self adaptive methods for mixed quasi variational inequalities it is well known that the variational inequalities involving the nonlinear term are equivalent to the fixed point problems and the resolvent equations in this paper we use these alternative equivalent formulations to suggest and analyze some new self adaptive iterative methods for solving mixed quasi variational inequalities our results can be viewed as significant extensions of the previously known results for mixed quasi variational inequalities an example is given to illustrate the efficiency of the proposed method

three step iterations for variational inequalities and nonexpansive mappings in this paper we introduce a new three step iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality using the technique of updating the solution we show that the sequence converges strongly to a common element of two sets under some control conditions results proved in this paper may be viewed as an improvement and refinement of the recent results of noor and huang m aslam noor z huang three step methods for nonexpansive mappings and variational inequalities appl math comput in press and yao and yao y yao j c yao on modified iterative method for nonexpansive mappings and monotone mappings appl math comput in press

numerical method for general mixed quasi variational inequalities abstract in this paper we use the resolvent operator to suggest and analyze a new numerical method for solving general mixed quasi variational inequalities coupled with a new direction and a new step size k under certain conditions the global convergence of the proposed method is proved some preliminary computational results are given to illustrate the efficiency of the proposed method since the general mixed quasi variational inequalities include general variational inequalities quasi variational inequalities and nonlinear implicit complementarity problems as special cases results proved in this paper continue to hold for these problems results proved in this paper may be viewed as a refinement of the previous known results

new approximation schemes for general variational inequalities in this paper we suggest and consider a class of new three step approximation schemes for general variational inequalities our results include ishikawa and mann iterations as special cases we also study the convergence criteria of these schemes

systems of generalized nonlinear variational inequalities and its projection methods abstract based on relaxed cocoercive monotonicity a new generalized class of nonlinear variational inequality problems is presented our results improve and extend the recent ones announced by h y huang m a noor an explicit projection method for a system of nonlinear variational inequalities with different r cocoercive mappings appl math comput 190 2007 356 361 s s chang h w joseph lee c k chan generalized system for relaxed cocoercive variational inequalities in hilbert spaces appl math lett 20 2007 329 334 r u verma generalized system for relaxed cocoercive variational inequalities and its projection methods j optim theory appl 121 2004 203 210 m a noor general variational inequalities appl math lett 1 1988 119 121 and many others

mixed quasi variational inequalities in this paper we use the resolvent operator and auxiliary principle techniques to suggest and analyze several iterative algorithms for solving mixed quasi variational inequalities and related problems we study the convergence criteria of these algorithms under mild conditions we also study the global stability and existence of a unique solution of these quasi variational inequalities by using the dynamical systems approach our results represent refinement and improvement of the previously known results for variational inequalities

three steps iterative algorithms for mixed variational inequalities it is well known that the mixed variational inequalities are equivalent to the fixed point problems and the resolvent equations using this equivalence we suggest and consider a new three step iterative method for solving mixed variational inequalities the new iterative method is obtained by using three steps under suitable conditions we prove that the new method is globally convergent our results can be viewed as significant extensions of the previously known results for mixed variational inequalities since mixed variational inequalities include variational inequalities as special cases our method appears to be a new one for solving variational inequalities preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method

a projection algorithm for general variational inequalities with perturbed constraint sets we consider the problem of general variational inequalities gvi with nonmonotone operator in a finite dimensional space we propose a method to solve gvi that at each iteration considers only one projection on an easy approximation of the constraint set which is important from a practical point of view we analyse the convergence of the algorithm under a weak cocoercivity condition using variational metric analysis computational experience is reported and comparative analysis with other two algorithms is also given for the monotone case

on an iterative method for variational inequalities a number of numerical solutions are presented as examples of a new iterative method for variational inequalities the iterative method is based on the reduction of variational inequalities to the wiener hopf equations for obstacle problems the convergence is guaranteed inw 1 p spaces forp 2 the examples presented are one and two dimensional obstacle problems in cases when the greens function is known but the method is very general

