las vegas algorithms for linear and integer programming when the dimension is small this paper gives an algorithm for solving linear programming problems for a problem with n constraints and d variables the algorithm requires an expected o d2n logn o d d 2 o 1 o d4 n logn arithmetic operations as n the constant factors do not depend on d also an algorithm is given for integer linear programming let 4 bound the number of bits required to specify the rational numbers defining an input constraint or the objective function vector let n and d be as before then the algorithm requires expected o 2ddn 8dd n l n n ln n do d 4 ln n operations on numbers with do 1 4 bits as n where the constant factors do not depend on d or 4 to other convex programming problems for example an algorithm for finding the smallest sphere enclosing a set of n points in ed has the same time bound

strong convergence theorems by hybrid methods for families of nonexpansive mappings in hilbert spaces abstract in this paper we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes nakajo and takahashi s theorems k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 simultaneously furthermore we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from nakajo and takahashi using this theorem we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a hilbert space

strong convergence of modified mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space we propose two modifications of the mann iterations in a uniformly smooth banach space one for nonexpansive mappings and the other for the resolvent of accretive operators the two modified mann iterations are proved to have strong convergence

linear programming in linear time when the dimension is fixed it is demonstrated that the linear programming problem in d variables and n constraints can be solved in o n time when d is fixed this bound follows from a multidimensional search technique which is applicable for quadratic programming as well there is also developed an algorithm that is polynomial in both n and d provided d is bounded by a certain slowly growing function of n

a quasi separation principle and newton like scheme for coherent quantum lqg control abstract this paper is concerned with the coherent quantum linear quadratic gaussian lqg control problem of constructing an optimal controller for linear quantum plants using a quadratic performance criterion coherent quantum feedback control does not employ classical measurements which inherently entail the loss of quantum information a coherent quantum controller is itself a quantum system and this imposes physical realizability pr constraints on the quantum stochastic differential equation which governs such a controller pr corresponds to the equivalence of the controller to an open quantum harmonic oscillator whereby its state space matrices are related to the hamiltonian and coupling operators of the oscillator the hamiltonian parameterization of the controller is combined with frechet differentiation of the lqg cost with respect to the state space matrices in order to obtain equations for the optimal controller a quasi separation property for the gain matrices of the quantum controller is established and a newton like iterative scheme for the numerical solution of the equations is outlined

shrinking projection methods for firmly nonexpansive mappings abstract the purpose of this paper is to study the shrinking projection method for firmly nonexpansive mappings the method gives us a strong convergence iteration for a family of firmly nonexpansive mappings and also permit us to obtain a sufficient condition for the existence of a fixed point of a firmly nonexpansive mapping

strong convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces the purpose of the paper is to introduce modified halpern and ishikawa iteration for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in banach spaces we also consider two strong convergence theorems for relatively nonexpansive mappings with some proper restriction

convergence of the modified mann s iteration method for asymptotically strict pseudo contractions abstract let c be a closed convex subset of a real hilbert space h and assume that t is an asymptotically strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the modified mann s algorithm generates a sequence x n via the formula x n 1 n x n 1 n t n x n n 0 it is proved that if the control sequence n is chosen so that n 1 for some 0 1 then x n converges weakly to a fixed point of t we also modify this iteration method by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strongly convergent sequence

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

a frequency domain condition for the physical realizability of linear quantum systems a recently emerging approach to the feedback control of linear quantum systems involves the use of a controller which itself is a quantum linear system this approach to quantum feedback control referred to as coherent quantum feedback control has the advantage that it does not destroy quantum information is fast and has the potential for efficient implementation an important issue which arises both in the synthesis of linear coherent quantum controllers and in the modeling of linear quantum systems is the issue of physical realizability this issue relates to the property of whether a given set of linear quantum stochastic differential equations corresponds to a physical quantum system satisfying the laws of quantum mechanics under suitable assumptions the paper shows that the question of physical realizability is equivalent to a frequency domain j j unitary condition this is important in controller synthesis since it is the transfer function matrix of the controller which determines the closed loop system behavior

a randomized algorithm for fixed dimensional linear programming we give a las vegas randomized algorithm for linear programming in a fixed dimensiond for which the expected computation time is o d 3 varepsilon d d n where limd e d 0 this improves the corresponding worst case complexity o 3 d 2 n the method is based on a recent idea of clarkson two variations on the algorithm are examined briefly

