treated by introducing an artificial sphere r of sufficiently large radius r and an approximate local radiation boundary condition on this sphere a variational formulation is obtained for this approximate problem that takes into account the approximate boundary condition on r as well as the natural interface condition i e the jump in the normal derivative on the resulting variational problem is discretized using the finite element method it is proved that the discretization error is optimal in the sense of the approximation properties of the finite element subspaces the discrete lagrange multiplier formulation is generalized to take into account various perturbations of the method that often occur in its implementation the error due to the perturbation is analyzed it is also proved that the error due to the artificial boundary and approximate boundary condition is of order o r 2 for large r

the evolution compressible navier stokes system on polygonal domains abstract the evolution compressible navier stokes system is considered on polygonal domains it is shown that the lowest order of the corner singularity of the system is the same as that of the heat equation in a suitable banach space the velocity is split into singular and regular parts and the coefficient of the singularity is expressed by convolution of some two functions in the time variable by a formula of the pressure we observe propagation of the corner singularity along the characteristic lines emanating from the corners and also unboundedness of derivatives of pressure there an increased regularity for the remainder part is established

a finite element capacitance matrix method for exterior helmholtz problems we introduce an algorithm for the efficient numerical solution of exterior boundary value problems for the helmholtz equation the problem is reformulated as an equivalent one on a bounded domain using an exact non local boundary condition on a circular artificial boundary an fft based fast helmholtz solver is then derived for a finite element discretization on an annular domain the exterior problem for domains of general shape are treated using an imbedding or capacitance matrix method the imbedding is achieved in such a way that the resulting capacitance matrix has a favorable spectral distribution leading to mesh independent convergence rates when krylov subspace methods are used to solve the capacitance matrix equation

detecting interfaces in a parabolic elliptic problem from surface measurements assuming that the heat capacity of a body is negligible outside certain inclusions the heat equation degenerates to a parabolic elliptic interface problem in this work we aim to detect these interfaces from thermal measurements on the surface of the body we deduce an equivalent variational formulation for the parabolic elliptic problem and give a new proof of the unique solvability based on lions s projection lemma for the case that the heat conductivity is higher inside the inclusions we develop an adaptation of the factorization method to this time dependent problem in particular this shows that the locations of the interfaces are uniquely determined by boundary measurements the method also yields to a numerical algorithm to recover the inclusions and thus the interfaces we demonstrate how measurement data can be simulated numerically by a coupling of a finite element method with a boundary element method and finally we present some numerical results for the inverse problem

neural network for quadratic optimization with bound constraints a recurrent neural network is presented which performs quadratic optimization subject to bound constraints on each of the optimization variables the network is shown to be globally convergent and conditions on the quadratic problem and the network parameters are established under which exponential asymptotic stability is achieved through suitable choice of the network parameters the system of differential equations governing the network activations is preconditioned in order to reduce its sensitivity to noise and to roundoff errors the optimization method employed by the neural network is shown to fall into the general class of gradient methods for constrained nonlinear optimization and in contrast with penalty function methods is guaranteed to yield only feasible solutions

a two phase optimization neural network a novel two phase neural network that is suitable for solving a large class of constrained or unconstrained optimization problem is presented for both types of problems with solutions lying in the interior of the feasible regions the phase one structure of the network alone is sufficient when the solutions of constrained problems are on the boundary of the feasible regions the proposed two phase network is capable of achieving the exact solutions in contrast to existing optimization neural networks which can obtain only approximate solutions furthermore the network automatically provides the corresponding lagrange multiplier associated with each constraint thus for linear programming the network solves both the primal problems and their dual problems simultaneously

an algebraic multigrid based shifted laplacian preconditioner for the helmholtz equation a preconditioner defined by an algebraic multigrid cycle for a damped helmholtz operator is proposed for the helmholtz equation this approach is well suited for acoustic scattering problems in complicated computational domains and with varying material properties the spectral properties of the preconditioned systems and the convergence of the gmres method are studied with linear quadratic and cubic finite element discretizations numerical experiments are performed with two dimensional problems describing acoustic scattering in a cross section of a car cabin and in a layered medium asymptotically the number of iterations grows linearly with respect to the frequency while for lower frequencies the growth is milder the proposed preconditioner is particularly effective for low frequency and mid frequency problems

the finite element method with non uniform mesh sizes applied to the exterior helmholtz problem the finite element method with non uniform mesh sizes is employed to approximately solve helmholtz type equations in unbounded domains the given problem on an unbounded domain is replaced by an approximate problem on a bounded domain with the radiation condition replaced by an approximate radiation boundary condition on the artificial boundary this approximate problem is then solved using the finite element method with the mesh graded systematically in such a way that the element mesh sizes are increased as the distance from the origin increases this results in a great reduction in the number of equations to be solved it is proved that optimal error estimates hold inl 2 h 1 andl provided that certain relationships hold between the frequency mesh size and outer radius