iterative methods for linear complementarity problems with upperbounds on primary variables this paper is concerned with iterative methods for the linear complementarity problem lcp of findingx and y in rn such thatc dx y 0 b x 0 andxt c dx y yt b x 0 whenb 0 this is the lcp m q withm l 0d t which is in turn equivalent to a linear variational inequality over a rectangle this type of problem arises for example from quadratic programming qp problems with upper and lower bounds ifd is symmetric and from multicommodity market equilibrium problems with institutional price controls imposed ifd is not necessarily symmetric iterative methods for the lcp m q with symmetricm are well developed and studied using qp applications for nonsymmetric cases withm being either an h matrix with positive diagonals or a z matrix there exists a robust iterative method with guaranteed convergence this paper extends this algorithm so that the lcp m q withm l 0d t which is neither symmetric nor an h matrix with positive diagonals nor a z matrix can be processed when onlyd notm satisfies such properties the case whered is nonsymmetric is explicitly discussed

some comments on nonlinear extended variational inequalities without differentiability applications and solution methods in a recent paper konnov 1 has considered and studied a class of variational inequalities which is called nonlinear extended variational inequalities we would like to point out that this class was introduced and studied by noor 2 in 1988 since then this class of variational inequalities has been studied extensively and is well documented in the literature to be more precise let k be a closed convex set in a real hilbert space whose norm and inner product are denoted by and respectively for given nonlinear operators g h k h find x k such that g x h x h x 0 x k 1

an inexact implicit method for general mixed variational inequalities in the present paper we present an inexact implicit method with a variable parameter for general mixed variational inequalities we use a self adaptive technique to adjust parameter r at each iteration the main advantage of this technique is that the method can adjust the parameter automatically and the numbers of iteration are not very sensitive to different initial parameter r 0

fluctuating fronts as correlated extreme value problems an example of gaussian statistics in this paper we view fluctuating fronts made of particles on a one dimensional lattice as an extreme value problem the idea is to denote the configuration for a single front realization at time t by the set of co ordinates k i t identical with k 1 t k 2 t k n t t of the constituent particles where n t is the total number of particles in that realization at time t when k i t are arranged in the ascending order of magnitudes the instantaneous front position can be denoted by the location of the rightmost particle i e by the extremal value k f t max k 1 t k 2 t k n t t due to interparticle interactions k i t at two different times for a single front realization are naturally not independent of each other and thus the probability distribution p k f t based on an ensemble of such front realizations describes extreme value statistics for a set of correlated random variables in view of the fact that exact results for correlated extreme value statistics are rather rare here we show that for a fermionic front model in a reaction diffusion system p k f t is gaussian in a bosonic front model however we observe small deviations from the gaussian

a typed lambda calculus with intersection types intersection types are well known to type theorists mainly for two reasons firstly they type all and only the strongly normalizable lambda terms secondly the intersection type operator is a meta level operator that is there is no direct logical counterpart in the curry howard isomorphism sense in particular its meta level nature implies that it does not correspond to the intuitionistic conjunction the intersection type system is naturally a type inference system system a la curry but the meta level nature of the intersection operator does not allow to easily design an equivalent typed system system a la church there are many proposals in the literature to design such systems but none of them gives an entirely satisfactory answer to the problem in this paper we will review the main results in the literature both on the logical interpretation of intersection types and on proposed typed lambda calculi the core of this paper is a new proposal for a true intersection typed lambda calculus without any meta level notion namely any typable term in the intersection type inference has a corresponding typed term which is the same as the untyped term by erasing the type decorations and the typed term constructors with the same type and vice versa the main idea is to introduce a relevant parallel term constructor which corresponds to the intersection type constructor in such a way that terms in parallel share the same resources that is the same context of free typed variables three rules allow us to generate all typed terms the first two rules application and lambda abstraction are performed on all the components of a parallel term in a synchronized way finally via the third rule of local renaming once a free typed variable is bounded by lambda abstraction each of the terms in parallel can do its local renaming with type refinement of that particular resource

an explicit projection method for a system of nonlinear variational inequalities with different cocoercive mappings in this paper we introduce and consider a new system of variational inequalities involving two different operators using the projection technique we suggest and analyze new explicit iterative methods for this system of variational inequalities we also study the convergence analysis of the new iterative method under certain mild conditions since this new system includes the system of variational inequalities involving the single operator variational inequalities and related optimization problems as special cases results obtained in this paper continue to hold for these problems our results can be viewed as a refinement and improvement of the previously known results for variational inequalities

intersection types and lambda models invariance of interpretation by conversion is one of the minimal requirements for any standard model for the calculus with the intersection type systems being a general framework for the study of semantic domains for the calculus the present paper provides a syntactic characterisation of the above mentioned requirement in terms of characterisation results ibr intersection type assignment systems instead of considering conversion as a whole reduction and expansion will be considered separately not only for usual computational rules like but also for a number of relevant restrictions of those characterisations will be also provided for intersection filter structures that are indeed models

