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 capable neural network model for solving the maximum flow problem this paper presents an optimization technique for solving a maximum flow problem arising in widespread applications in a variety of settings on the basis of the karush kuhn tucker kkt optimality conditions a neural network model is constructed the equilibrium point of the proposed neural network is then proved to be equivalent to the optimal solution of the original problem it is also shown that the proposed neural network model is stable in the sense of lyapunov and it is globally convergent to an exact optimal solution of the maximum flow problem several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper

an efficient simplified neural network for solving linear and quadratic programming problems we present a high performance and efficiently simplified new neural network which improves the existing neural networks for solving general linear and quadratic programming problems the network having no need for parameter setting results in a simple hardware requiring no analog multipliers is shown to be stable and converges globally to the exact solution moreover using this network we can solve both linear and quadratic programming problems and their duals simultaneously high accuracy of the obtained solutions and low cost of implementation are among the features of this network we prove the global convergence of the network analytically and verify the results numerically

quasi lagrangian neural network for convex quadratic optimization a new neural network for convex quadratic optimization is presented in this brief the proposed network can handle both equality and inequality constraints as well as bound constraints on the optimization variables it is based on the lagrangian approach but exploits a partial dual method in order to keep the number of variables at minimum the dynamic evolution is globally convergent and the steady state solutions satisfy the necessary and sufficient conditions of optimality the circuit implementation is simpler with respect to existing solutions for the same class of problems the validity of the proposed approach is verified through some simulation examples

numerical solution for linear and quadratic programming problems using a recurrent neural network a recurrent neural network is proposed in this paper for solving linear and quadratic programming problems the main advantage of this network is that here we are not in need of parameters setting moreover using this network we can solve primal programming problems and their duals simultaneously we prove the global convergence of the neural network and demonstrate the advanced performance of the proposed network by means of simulation of several numerical examples

a discrete time neural network for solving nonlinear convex problems with hybrid constraints this paper investigates a discrete time neural network model for solving nonlinear convex programming problems with hybrid constraints the neural network finds the solution of both primal and dual problems and converges to the corresponding exact solution globally we prove here that the proposed neural network is globally exponentially stable furthermore we extend the proposed neural network for solving a class of monotone variational inequality problems with hybrid constraints compared with other existing neural networks for solving such problems the proposed neural network has a low complexity for implementation without a penalty parameter and converge an exact solution to convex problem with hybrid constraints some numerical simulations for justifying the theoretical analysis are also given the numerical simulations are shown that in the new model note only the cost of the hardware implementation is not relatively expensive but also accuracy of the solution is greatly good

a neural network for linear matrix inequality problems gradient type hopfield networks have been widely used in optimization problems solving the paper presents a novel application by developing a matrix oriented gradient approach to solve a class of linear matrix inequalities lmis which are commonly encountered in the robust control system analysis and design the solution process is parallel and distributed in neural computation the proposed networks are proven to be stable in the large representative lmis such as generalized lyapunov matrix inequalities simultaneous lyapunov matrix inequalities and algebraic riccati matrix inequalities are considered several examples are provided to demonstrate the proposed results to verify the proposed control scheme in real time applications a high speed digital signal processor is used to emulate the neural net based control scheme

zero temperature properties of rna secondary structures we analyze different microscopic rna models at zero temperature we discuss both the most simple model which suffers a large degeneracy of the ground state and models in which the degeneracy has been removed in a more or less severe manner we calculate low energy density of states using a coupling perturbing method where the ground state of a modified hamiltonian that repels the original ground state is determined we evaluate scaling exponents starting from measurements of overlaps and energy differences in the case of models without accidental degeneracy of the ground state we are able to clearly establish the existence of a glassy phase with ensuremath theta ensuremath simeq 1 3 87 15 aa 64 60 fr

a generalized least absolute deviation method for parameter estimation of autoregressive signals this paper proposes a generalized least absolute deviation glad method for parameter estimation of autoregressive ar signals under non gaussian noise environments the proposed glad method can improve the accuracy of the estimation of the conventional least absolute deviation lad method by minimizing a new cost function with parameter variables and noise error variables compared with second and high order statistical methods the proposed glad method can obtain robustly an optimal ar parameter estimation without requiring the measurement noise to be gaussian moreover the proposed glad method can be implemented by a cooperative neural network nn which is shown to converge globally to the optimal ar parameter estimation within a finite time simulation results show that the proposed glad method can obtain more accurate estimates than several well known estimation methods in the presence of different noise distributions