regularity of solutions to the navier stokes equations for compressible barotropic flows on a polygon the navier stokes system for a steady state barotropic nonlinear compressible viscous flow with an inflow boundary condition is studied on a polygon d a unique existence for the solution of the system is established it is shown that the lowest order corner singularity of the nonlinear system is the same as that of the laplacian in suitable l q spaces let be the interior angle of a vertex p of d if and then the velocity u is split into singular and regular parts near the vertex p if 2 and or if 2 and 2 q it is shown that u h 2 q d 2

an operator splitting scheme with a distributed lagrange multiplier based fictitious domain method for wave propagation problems we propose a novel fictitious domain method based on a distributed lagrange multiplier technique for the solution of the time dependent problem of scattering by an obstacle we study discretizations that include a fully conforming approach as well as mixed finite element formulations utilizing the lowest order nedelec edge elements in 2d on rectangular grids we also present a symmetrized operator splitting scheme for the scattering problem which decouples the operator that propagates the wave from the operator that enforces the dirichlet condition on the boundary of an obstacle a new perfectly matched layer pml model is developed to model the unbounded problem of interest this model is based on a formulation of the wave equation as a system of first order equations and uses a change of variables approach that has been developed to construct pml s for maxwell s equations we present an analysis of our fictitious domain approach for a one dimensional wave problem based on calculations of reflection coefficients we demonstrate the advantages of our fictitious domain approach over the staircase approximation of the finite difference method we also demonstrate some important properties of the distributed multiplier approach that are not shared by a boundary multiplier fictitious domain approach for the same problem numerical results for two dimensional wave problems that validate the effectiveness of the different methods are presented

neural network for solving extended linear programming problems a neural network for solving extended linear programming problems is presented and is shown to be globally convergent to exact solutions the proposed neural network only uses simple hardware in which no analog multiplier for variables is required and has no parameter tuning problem finally an application of the neural network to the l sub 1 norm minimization problem is given

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

an evolution compressible stokes system in a polygon abstract an evolution compressible stokes system is studied in a polygon a lowest order corner singularity by the laplacian operator is sorted out and an increased regularity is established in a suitable banach space in the lowest level for each time the order of the corner singularity of the system is the same as that of the laplacian in addition a singular function for pressure is defined and shows that the corner singularities originated from the corners of polygon may propagate along the directed streamlines

coupling scalar and vector potentials on nonmatching grids for eddy currents in a moving conductor the t formulation of the magnetic field has been introduced in many papers for the approximation of the magnetic quantities modelled by the eddy current equations this decomposition allows to use a scalar function in the main part of the computational domain reducing the use of vector quantities to the conducting parts we propose to approximate these two quantities on nonmatching grids so as to be able to tackle a problem where the conducting part can move in the global domain the connection between the two grids is managed with mortar element techniques

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

rapid solution of integral equations of scattering theory in two dimensions abstract the present paper describes an algorithm for rapid solution of boundary value problems for the helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory cpu time requirements of previously published algorithms of this type are of the order n 2 where n is the number of nodes in the discretization of the boundary of the scatterer the cpu time requirements of the algorithm of the present paper are n 4 3 and can be further reduced making it considerably more practical for large scale problems

compressible stokes problem on nonconvex polygonal domains abstract the compressible stokes system with the inflow boundary condition is studied on the polygonal domain d it is shown that the lowest order corner singularity of the system is the same as that of the laplacian the velocity u is split into a singular and regular part near each concave vertex if the polygon is convex it is shown that u h 2 d 2

on the synthesis of brain state in a box neural models with application to associative memory in this article we present techniques for designing associative memories to be implemented by a class of synchronous discrete time neural networks based on a generalization of the brain state in a box neural model first we address the local qualitative properties and global qualitative aspects of the class of neural networks considered our approach to the stability analysis of the equilibrium points of the network gives insight into the extent of the domain of attraction for the patterns to be stored as asymptotically stable equilibrium points and is useful in the analysis of the retrieval performance of the network and also for design purposes by making use of the analysis results as constraints the design for associative memory is performed by solving a constraint optimization problem whereby each of the stored patterns is guaranteed a substantial domain of attraction the performance of the designed network is illustrated by means of three specific examples

neural network for solving linear programming problems with bounded variables a new neural network for solving linear programming problems with bounded variables is presented the network is shown to be completely stable and globally convergent to the solutions to the linear programming problems the proposed new network is capable of achieving the exact solutions in contrast to existing optimization neural networks which need a suitable choice of the network parameters and thus can obtain only approximate solutions furthermore both the primal problems and their dual problems are solved simultaneously by the new network