merit functions for general variational inequalities in this paper we consider some classes of merit functions for general variational inequalities using these functions we obtain error bounds for the solution of general variational inequalities under some mild conditions since the general variational inequalities include variational inequalities quasivariational inequalities and complementarity problems as special cases results proved in this paper hold for these problems in this respect results obtained in this paper represent a refinement of previously known results for classical variational inequalities

a new iterative method for variational inequalities it is well known that the variational inequalities are equivalent to the fixed point problems using this equivalence we suggest and consider a new three step iterative method for solving variational inequalities the new iterative method is obtained by using three steps under suitable conditions we prove that the new method is globally convergent our results can be viewed as significant extensions of the previously known results for variational inequalities preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method

a self adaptive method for solving general mixed variational inequalities abstract the general mixed variational inequality containing a nonlinear term is a useful and an important generalization of variational inequalities the projection method cannot be applied to solve this problem due to the presence of the nonlinear term to overcome this disadvantage noor m a noor pseudomonotone general mixed variational inequalities appl math comput 141 2003 529 540 used the resolvent equations technique to suggest and analyze an iterative method for solving general mixed variational inequalities in this paper we present a new self adaptive iterative method which can be viewed as a refinement and improvement of the method of noor global convergence of the new method is proved under the same assumptions as noor s method some preliminary computational results are given

on an iterative algorithm for general variational inequalities in this paper we suggest and analyze a new three step iterative algorithm for solving the general variational inequalities we also study the global convergence of the proposed method under some mild conditions since the general variational inequalities include variational inequalities quasi variational inequalities and quasi complementarity problems as special cases one can deduce similar results for these problems our results can be viewed as an improvement and refinement of the previously known and new results preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method

numerical comparison between prediction correction methods for general variational inequalities in this paper we propose two prediction correction methods for solving general variational inequalities the first method makes use of a descent direction to produce the new iterate while the second method generates the corrector by the improved extragradient method under certain conditions the global convergence of both methods is proved it is proved theoretically that the lower bound of the progress obtained by the second method is greater than that by the first one numerical results are given to verify and compare the numerical efficiency of these two predictor corrector methods

generalized nash games and quasi variational inequalities abstract a generalized nash game is an n person noncooperative game with nondisjoint strategy sets other names for this game form include social equilibria and pseudo nash games this paper explores both the qualitative and quantitative properties of such games through the use of quasi variational inequality theory several interesting relationships between the variational and quasi variational inequality forms of this class of games are described and the practical implementation of generalized nash games are explored at length

general variational inequalities and nonexpansive mappings in this paper we suggest and analyze some three step iterative schemes for finding the common elements of the set of the solutions of the noor variational inequalities involving two nonlinear operators and the set of the fixed points of nonexpansive mappings we also consider the convergence analysis of the suggested iterative schemes under some mild conditions since the noor variational inequalities include variational inequalities and complementarity problems as special cases results obtained in this paper continue to hold for these problems results obtained in this paper may be viewed as an refinement and improvement of the previously known results

on the relation between one species diffusion limited coalescence and annihilation in one dimension the close similarity between the hierarchies of multiple point correlation functions for the diffusion limited coalescence and annihilation processes has caused some recent confusion raising doubts as to whether such hierarchies uniquely determine an infinite particle system we elucidate the precise relations between the two processes arriving at the conclusion that the hierarchy of correlation functions does provide a complete representation of a particle system on the line we also introduce a new hierarchy of probability density functions for finding particles at specified locations and none in between this hierarchy is computable for coalescence through the method of empty intervals and is naturally suited for questions concerning the ordering of particles on the line

wigner surmise for domain systems in random matrix theory the spacing distribution functions p n s are well fitted by the wigner surmise and its generalizations in this approximation the spacing functions are completely described by the behavior of the exact functions in the limits s 0 and s most non equilibrium systems do not have analytical solutions for the spacing distribution and correlation functions because of that we explore the possibility to use the wigner surmise approximation in these systems we found that this approximation provides a first approach to the statistical behavior of complex systems in particular we use it to find an analytical approximation to the nearest neighbor distribution of the annihilation random walk

