asymptotic behavior of nonlinear difference systems in this paper we consider two dimensional nonlinear difference systems of the email protected n a nf y n dy n 1 b ng x n we classify their solutions according to asymptotic behavior and give some necessary and sufficient conditions for the existence of solutions of such classes

existence of uncountably many bounded nonoscillatory solutions and their iterative approximations for second order nonlinear neutral delay difference equations in this paper the banach fixed point theorem is employed to establish several existence results of uncountably many bounded nonoscillatory solutions for the second order nonlinear neutral delay difference email protected n dx n b n x email protected email protected n x h 1 n x h 2 n x h k n f n x f 1 n x f 2 n x f k n c n n n 0 where t email protected n n email protected n 0 a b c n n 0 r with a n 0 for email protected n n 0 h f n n 0xr k r and h l f l n n 0 z withlimn h l n limn f l n email protected 1 2 k a few mann type iterative approximation schemes with errors are suggested and the errors estimates between the iterative approximations and the nonoscillatory solutions are discussed seven nontrivial examples are given to illustrate the advantages of our results

a network penalty method we consider the minimum cost network flow problem and describe how the non linear penalty function methods of conn and bartels can be specialized to a combinatorial algorithm for this problem we report on preliminary computational results which show that this method can require fewer pivots than the simplex method while the amount of work required for each pivot is comparable the algorithm can be proven finite using a modification of cunningham s strongly feasible basis pivoting rule

oscillatory and asymptotic behavior of second order neutral difference equations with maxima abstract in this paper the asymptotic behavior of the non oscillatory solutions of neutral difference equations with maxima is considered sufficient conditions for oscillation of all solutions are also obtained

oscillation for difference equations with continuous variable consider the delay difference equation y t y t p t h y t t t 0 where 0 0 and p c r r f c r r h c r r some oscillation criteria for this equation are obtained

oscillation and nonoscillation theorems for second order nonlinear difference equations abstract some new oscillation and nonoscillation theorems are obtained for second order nonlinear difference equations a p n a x n q n a x n f n x n b x n which generalize and improve all results proved by popenda in j math anal appl 123 1987 34 48

oscillation and asymptotic behavior of second order difference equations abstract the oscillation of the second order difference equation c n y n p n y v n 1 0 n 0 1 2 1 1 is investigated where yn yn 1 yn v is a quotient of odd positive integers some necessary and sufficient conditions for oscillation of 1 1 with v 1 and v

periodic solutions for nonlinear second order difference equations abstract this paper is devoted to introduce a new approach to investigate the existence of periodic solutions for nonlinear difference equations transforming a second order nonlinear difference equation on a finite discrete segment with periodic boundary conditions into a continuous system we obtain the existence conditions of periodic solutions of the equation the proof relies on coincidence degree theory and matrix theory without using green s function

existence of uncountably many bounded positive solutions for a third order nonlinear neutral delay difference equation this paper deals with the solvability of the third order nonlinear neutral delay difference equation d 2 a n d x n b nx n t d 2f n x n b 1 n x n b 2 n x n b k n dg n x n c 1 n x n c 2 n x n c k n h n x n d 1 n x n d 2 n x n d k n n n 0 relative to the sequence b n n n n 0 r using the krasnoselskii s fixed point theorem and schauder s fixed point theorem a few sufficient conditions of the existence of uncountably many bounded positive solutions for the equation are presented seven examples are included to demonstrate the advantages and effectiveness of the results presented in this paper

oscillation and nonoscillation theorems for second order difference equations in this paper we are concerned with the oscillatory and nonoscillatory behavior of the solutions of some second order difference equations let r be the set of real numbers n n n l where n is given nonnegative integer for the function x n t r the difference operator d l1 a is fixed real constant will be defined as follows d x x ax n e n instead of a we shall write a we define inductively a x a atix for k 1 we shall study difference equations of the form

iterative processes with mixed errors for nonlinear equations with perturbed m accretive operators in banach spaces let x be a real uniformly smooth banach space of which the dual x has a frechet differentiable norm let a d a x 2 x be an m accretive operator with closed domain d a and bounded range r a and s x x a continuous and a strongly accretive operator with bounded range r i s it is proved that the ishikawa and mann iterative processes with mixed errors converge strongly to the unique solution of the equation z sx lax for given z x and l 0