a geometric characterization of optimal designs for regression models with correlated observations we consider the problem of optimal design of experiments for random effects models especially population models where a small number of correlated observations can be taken on each individual whereas the observations corresponding to different individuals are assumed to be uncorrelated we focus on c optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of elfving from the case of uncorrelated data can be adapted to the problem of selecting optimal sets of observations for the n individual patients the theory is demonstrated by finding optimal designs for a linear model with correlated observations and a non linear random effects population model which is commonly used in pharmaco kinetics

numerical solutions for constrained quadratic problems using high performance neural networks two new classes of neural networks for solving constrained quadratic programming problems are presented the main advantage of these networks is the requirement to use economic analog multipliers for variables the numerical simulations demonstrate that in the new neural networks not only the cost of the hardware implementation is not relatively expensive but also accuracy of the solution is greatly good the network dynamic behaviors are discussed the numerical simulations are shown that an optimal solution of the quadratic problems is an equilibrium point of the neural dynamics and vise versa we show that these networks find the solution of both primal and dual problems and converge to the corresponding exact solutions globally the proposed new neural networks models are fully stable

universality classes for extreme value statistics the equilibrium low temperature physics of disordered systems is governed by the statistics of extremely low energy states it is thus relevant to discuss the possible universality classes for extreme value statistics we compare the usual probabilistic classification to the results of the replica approach we show in detail for several problems including the random energy model and the decaying burgers turbulence that one class of independent variables corresponds exactly to the so called one step replica symmetry breaking solution in the replica language we argue that this universality class holds if the correlations are sufficiently weak and propose a conjecture on the level of correlations which leads to different universality classes

global exponential stability of recurrent neural networks for solving optimization and related problems global exponential stability is a desirable property for dynamic systems the paper studies the global exponential stability of several existing recurrent neural networks for solving linear programming problems convex programming problems with interval constraints convex programming problems with nonlinear constraints and monotone variational inequalities in contrast to the existing results on global exponential stability the present results do not require additional conditions on the weight matrices of recurrent neural networks and improve some existing conditions for global exponential stability therefore the stability results in the paper further demonstrate the superior convergence properties of the existing neural networks for optimization

a derivative algorithm for inexact quadratic program application to environmental decision making under uncertainty abstract inexact quadratic programming iqp is an extension of conventional quadratic programming for handling both nonlinearities in cost objectives and uncertainties with modeling parameters it has been a useful tool for environmental systems analysis however inefficiency in its solution method has existed leading to difficulties in its practical application in this study a derivative algorithm dam is proposed for solving the iqp it improves upon the existing method through provision of a quantitative expression for uncertain relationships between the quadratic objective function and the decision variables the dam requires much lower computational efforts than the existing algorithm which is especially meaningful for the iqp s application to large scale problems the developed dam is applied to a hypothetical problem of municipal solid waste management and planning detailed solution steps are provided to clearly demonstrate the method s advantages

elfving s theorem for d optimality we consider a model robust version of the c optimality criterion minimizing a weighted product with factors corresponding to the variances of the least squares estimates for linear combinations of the parameters in different models a generalization of elfving s theorem is proved for the optimal designs with respect to this criterion by an application of an equivalence theorem for mixtures of optimality criteria as a special case an elfving theorem for the d optimal design problem is obtained in the case of identical models the connection between the a optimality criterion and the model robust criterion is investigated the geometric characterizations of the optimal designs are illustrated by a couple of examples

a generalized neural network for solving a class of minimax optimization problems with linear constraints abstract in this paper a generalized neural network was proposed based on projection method and differential inclusions which is contributed to solve a class of minimax optimization problems with linear constraints it is proved that the solution trajectory can converge to the feasible region in the finite time when the initial point is not in the feasible region once the solution trajectory reaches the feasible region it will stay therein thereafter in addition we investigate the global convergence and exponential convergence furthermore three illustrative examples are given to show the efficiency of the proposed neural network