alternating kinetics of annihilating random walks near a free interface the kinetics of annihilating random walks in one dimension with the half line x 0 initially filled is investigated the survival probability of the nth particle from the interface exhibits power law decay with for n 1 and all odd values of n for all n even a faster decay with is observed from consideration of the eventual survival probability in a finite cluster of particles the rigorous bound is derived while a heuristic argument gives numerically this latter value appears to be a lower bound for the average position of the first particle moves to the right approximately as with a relatively sharp and asymmetric probability distribution

mean field approximation for spacing distribution functions in classical systems we propose a mean field method to calculate approximately the spacing distribution functions p n s in one dimensional classical many particle systems we compare our method with two other commonly used methods the independent interval approximation and the extended wigner surmise in our mean field approach p n s is calculated from a set of langevin equations which are decoupled by using a mean field approximation we find that in spite of its simplicity the mean field approximation provides good results in several systems we offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system the physical interpretation of each method is also discussed

pseudomonotone general mixed variational inequalities in this paper we use the resolvent equations and the auxiliary principle techniques to suggest a class of iterative resolvent methods for solving general mixed variational inequalities the convergence of the proposed methods only requires the pseudomonotonicity of the operator which is weaker than monotonicity as special cases we obtain various known and new results for solving various classes of variational inequalities and related problems

multi scaling of the n point density function for coalescing brownian motions this paper gives a derivation for the large time asymptotics of the n point density function of a system of coalescing brownian motions on r

self adaptive methods for general variational inequalities abstract it is well known that the general variational inequalities are equivalent to the fixed point problems and the wiener hopf equations in this paper we use these alternative equivalent formulations to suggest and analyze some new self adaptive iterative methods for solving the general variational inequalities our results can be viewed as a significant extension of the previously known results for variational inequalities an example is given to illustrate the efficiency of the proposed method

stochastic evolution of systems of particles obeying an exclusion principle abstract we present numerical solutions of a nonlinear fokker planck equation to describe a fermi gas the model equation g kaniadakis p quarati phys rev e 49 1994 5103 includes a nonlinear term due to the pauli exclusion principle which has been disregarded up to now a new numerical method to study the time evolution of the distribution function is presented the method can be applied to any potential and allows us to describe accurately and efficiently a fermi gas in this work we focus on the differences between the results of the linear case in which the effects of the exclusion principle are not considered and the nonlinear case in which these effects are taken into account

tangent projection equations and general variational inequalities in this paper we establish the equivalence between the general variational inequalities and tangent projection equations this equivalence is used to discuss the local convergence analysis of a wide class of iterative methods for solving the general variational inequalities we show that some existing methods can identify the optimal face after finitely many iterations under the degenerate assumption

quasi variational inequalities and applications to the traffic equilibrium problem discussion of a paradox abstract this paper attempts to explore the possibility of solving the traffic assignment problem with elastic demands by way of a quasi variational inequality it is shown that the solving procedure proposed by maugeri 1987 with respect to the fixed demands model is also available when the equilibrium problem with elastic demands is expressed in terms of a quasi variational inequality a numerical example is presented to illustrate the computational procedure and to discuss a paradox moreover a theorem that ensures the existence of a solution of the quasi variational inequality is exhibited

self adaptive projection algorithms for general variational inequalities in this paper we consider and analyze a new class of self adaptive projection algorithms for solving general variational inequalities by using the technique of updating the solution we prove that the convergence of these new methods only requires the pseudomonotonicity which is a weaker condition than monotonicity these new methods differ from the previously known splitting methods for solving variational inequalities and related complementarity problems proof of convergence is very simple as special cases we can obtain a number of four step forward backward splitting methods of noor for solving variational inequalities

general nonlinear variational inequalities abstract the fixed point technique is used to prove the existence of a unique solution of a new unified and general class of nonlinear variational inequalities several special cases which can be obtained from our main result are also discussed

exchange price equilibria and variational inequalities the aim of this paper is to show the relevance of the concept and the theory of variational inequalities in the study of economic equilibria

intersection types a la church in this paper we present a fully typed calculus based on the intersection type system discipline which is a counterpart a la church of the type assignment system as invented by coppo and dezani the relationship between and the intersection type assignment system is the standard isomorphism between typed and type assignment system and so the typed language inherits from the untyped system all the good properties like subject reduction and strong normalization moreover both type checking and type reconstruction are decidable

sensitivity analysis framework for variational inequalities in this paper a sensitivity analysis framework is developed for variational inequalities the perturbed solution to a parametric variational inequality problem is shown to be continuous and directionally differentiable under appropriate second order and regularity assumptions moreover this solution is once continuously differentiable if strict complementarity also holds