optimal coalition formation and surplus distribution two sides of one coin abstract a fuzzy coalitional game represents a situation in which players can vary the intensity at which they participate in the coalitions accessible to them as opposed to the treatment as a binary choice in the non fuzzy crisp game building on the property not made use of so far in the literature of fuzzy games that a fuzzy game can be represented as a convex program this paper shows that the optimum of such a program determines the optimal coalitions as well as the optimal rewards for the players two sides of one coin furthermore this program is seen to provide a unifying framework for representing the core the least core and the fuzzy nucleolus among others next we derive conditions for uniqueness of core rewards and to deal with non uniqueness we introduce a family of parametric perturbations of the convex program that encompasses a large number of well known concepts for selection from the core including the dutta ray solution dutta and ray 1989 the equal sacrifice solution yu 1973 the equal division solution selten 1972 and the tau value tijs 1981 we also generalize the concept of the grand coalition of contracting players by allowing for multiple technologies and we specify the conditions for this allocation to be unique and egalitarian finally we show that our formulation offers a natural extension to existing models of production economies with threats and division rules for common surplus

linearized oscillation of first order nonlinear neutral delay differential equations abstract in this paper we establish a equivalence of oscillation for the first order nonlinear neutral delay differential equation x t px t i 1 m q i f i x t i 0 and its corresponding linear equation x t px t i 1 m q i x t i 0 under a weaker condition on fi

kac van moerbeke equations associated with two dimensional su n 1 periodic toda lattices various results known for one dimensional periodic toda lattice equations are generalised to two dimensions in particular a generalisation of the kac van moerbeke equations is derived from a set of first order differential equations of which the zero gauge field strength is an integrability condition the generalised equations are shown to be the unification of two different periodic toda lattice equations and they naturally produce the backlund transformation the two lattice equations are simultaneously derived from a pair of 2 n 1 2 n 1 potentials satisfying the zero field strength condition

derivation and solution of the two dimensional toda lattice equations by use of the iwasawa decomposition the iwasawa decomposition is applied to the complexification of an arbitrary gauge group g over a two dimensional space the two dimensional toda lattice equations arise from the condition that the gauge field strength vanishes the method is based on the generalisation of yang s r gauge for su 2 to any semisimple lie group g a parametrisation for the solutions to the equations governed by arbitrary classical groups is obtained

a second derivative sqp method global convergence sequential quadratic programming sqp methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems although second derivative information may often be calculated there is little practical theory that justifies exact hessian sqp methods in particular the resulting quadratic programming qp subproblems are often nonconvex and thus finding their global solutions may be computationally nonviable this paper presents a second derivative sqp method based on quadratic subproblems that are either convex and thus may be solved efficiently or need not be solved globally additionally an explicit descent constraint is imposed on certain qp subproblems which guides the iterates through areas in which nonconvexity is a concern global convergence of the resulting algorithm is established

bounded oscillation for second order nonlinear delay differential equation in a critical state in this paper we establish sufficient conditions for bounded oscillation of the second order nonlinear delay differential equation x t i 1m pix t i f t x t 1 t x t n t under a critical state by the second order ordinary differential equation y t 1 e e 0t f t e 0 t 1 t y t e 0 t t y t 0 at the same time necessary conditions for the above bounded oscillation equation are obtained

oscillation criteria for second order functional difference equations with summation small coefficient we consider the second order functional difference equation a n n p n x g n 0 where n p n are sequences of integers with a n 0 0 g n n limn g n p n 0 and p n 0 we obtain some necessary conditions for equation 1 exists nonoscillatory solutions and some sufficient conditions for equation 1 is oscillatory

a second derivative sqp method local convergence and practical issues gould and robinson siam j optim 20 2010 pp 2023 2048 proved global convergence of a second derivative sqp method for minimizing the exact ell 1 merit function for a fixed value of the penalty parameter this result required the properties of a so called cauchy step which was itself computed from a so called predictor step in addition they allowed for the additional computation of a variety of optional accelerator steps that were intended to improve the efficiency of the algorithm the main purpose of this paper is to prove that a nonmonotone variant of the algorithm is quadratically convergent for two specific realizations of the accelerator step this is verified with preliminary numerical results on the hock and schittkowski test set once fast local convergence is established we consider two specific aspects of the algorithm that are important for an efficient implementation first we discuss a strategy for defining the positive definite matrix b k used in computing the predictor step that is based on a limited memory bfgs update second we provide a simple strategy for updating the penalty parameter based on approximately minimizing the ell 1 penalty function over a sequence of increasing values of the penalty parameter