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

an improved dual neural network for solving a class of quadratic programming problems and its k winners take all application this paper presents a novel recurrent neural network for solving a class of convex quadratic programming qp problems in which the quadratic term in the objective function is the square of the euclidean norm of the variable this special structure leads to a set of simple optimality conditions for the problem based on which the neural network model is formulated compared with existing neural networks for general convex qp the new model is simpler in structure and easier to implement the new model can be regarded as an improved version of the dual neural network in the literature based on the new model a simple neural network capable of solving the k winners take all k wta problem is formulated the stability and global convergence of the proposed neural network is proved rigorously and substantiated by simulation results

a neural network for a class of convex quadratic minimax problems with constraints in this paper we propose a neural network for solving a class of convex quadratic minimax problems with constraints four sufficient conditions are provided to ensure the asymptotic stability of the proposed network furthermore the exponential stability of the proposing network is also proved under certain conditions the results obtained here can be further extended to the globally projected dynamical system in addition some new stability conditions for the system are also obtained since our stability conditions can be easily checked in practice these results becomes more attractive in real applications

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 delayed neural network for solving linear projection equations and its analysis in this paper we present a delayed neural network approach to solve linear projection equations the lyapunov krasovskii theory for functional differential equations and the linear matrix inequality lmi approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network compared with the existing linear projection neural network theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems

a one layer recurrent neural network with a discontinuous hard limiting activation function for quadratic programming in this paper a one layer recurrent neural network with a discontinuous hard limiting activation function is proposed for quadratic programming this neural network is capable of solving a large class of quadratic programming problems the state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints in addition a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming simulation results on numerical examples and support vector machine svm learning show the effectiveness and performance of the neural network

optimal designs for identifying the degree of a polynomial regression if an experimenter wants to determine the degree of a polynomial regression on the basis of a sample of observations anderson showed that the following method is optimal starting with the highest specified degree the procedure is to test in sequence whether the coefficients are 0 in this paper optimal designs for anderson s procedure are determined explicitly the optimal design maximizes the minimum power of a given set of alternatives

extremal properties of random systems we find that the probability distribution for the largest intervals p l exhibits universal properties for different systems including random walk and random cutting models in particular p l has an infinite set of singularities at l 1 k with k 2 3 which become weaker and weaker as k ensuremath rightarrow ensuremath infty additionally p l has an essential singularity at l 0 these properties are also found in many dimensional situations

a lagrangian network for kinematic control of redundant robot manipulators a recurrent neural network called the lagrangian network is presented for the kinematic control of redundant robot manipulators the optimal redundancy resolution is determined by the lagrangian network through real time solution to the inverse kinematics problem formulated as a quadratic optimization problem while the signal for a desired velocity of the end effector is fed into the inputs of the lagrangian network it generates the joint velocity vector of the manipulator in its outputs along with the associated lagrange multipliers the proposed lagrangian network is shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators

optimal designs for dose response models with restricted design spaces in dose response studies the dose range is often restricted due to concerns over drug toxicity and or efficacy we present restricted and unrestricted interval locally optimal designs with respect to a very general class of optimality criteria for estimating the underlying dose response curve the underlying curve belongs to a diversified set of link functions suitable for the dose response studies and having a common canonical form these include the fundamental binary response models the logit and the probit as well as the skewed versions of these models the results are illustrated through the re design of a dose ranging trial conducted at the merck research laboratories zeng and zhu 1997 this work is a generalization of the results of dai and zhu 2002 in terms of the design interval the underlying dose response curve and the optimality criterion

a measurement fusion method for nonlinear system identification using a cooperative learning algorithm identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article a measurement fusion method for the predictor function estimate is proposed in the proposed scheme observed data are first fused by using an optimal fusion technique and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine ls svm a cooperative learning algorithm is proposed to implement the proposed measurement fusion method compared with related identification methods the proposed method can minimize both the approximation error and the noise error the performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the ls svm function estimate moreover the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate finally the proposed measurement fusion method is applied to arma signal and spatial temporal signal modeling experimental results show that the proposed measurement fusion method can provide a more accurate model

global mu synchronization of linearly coupled unbounded time varying delayed neural networks with unbounded delayed coupling in this brief we study the global synchronization of linearly coupled neural networks with delayed couplings where the intrinsic systems are recurrently connected neural networks with unbounded time varying delays and the couplings include instant couplings and unbounded delayed couplings the concept of mu synchronization is introduced some sufficient conditions are derived for the global mu synchronization for the underlined coupled systems