an exact solution for travelling waves of ut duxx u uk abstract an exact analytical solution for travelling waves of the fisher equation with a general nonlinearity is found the boundary values the boundedness and the stability of the solution are discussed the reduced ordinary differential equation of the equation of our study is investigated for the painleve property

variational inequalities for fuzzy mappings ii in this paper we establish the equivalence between the variational inequalities for fuzzy mappings and the wiener hopf equations for fuzzy mappings we use this equivalence to suggest a number of new iterative algorithms for solving the variational inequalities for fuzzy mappings we also study the convergence criteria of these iterative algorithms the auxiliary principle technique is used to study the existence of a solution of the variational inequality for fuzzy mappings and to suggest a novel and innovative iterative algorithm for computing the approximate solution the results proved in this paper represent an improvement of previously known results

projection proximal methods for general variational inequalities in this paper we consider and analyze some new projection proximal methods for solving general variational inequalities the modified methods converge for pseudomonotone operators which is a weaker condition than monotonicity the proposed methods include several new and known methods as special cases our results can be considered as a novel and important extension of the previously known results since the general variational inequalities include the quasi variational inequalities and implicit complementarity problems as special cases results proved in this paper continue to hold for these problems

some resolvent iterative methods for variational inclusions and nonexpansive mappings in this paper we suggest and analyze three step iterations for finding the common element of the set of fixed points of a nonexpansive mappings and the set of the solutions of the variational inclusions using the resolvent operator technique we also study the convergence criteria of three step iterative method under some mild conditions our results include the previous results of noor m aslam noor general variational inequalities and nonexpansive mappings j math anal appl 331 2007 810 822 and noor and huang m aslam noor zhenyu huang three step methods for nonexpansive mappings and variational inequalities appl math comput in press doi 10 1016 j amc 2006 08 088 as special cases and may be considered as an improvement and refinement of the previously known results

a subgradient extragradient algorithm for solving multi valued variational inequality in this paper we propose a subgradient extragradient method for solving multi valued variational inequality it is showed that the method converges globally to a solution of multi valued variational inequality provided the multi valued mapping is pseudomonotone with nonempty compact convex values convergence rate is analyzed preliminary computational experience is also reported

microscopic spatial correlations induced by external noise in a reaction diffusion system abstract the reversible single species reaction scheme x 2x has long served as an example of a system with nonlinear macroscopic dynamics in recent years a microscopic version of this interacting particle system namely the diffusion controlled limit has been solved exactly in one spatial dimension the effects of internal fluctuations correlations arising in nonequilibrium situations and external noise can all be studied in this model diffusion reaction system without approximation here we review some recent results focusing on an exact treatment of the effect of spatially homogeneous temporal fluctuations in the growth rate of the process the rate for the x 2x process we find that the nonequilibrium steady state possesses new microscopic length scales resulting from the nonequilibrium constraints demonstrating that spatially homogeneous external noise can introduce spatial correlations

strong convergence of three step relaxed hybrid steepest descent methods for variational inequalities in this paper we prove the strong convergence of a three step relaxed hybrid steepest descent method for solving variational inequalities under some suitable conditions our result can be considered as an improvement and refinement of the previously known results

some developments in general variational inequalities general variational inequalities provide us with a unified natural novel and simple framework to study a wide class of equilibrium problems arising in pure and applied sciences in this paper we present a number of new and known numerical techniques for solving general variational inequalities using various techniques including projection wiener hopf equations updating the solution auxiliary principle inertial proximal penalty function dynamical system and well posedness we also consider the local and global uniqueness of the solution and sensitivity analysis of the general variational inequalities as well as the finite convergence of the projection type algorithms our proofs of convergence are very simple as compared with other methods our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems since the general variational inequalities include quasi variational inequalities and quasi implicit complementarity problems as special cases results presented here continue to hold for these problems several open problems have been suggested for further research in these areas

on convergence criteria of generalized proximal point algorithms we analyze some generalized proximal point algorithms which include the previously known proximal point algorithms as special cases weak and strong convergence of the proposed proximal point algorithms are proved under some mild conditions