a second order nonlinear difference equation oscillation and asymptotic behavior discrete analogues are investigated for well known results on oscillation growth and asymptotic behavior of solutions of y q t y 0 for q t 0 and for q t 0 the analogue of atkinson s oscillation criterion is shown to be true for 2yn 1 qn yn 0 but the analogue for atkinson s nonoscillation criterion is shown to be false

a line search exact penalty method with bi object strategy for nonlinear constrained optimization the exact penalty methods are very popular because of their ability to handle degenerate problems and inconsistent constraint linearizations this paper presents a line search exact penalty method with bi object strategy lsbo for nonlinear constrained optimization in the algorithm lsbo the penalty parameter is selected at every iteration such that the sufficient progress toward feasibility and optimality is guaranteed along the search direction in contrast with classical exact penalization approaches lsbo method has two goals to determine whether the current iteration is successful or not one is improving the feasibility and the other is reducing the value of the objective function moreover the penalty parameter is only related to the information at the current iterate point the sequence of the penalty parameter is non monotone which does not affect the global convergence in theory and is seen to be advantageous in practice it is shown that the algorithm enjoys favorable global convergence properties under the weaker assumptions numerical experiments illustrate the behavior of the algorithm on various difficult situations penalty factor is only related to the information at the current iterate point the sequence of the penalty parameter is non monotone the search direction is related to the penalty factor the acceptable criterion is not related to the penalty factor method can handle degenerate problems and inconsistent constraint linearizations

asymptotic properties of solutions of second order neutral difference equations abstract in this paper we study asymptotic behavior of solutions of second order neutral difference equation 2 x n px n k f n x n 0 we present conditions under which all nonoscillatory solutions of the above equation have the property x n cn o n for some c r as well as sufficient conditions under which all nonoscillatory solutions are asymptotically linear

automatic decrease of the penalty parameter in exact penalty function methods this paper presents an analysis of the involvement of the penalty parameter in exact penalty function methods that yields modifications to the standard outer loop which decreases the penalty parameter typically dividing it by a constant the procedure presented is based on the simple idea of making explicit the dependence of the penalty function upon the penalty parameter and is illustrated on a linear programming problem with the l1 exact penalty function and an active set approach the procedure decreases the penalty parameter when needed to the maximal value allowing the inner minimization algorithm to leave the current iterate it moreover avoids unnecessary calculations in the iteration following the step in which the penalty parameter is decreased we report on preliminary computational results which show that this method can require fewer iterations than the standard way to update the penalty parameter this approach permits a better understanding of the performance of exact penalty methods

monotone properties of certain classes of solutions of second order difference equations the authors consider the difference equations an xn qnxn 1 and an xn qnf xn 1 where an 0 qn 0 and f r r is continuous with uf u 0 for u 0 they obtain necessary and sufficient conditions for the asymptotic behavior of certain types of nonoscillatory solutions of and sufficient conditions for the asymptotic behavior of certain types of nonoscillatory solutions of sufficient conditions for the existence of these types of nonoscillatory solutions are also presented some examples illustrating the results and suggestions for further research are included

bounded oscillation of second order delay difference equations of unstable type abstract a series of sufficient conditions are obtained for the bounded oscillation of second order delay difference equations of unstable type some of them are sharp

oscillation theorems for second order advanced functional difference equations abstract we consider the second order advanced functional difference equation a n n p n g n 0 where a n 0 s n 0 1 a s p n 0 p n 0 g n n 1 g n is a monotone increasing integer sequence we obtain some new oscillation criteria through an appropriate riccati equation

new oscillation criteria for second order nonlinear neutral delay difference equations in this paper we will establish some new oscillation criteria for the second order nonlinear neutral delay difference equation d a n dx n p nx n t c f n x n s 0 n 0 1 2 where c 0 is a quotient of odd positive integers