strong convergence theorems for strongly nonexpansive sequences the aim of this paper is to prove a strong convergence theorem for a pair of sequences of nonexpansive mappings in a hilbert space where one of them is a strongly nonexpansive sequence and provide some applications of the theorem

weak and strong convergence theorems for strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t is a strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the mann s algorithm generates a sequence x n by the formula x n 1 n x n 1 n t x n n 0 it is proved that if the control sequence n is chosen so that n 1 and n 0 n 1 n then x n converges weakly to a fixed point of t however this convergence is in general not strong we then modify mann s algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence this result extends a recent result of nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 from nonexpansive mappings to strict pseudo contractions

realization of the hybrid method for mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space h in order to overcome this weakness nakajo and takahashi proposed the hybrid method for mann s iteration process x 0 c chosen arbitrarily y n n x n 1 n tx n c n z c y n z x n z q n z c x 0 x n z x n 0 x n 1 p c n q n x 0 n 0 1 2 where c is a nonempty closed convex subset of h t c c is a nonexpansive mapping and p k is the metric projection from h onto a closed convex subset k of h however it is difficult to realize this iteration process in actual computing programs because the specific expression of p c n q n x 0 cannot be got in general in the case where c h we obtain the specific expression of p c n q n x 0 and thus the hybrid method for mann s iteration process can be realized easily numerical results show advantages of our result

a numerical approach to optimal coherent quantum lqg controller design using gradient descent abstract this paper is concerned with coherent quantum linear quadratic gaussian cqlqg control the problem is to find a stabilizing measurement free quantum controller for a quantum plant so as to minimize a mean square cost for the fully quantum closed loop system the plant and controller are open quantum systems interconnected through bosonic quantum fields in comparison with the observation actuation structure of classical controllers coherent quantum feedback is less invasive to the quantum dynamics the plant and controller variables satisfy the canonical commutation relations ccrs of a quantum harmonic oscillator and are governed by linear quantum stochastic differential equations qsdes in order to correspond to such oscillators these qsdes must satisfy physical realizability pr conditions in the form of quadratic constraints on the state space matrices reflecting the ccr preservation in time the symmetry of the problem is taken into account by introducing equivalence classes of coherent quantum controllers generated by symplectic similarity transformations we discuss a modified gradient flow which is concerned with norm balanced realizations of controllers a line search gradient descent algorithm with adaptive stepsize selection is proposed for the numerical solution of the cqlqg control problem the algorithm finds a local minimum of the lqg cost over the parameters of the hamiltonian and coupling operators of a stabilizing coherent quantum controller thus taking the pr constraints into account a convergence analysis of the algorithm is presented numerical examples of designing locally optimal cqlqg controllers are provided in order to demonstrate the algorithm performance

strong convergence of modified ishikawa iteration for two asymptotically nonexpansive mappings and semigroups abstract in this paper we established strong convergence theorems for a common fixed point of two asymptotically nonexpansive mappings and for a common fixed point of two asymptotically nonexpansive semigroups by using the hybrid method in a hilbert space moreover we also proved a strong convergence theorem for a common fixed point of two nonexpansive mappings our results extend and improve the recent ones announced by kim and xu t w kim h w xu strong convergence of modified mann iteration for asymptotically nonexpansive mappings and semigroups nonlinear anal 64 2006 1140 1152 nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 and many others

strong convergence theorems for a finite family of asymptotically nonexpansive mappings and semigroups strong convergence theorems are obtained for a finite family of asymptotically nonexpansive mappings and semigroups by the modified mann method

strong convergence of the modified mann iterative method for strict pseudo contractions in this paper we introduce a modified mann iterative process for approximating a common fixed point of a finite family of strict pseudo contractions in hilbert spaces we establish the strong convergence theorem of the general iteration scheme under some mild conditions our results extend and improve the recent ones announced by many others

strong and weak convergence theorems for general mixed equilibrium problems and variational inequality problems and fixed point problems in hilbert spaces in this paper we introduce two iterative algorithms for finding a common element of the set of solutions of finite general mixed equilibrium problems and the set of solutions of finite variational inequalities for inverse strongly monotone mappings and the set of common fixed points of an asymptotically k strictly pseudocontractive mapping in the intermediate sense in a real hilbert space we prove some strong and weak convergence theorems by using the proposed algorithms under some suitable conditions our results improve and extend the corresponding results announced by many others