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

on a class of variational inequalities in this paper we introduce and study a new unified and general class of variational inequalities we derive the general error estimates for the finite element solutions of variational inequalities it has been shown that a class of contact problems with friction terms arising in elastostatics can be studied in the framework of variational inequalities several special cases which can be obtained from the general results are also discussed

some new extragradient iterative methods for variational inequalities abstract in this paper we suggest and analyze some new extragradient iterative methods for finding the common element of the fixed points of a nonexpansive mapping and the solution set of the variational inequality for an inverse strongly monotone mapping in a hilbert space we also consider the strong convergence of the proposed method under some mild conditions several special cases are also discussed results proved in this paper may be viewed as improvement and refinement of the previously known results

new extragradient type methods for general variational inequalities in this paper we consider and analyze a new class of extragradient type methods for solving general variational inequalities the modified methods converge for pseudomonotone operators which is weaker condition than monotonicity our proof of convergence is very simple as compared with other methods the proposed methods include several new and known methods as special cases our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems

iterative methods for solving extended general mixed variational inequalities in this paper we introduce and consider a new class of mixed variational inequalities involving four operators which are called extended general mixed variational inequalities using the resolvent operator technique we establish the equivalence between the extended general mixed variational inequalities and fixed point problems as well as resolvent equations we use this alternative equivalent formulation to suggest and analyze some iterative methods for solving general mixed variational inequalities we study the convergence criteria for the suggested iterative methods under suitable conditions our methods of proof are very simple as compared with other techniques the results proved in this paper may be viewed as refinements and important generalizations of the previous known results

a parallel projection method for a system of nonlinear variational inequalities in this paper we introduce and consider a new system of nonlinear variational inequalities involving two different operators using the parallel projection technique we suggest and analyze an iterative method for this system of variational inequalities we establish a convergence result for the proposed method under certain conditions our results can be viewed as a refinement and improvement of the previously known results for variational inequalities

a modified inexact implicit method for mixed variational inequalities in this paper we suggest and analyze an inexact implicit method with a variable parameter for mixed variational inequalities by using a new inexactness restriction under certain conditions the global convergence of the proposed method is proved some preliminary computational results are given to illustrate the efficiency of the new inexactness restriction the results proved in this paper may be viewed as improvement and refinement of the previously known results

multiscaling of correlation functions in single species reaction diffusion systems we derive the multi scaling of probability distributions of multi particle configurations for the binary reaction diffusion system in a a o in d o in d 1 for the binary reaction we find that the probability pt n delta v of finding n particles in a fixed volume element delta v at time t decays in the limit of large time as ln t t n ln t n n 1 2 for d 2 and t nd 2 t n n 1 epsilon 4 o epsilon2 for d 2 here epsilon 2 d for the ternary reaction in one dimension we find that pt n delta v approximately ln t t n 2 ln t n n 1 n 2 6 the principal tool of our study is the dynamical renormalization group we compare predictions of epsilon expansions for pt n delta v for a binary reaction in one dimension against the exact known results we conclude that the epsilon corrections of order two and higher are absent in the previous answer for pt n delta v for n 1 2 3 4 furthermore we conjecture the absence of epsilon2 corrections for all values of n

optimal stochastic scheduling of power generation systems with scheduling delays and large cost differentials the optimal scheduling or unit commitment of power generation systems to meet a random demand involves the solution of a class of dynamic programming inequalities for the optimal cost and control law we study the behavior of this optimality system in terms of two parameters i a scheduling delay e g the startup time of a generation unit and ii the relative magnitudes of the costs operating or starting of different units in the first case we show that under reasonable assumptions the optimality system has a solution for all values of the delay and as the delay approaches zero that the solutions converge uniformly to those of the corresponding system with no delays in the second case we show that as the cost of operating or starting a given machine increases relative to the costs of the other machines there is a point beyond which the expensive machine is not used except in extreme situations we give a formula for the relative costs that characterize this point moreover we show that as

modified descent projection method for solving variational inequalities in this paper we propose a modified descent projection method for solving variational inequalities the method makes use of a descent direction to produce the new iterate and can be viewed as an improvement of the descent projection method by using a new step size under certain conditions the global convergence of the proposed method is proved in order to demonstrate the efficiency of the proposed method we provide numerical results for a traffic equilibrium problems

generalized viscosity approximation methods for mixed equilibrium problems and fixed point problems in this paper we present a new iterative method based on the hybrid viscosity approximation method and the hybrid steepest descent method for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of common fixed points of a finite family of nonexpansive mappings in hilbert spaces furthermore we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters the results presented in this paper improve and extend the corresponding results reported by some authors recently