local conservation laws for the two dimensional periodic su n 1 toda lattices an infinite number of local conservation laws are derived for the two dimensional periodic su n 1 toda lattice equations following the well known method for the sine gordon equation

existence of bounded positive solutions for a system of difference equations abstract this paper deals with the second order nonlinear neutral delay system of difference equations a n x n b n x n f n x h 1 n x h kn y w 1 n y w kn c n n n 0 p n y n q n y n g n x s 1 n x s kn y t 1 n y t kn r n n n 0 by virtue of the banach fixed point theorem and some natural modifications of the techniques in the literature we prove the existence results of uncountably many bounded positive solutions for the system of difference equations seven examples are constructed to explain the main results presented in this paper

oscillation and non oscillation of solutions of second order difference equations involving generalized difference abstract in this paper sufficient conditions are obtained for oscillation non oscillation of solutions of second order difference equations involving generalized difference of the form a p n 1 a y n 1 q n y n 0 n 1 and a p n 1 a y n 1 q n y n f n n 1 where a is defined by a y n y n 1 ay n a 0 necessary and sufficient conditions are obtained for oscillation of the first equation with a 0 and q n q a non zero constant the signs of q n and a play an important role for oscillation non oscillation of these two equations

primal methods are better than dual methods for solving overdetermined linear systems in the l sense it is generally believed that methods based upon solving the dual of the linear programming formulation of the linear l infty problem are superior to methods based upon the primal formulation a primal approach is presented along with evidence that for random problems primal methods are to be preferred it is then shown that the method generally considered to be the best algorithm for discrete linear approximation in the l infty norm actually owes much of its efficiency to effective choice of a starting point this phenomenon is explained with the aid of results from classical minimax theory which are then used to determine a suitable initial point for a primal method with this enhancement it would appear that the primal approach is also preferable for problems arising from function approximations

exact penalty functions in constrained optimization in this paper formal definitions of exactness for penalty functions are introduced and sufficient conditions for a penalty function to be exact according to these definitions are stated thus providing a unified framework for the study of both nondifferentiable and continuously differentiable penalty functions in this framework the best known classes of exact penalty functions are analyzed and new results are established concerning the correspondence between the solutions of the constrained problem and the unconstrained minimizers of the penalty functions

oscillation theorems for second order neutral difference equations abstract oscillation criteria for the second order difference equations of the form 2xn qnf xn r 0 and the neutral difference equation 2 xn pxn k qnf xn r 0 are established here xn xn 1 xn is the forward difference operator 1 p is a real number and k are nonnegative integers qn is a sequence of nonnegtive real numbers and f r r is continuous

existence and multiple solutions for a second order difference boundary value problem via critical point theory in this paper the critical point theory is employed to establish existence and multiple solutions for a second order difference boundary value problem

existence of uncountably many bounded positive solutions for second order nonlinear neutral delay difference equations this paper deals with the second order nonlinear neutral delay difference equation d a n d x n b n x n t c n f n x f 1 n x f 2 n x f k n d n n n 0 by using krasnoselskii s fix

asymptotic behavior of nonlinear difference systems in this paper we study a general variational stability introduced mainly for weakly stable difference systems moreover we obtain asymptotic formulae for these systems which state new results about asymptotic behavior for perturbed systems under general hypotheses

infeasibility detection and sqp methods for nonlinear optimization this paper addresses the need for nonlinear programming algorithms that provide fast local convergence guarantees regardless of whether a problem is feasible or infeasible we present a sequential quadratic programming method derived from an exact penalty approach that adjusts the penalty parameter automatically when appropriate to emphasize feasibility over optimality the superlinear convergence of such an algorithm to an optimal solution is well known when a problem is feasible the main contribution of this paper however is a set of conditions under which the superlinear convergence of the same type of algorithm to an infeasible stationary point can be guaranteed when a problem is infeasible numerical experiments illustrate the practical behavior of the method on feasible and infeasible problems

general a monotone operators and perturbed iterations for nonlinear set valued relaxed cocoercive operator inclusion problems in this paper we introduce the notion of general a monotone operators in banach spaces study some properties of general a monotone operator and the new proximal mapping associated with the general a monotone operators by using alber s inequalities nalder s results and the new proximal mapping technique we also construct two new class of perturbed iterative algorithms with mixed errors for solving a new class of nonlinear set valued relaxed cocoercive operator inclusions and study applications of general a monotone operators to the approximation solvability of the nonlinear set valued relaxed cocoercive operator inclusion problems in banach spaces furthermore the general a monotone operators are illustrated by some examples the results presented in this paper improve and generalize the corresponding results on strongly monotone quasi variational inclusions and nonlinear implicit quasi variational inclusions