parallel linear programming in fixed dimension almost surely in constant time for any fixed dimension d thelinear programming problem with n inequality constraints can be solved on a probabilistic crcw pram with o n processors almost surely in constant time the algorithm always findsthe correct solution with nd log 2 d processors the probability that the algorithm will not finish within o d 2 log 2 d time tends to zero exponentially with n authors abstract

a modified halpern type iteration algorithm for totally quasi ϕ asymptotically nonexpansive mappings with applications abstract the purpose of this article is to modify the halpern type iteration algorithm for total quasi asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of banach spaces the results presented in the paper improve and extend the corresponding results of x l qin y j cho s m kang h y zhou convergence of a modified halpern type iterative algorithm for quasi nonexpansive mappings appl math lett 22 2009 1051 1055 z m wang y f su d x wang y c dong a modified halpern type iteration algorithm for a family of hemi relative nonexpansive mappings and systems of equilibrium problems in banach spaces j comput appl math 235 2011 2364 2371 y f su h k xu x zhang strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications nonlinear anal 73 2010 3890 3906 c martinez yanes h k xu strong convergence of the cq method for fixed point iteration processes nonlinear anal 64 2006 2400 2411 and others

strong convergence theorems for solving equilibrium problems and fixed point problems of ξ strict pseudo contraction mappings by two hybrid projection methods in this paper we introduce an iterative scheme by using the hybrid projection methods for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a x strict pseudo contraction mapping in hilbert spaces we obtain two strong convergence theorems under mild assumptions on parameters for the sequences generated by these processes the results presented in the paper extend and improve some recent results of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 329 2007 336 346 tada and takahashi a tada w takahashi weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem j optim theory appl 133 2007 359 370 and ceng et al l c ceng s al homidan q h ansari j c yao an iterative scheme for equilibrium problems and fixed point problems of strict pseudo contraction mappings j comput appl math 223 2009 967 974 and many others

coherent quantum lqg control based on a recently developed notion of physical realizability for quantum linear stochastic systems we formulate a quantum lqg optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum such a control scheme is often referred to in the quantum control literature as coherent feedback control it distinguishes the present work from previous works on the quantum lqg problem where measurement is performed on the plant and the measurement signals are used as the input to a fully classical controller with no quantum degrees of freedom the difference in our formulation is the presence of additional non linear and linear constraints on the coefficients of the sought after controller rendering the problem as a type of constrained controller design problem due to the presence of these constraints our problem is inherently computationally hard and this also distinguishes it in an important way from the standard lqg problem we propose a numerical procedure for solving this problem based on an alternating projections algorithm and as an initial demonstration of the feasibility of this approach we provide fully quantum controller design examples in which numerical solutions to the problem were successfully obtained for comparison we also consider the case of classical linear controllers that use direct or indirect measurements and show that there exists a fully quantum linear controller which offers an improvement in performance over the classical ones

on hybrid projection methods for asymptotically quasi φ nonexpansive mappings the purpose of this paper is to consider the problem of approximating a common fixed point of two asymptotically quasi f nonexpansive mappings based on hybrid projection methods strong convergence theorems are established in a real banach space

on the stable equilibrium points of gradient systems this paper studies the relations between the local minima of a cost function f and the stable equilibria of the gradient descent flow of f in particular it is shown that under the assumption that f is real analytic local minimality is necessary and sufficient for stability under the weaker assumption that f is indefinitely continuously differentiable local minimality is neither necessary nor sufficient for stability

a hybrid algorithm with variable coefficients for asymptotically pseudocontractive mappings in the intermediate sense on unbounded domains abstract the purpose of this article is to propose a new hybrid algorithm with variable coefficients and prove convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense on unbounded domains the results of the paper improve and extend the recent results of qin et al x l qin s y cho j k kim convergence theorems on asymptotically pseudocontractive mappings in the intermediate sense fixed point theory appl 2010 doi 10 1155 2010 186874 article id 186874 14 pages and several others the algorithm with variable coefficients introduced in this paper is of independent interest

synthesis of linear coherent quantum control systems using a differential evolution algorithm we propose a new method to construct an optimal linear coherent quantum controller based on an evolutionary optimization method namely a differential evolution algorithm the aim is to provide a straightforward approach to deal with both nonlinear and nonconvex constraints arising in the coherent quantum controller synthesis the solution to this control problem involves a complex algebraic riccati equation which corresponds to a physical realizability condition for the coherent quantum controller the proposed method is demonstrated through an example of an entanglement control problem for a quantum network comprising two cascaded optical parametric amplifiers