a note on bayesian c and d optimal designs in nonlinear regression models we present a version of elfving s theorem for the bayesian d optimality criterion in nonlinear regression models the bayesian optimal design can be characterized as a design which allows a representation of a uniquely determined boundary point of a convex subset of l 2 integrable functions a similar characterization is given for the bayesian c optimality criterion where a possible nonlinear function of the unknown parameters has to be estimated the results are illustrated in the example of an exponential growth model using a gamma prior distribution

a recurrent neural network for solving nonlinear convex programs subject to linear constraints in this paper we propose a recurrent neural network for solving nonlinear convex programming problems with linear constraints the proposed neural network has a simpler structure and a lower complexity for implementation than the existing neural networks for solving such problems it is shown here that the proposed neural network is stable in the sense of lyapunov and globally convergent to an optimal solution within a finite time under the condition that the objective function is strictly convex compared with the existing convergence results the present results do not require lipschitz continuity condition on the objective function finally examples are provided to show the applicability of the proposed neural network

freezing transition of the random bond rna model statistical properties of the pairing weights to characterize the pairing specificity of rna secondary structures as a function of temperature we analyze the statistics of the pairing weights as follows for each base i of the sequence of length n we consider the n 1 pairing weights w i j with the other bases j not equal i of the sequence we numerically compute the probability distributions p1 w of the maximal weight w i max max j w i j the probability distribution pi y 2 of the parameter y2 i summation operator j w i 2 j as well as the average values of the moments y k i summation operator j w i k j we find that there are two important temperatures t c t gap the distribution p1 w vanishes at some value w 0 t 1 and accordingly the moments y k i decay exponentially as w 0 t k in k for t t gap the distributions p1 w and pi y2 present the characteristic derrida flyvbjerg singularities at w 1n and y 2 1 n for n 1 2 in particular there exists a temperature dependent exponent mu t that governs the singularities p1 w approximately 1 w mu t 1 and pi y2 approximately 1 y 2 mu t 1 as well as the power law decay of the moments y k i approximately 1k mu t the exponent mu t grows from the value mu t 0 0 up to mu t gap approximately 2 the study of spatial properties indicates that the critical temperature t c where the large scale roughness exponent changes from the low temperature value zeta approximately 0 67 to the high temperature value zeta approximately 0 5 corresponds to the exponent mu t c 1 for t t c there exists frozen pairs of all sizes whereas for t c t t gap there exists frozen pairs but only up to some characteristic length diverging as xi t approximately 1 t c t nu with nu approximately 2 the similarities and differences with the weight statistics in levy sums and in derrida s random energy model are discussed

a new regression estimator with neural network realization a new regression estimator viewed as the solution of a strictly convex quadratic programming problem is introduced in this paper two recurrent neural networks in continuous time and discrete time respectively are proposed to solve the quadratic programming problem in real time the continuous time neural network is shown to have a global stability including the global asymptotic and exponential stability the discrete time neural network is shown to have a global convergence with a fixed step length this fixed step length can be independent of the regression problem size by scaling a design parameter since the sizes of the proposed neural networks depend only on the constraints of the optimization problems the proposed new regression estimator can obtained by two novel neural networks with lower implementation costs than the conventional methods our simulation results confirm that the proposed neural networks are effective in solving various kind of regression problems

minimax designs in linear regression models in the usual linear regression model we investigate the geometric structure of a class of minimax optimality criteria containing elfving s minimax and kiefer s phi p criteria as special cases it is shown that the optimal designs with respect to these criteria are also optimal for a theta where a is any inball vector in an appropriate norm of a generalized elfving set the results explain the particular role of the a and e optimality criterion and are applied for determining the optimal design with respect to elfving s minimax criterion in polynomial regression up to degree 9

a high performance feedback neural network for solving convex nonlinear programming problems based on a new idea of successive approximation this paper proposes a high performance feedback neural network model for solving convex nonlinear programming problems differing from existing neural network optimization models no dual variables penalty parameters or lagrange multipliers are involved in the proposed network it has the least number of state variables and is very simple in structure in particular the proposed network has better asymptotic stability for an arbitrarily given initial point the trajectory of the network converges to an optimal solution of the convex nonlinear programming problem under no more than the standard assumptions in addition the network can also solve linear programming and convex quadratic programming problems and the new idea of a feedback network may be used to solve other optimization problems feasibility and efficiency are also substantiated by simulation examples