oscillation of solutions for second order nonlinear difference equations with nonlinear neutral term abstract some riccati type difference inequalities are given for the second order nonlinear difference equations with nonlinear neutral term and using these inequalities we obtain some oscillation criteria for the above equation

oscillation theorems for perturbed nonlinear second order difference equations abstract sufficient conditions for the oscillation of all solutions of perturbed difference equations of the form a n 1 y n 1 q n y n p n y n y n n n are obtained examples are inserted to illustrate the results

oscillation criteria for a nonlinear difference equation abstract essential and nontrivial improvements and extensions of several recent oscillation criteria are obtained for the nonlinear difference equation 1 below

global existence and mann iterative algorithms of positive solutions for first order nonlinear neutral delay differential equations abstract this paper deals with the first order nonlinear neutral delay differential equation d dt x t p t x t f t x 1 t x 2 t x n t 0 t t 0 where 0 p c t 0 r f c t 0 r n r and l c t 0 r with limt l t for l 1 2 n by using the banach fixed point theorem we prove the global existence of uncountably many bounded positive solutions for the above equation relative to all ranges of the function p construct some mann type iterative algorithms with errors to approximate these positive solutions and discuss several error estimates between the sequences generated by the iterative algorithms and these positive solutions seven examples are presented to illuminate the results obtained in this paper

nonoscillation and oscillation of solutions of a class of third order difference equations in this paper sufficient conditions are obtained for nonoscillation oscillation of all solutions of a class of nonlinear third order difference equations of the form a pn a2yn qn a2yn f n yn ayn a2yn involving the generalized difference operator a which is defined as ayn yn 1 ayn a 0

solvable systems of wave equations and non abelian toda lattices relates equivalence classes of coupled systems of n linear wave equations to motions of an n n matrix dynamical systems the two dimensional non abelian toda lattice in particular the correspondence is shown to relate those coupled systems of wave equations with progressing wave general solutions to motions of the finite non abelian toda lattice with free ends generalizing a known result for the n 1 case some non trivial motions of such toda lattices are found and the corresponding coupled wave equations and their progressing wave general solutions are given other consequences of the correspondence and possible application of the progressing waves are discussed

bounded and zero convergent solutions of second order difference equations abstract in this paper we study boundedness and monotonicity properties of a homogeneous second order linear difference equation under certain conditions it is shown that every solution must eventually be monotonic the question of when such monotonic solutions diverge to infinity or converge to zero and the corresponding impact this behavior has on recessive and dominant solutions is investigated a necessary and sufficient condition for all solutions to be bounded is presented comparison theorems are also discussed

discontinuous piecewise linear optimization a theoretical framework and a practical algorithm are presented to solve discontinuous piecewise linear optimization problems dealing with functions for which theridges are known a penalty approach allows one to consider such problems subject to a wide range of constraints involving piecewise linear functions although the theory is expounded in detail in the special case of discontinuous piecewiselinear functions it is straightforwardly extendable using standard nonlinear programming techniques tononlinear discontinuous piecewise differentiable functions the descent algorithm which is elaborated uses active set and projected gradient approaches it is a generalization of the ideas used by conn to deal with nonsmoothness in thel1 exact penalty function and it is based on the notion ofdecomposition of a function into a smooth and a nonsmooth part the constrained case is reduced to the unconstrained minimization of a piecewise linear l1 exact penalty function we also discuss how the algorithm is modified when it encounters degenerate points preliminary numerical results are presented the algorithm is applied to discontinuous optimization problems from models in industrial engineering 1998 the mathematical programming society inc published by elsevier science b v

bounded oscillation for second order nonlinear neutral difference equations in critical and non critical states the sufficient and necessary conditions for the bounded oscillation of the second order nonlinear neutral delay difference email protected 2 x n px email protected email protected i 1mq ix email protected i f n x email protected 1 n x email protected l n are obtained in critical and non critical cases