a geometric approach to optimal design for one parameter non linear models summary a geometric framework for constructing optimal bayesian designs and maximin designs for non linear models with a single unknown parameter and a prior distribution on that parameter which is restricted in that it comprises exactly two points of support is presented the approach is illustrated by means of selected examples involving logistic regression and the simple exponential model and its applicability to the construction of optimal designs for models with uncontrolled variation and to model robust designs is also demonstrated in addition the method is shown to provide some valuable insights into the general properties of optimal bayesian designs for non linear models

dependence of rna secondary structure on the energy model we analyze a microscopic rna model which includes two widely used models as limiting cases namely it contains terms for bond as well as for stacking energies we numerically investigate possible changes in the qualitative and quantitative behavior while going from one model to the other in particular we test whether a transition occurs when continuously moving from one model to the other for this we calculate various thermodynamic quantities at both zero temperature and finite temperatures all calculations can be done efficiently in polynomial time by a dynamic programming algorithm we do not find a sign for the transition between the models but the critical exponent ensuremath nu of the correlation length describing the phase transition in all models to an ordered low temperature phase seems to depend continuously on the model finally we apply the ensuremath epsilon coupling method to study low energy excitations the exponent ensuremath theta describing the energy scaling of the excitations seems to depend not much on the energy model

a high performance neural network for solving linear and quadratic programming problems two classes of high performance neural networks for solving linear and quadratic programming problems are given we prove that the new system converges globally to the solutions of the linear and quadratic programming problems in a neural network network parameters are usually not specified the proposed models can overcome numerical difficulty caused by neural networks with network parameters and obtain desired approximate solutions of the linear and quadratic programming problems

statistical properties of randomly broken objects and of multivalley structures in disordered systems the statistical properties of the multivalley structure of disordered systems and of randomly broken objects have many features in common for all these problems if w denotes the weight of the sth piece we show that the probability distributions pi w of the largest piece w p2 w of the second largest piece and n y of y 1 wi always have singularities at w l n w2 l n and y ijn n 1 2 3

novel artificial neural network with simulation aspects for solving linear and quadratic programming problems in this paper linear and quadratic programming problems are solved using a novel recurrent artificial neural network the new model is simpler and converges very fast to the exact primal and dual solutions simultaneously the model is based on a nonlinear dynamical system using arbitrary initial conditions in order to construct an economy model here we avoid using analog multipliers the dynamical system is a time dependent system of equations with the gradient of specific lyapunov energy function in the right hand side block diagram of the proposed neural network model is given fourth order runge kutta method with controlled step size is used to solve the problem numerically global convergence of the new model is proved both theoretically and numerically numerical simulations show the fast convergence of the new model for the problems with a unique solution or infinitely many this model converges to the exact solution independent of the way that we may choose the starting points i e inside outside or on the boundaries of the feasible region

the bsb neural network in the convex body spanned by the prototype patterns for associative memory this paper presents a kind of general brain state in a box bsb neural network for associative memory it can guarantee that the set of prototype patterns is the same as the set of asymptotically stable equilibrium points an equilibrium point which is not asymptotically stable is just the state that cannot be recognized furthermore the basin of attraction of each desired memory pattern is distributed reasonably in hamming distance sense the proposed network improves classical bsb as an idea model for associative memory the network considered herein is a generalization of traditional bsb its state is allowed to lie in a general closed convex set which is spanned by the prototype patterns the performance of the proposed network is demonstrated by means of simulation of one numerical example

solving complementarity and variational inequalities problems using neural networks in this paper we propose a recurrent neural network model for solving a class of monotone variational inequalities problem with linear constraints the neural network is stable in the sense of lyapunov and globally convergent to an optimal solution compared with the existing convergence results the present proof do not require lipschitz continuity condition on the objective function this neural network model has no adjustable parameter thus its structure is very simple variational inequalities problem with general set of constraints plus a general form of the complementarity problems are solved using the proposed neural networks some examples demonstrated to show the applicability of the proposed neural networks to solve various nonlinear optimization problems numerically

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