explicit averaging cyclic algorithm for common fixed points of asymptotically strictly pseudocontractive maps weak and strong convergence theorems for the approximation of common fixed points of a finite family of asymptotically strictly pseudocontractive mappings are proved in hilbert spaces using an explicit averaging cyclic algorithm

strong convergence of a new iterative scheme for a finite family of strict pseudo contractions the purpose of this paper is to introduce a new iterative scheme for finding a common fixed point of a finite family of strict pseudo contractions the results obtained in this paper extend and improve the corresponding results of marino colao qin and kang g marino v colao x qin s m kang strong convergence of the modified mann iterative method for strict pseudo contractions comput math appl 57 2009 455 465

approximation theorems for solving common solution of a system of mixed equilibrium problems and variational inequality problems and fixed point problems for asymptotically strict pseudocontractions in the intermediate sense abstract in this paper we introduce a new iterative algorithm which is constructed by using the hybrid projection method for finding the common solution of a system of mixed equilibrium problems of bifunctions satisfying certain the conditions and the common solution of variational inequality problems of inverse strongly monotone mappings and the common solution of fixed point problems for a family of uniformly lipschitzian continuous and asymptotically i strict pseudocontractive mapping in the intermediate sense we prove the strong convergence theorem for a new iterative algorithm under some mild conditions in hilbert spaces finally we also give some numerical examples for support our results

iterative methods for the computation of fixed points of demicontractive mappings this paper surveys some of the main convergence properties of the mann type iteration for the demicontractive mappings some variants of the mann iteration that ensure the strong convergence like the cq algorithm and a variant for the asymptotically demicontractive mappings are also considered the usual framework of our study is a real hilbert space and only to a certain extent some particular banach spaces historical aspects are pointed out and some applications for the convex feasibility problem are discussed

a hybrid iterative scheme for asymptotically k strict pseudo contractions in hilbert spaces abstract in this paper we introduce an explicit iterative process for a finite family of asymptotically k strict pseudo contractions by using the iterative process we get a weak convergence theorem for a finite family of asymptotically k strict pseudo contractions and then we modify these algorithms to have strong convergence in the framework of hilbert spaces our results improve and extend the recent ones announced by g l acedo h k xu iterative methods for strict pseudo contractions in hilbert spaces nonlinear anal 67 2007 2258 2271 t h kim h k xu strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups nonlinear anal 64 2006 1140 1152 c martinez yanes h k xu strong convergence of the cq method for fixed point iteration processes nonlinear anal 64 2006 2400 2411 k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert space j math anal appl 329 2007 336 346 t h kim h k xu convergence of the modified manns iteration method for asymptotically strict pseudo contractions nonlinear anal 2007 doi 10 1016 j na 2007 02 029 and many others

linear programming with two variables per inequality in poly log time the parallel time complexity of the linear programming problem with at most two variables per inequality is discussed let n and m denote the number of variables and the number of inequalities respectively in a linear programming problem it is assumed that all inequalities are weak under the concurrent read exclusive write pram model an o log m log 2 n log 2 n time parallel algorithm for deciding feasibility is described it requires mn o log n processors in the worst case though it is not known whether this bound is tight when the problem is feasible a solution can be computed within the same complexity moreover linear programming problems with at most two nonzero coefficients in the objective function can be solved in poly log time on a similar number of processors consequently all these problems can be solved sequentially with only o log m log 2 n 2 log 2 n space these bounds assume that numbers take o 1 space and arithmetic on them takes o 1 time the p

degree of convergence of modified averaged iterations for fixed points problems and operator equations abstract let h be a real hilbert space we propose a modification for averaged mappings to approximate the unique fixed point of a mapping t h h such that t is boundedly lipschitzian and t is monotone we not only prove strong convergence theorems but also determine the degree of convergence using this result an iteration process is given for finding the unique solution of the equation a x f where a h h is strongly monotone and boundedly lipschitzian

strong convergence of the cq method for fixed point iteration processes strong convergence theorems are obtained for the cq method for an ishikawa iteration process a contractive type iteration process for nonexpansive mappings and the proximal point algorithm for maximal monotone operators in hilbert spaces

algorithms and hardness results for parallel large margin learning we consider the problem of learning an unknown large margin halfspace in the context of parallel computation giving both positive and negative results as our main positive result we give a parallel algorithm for learning a large margin half space based on an algorithm of nesterov s that performs gradient descent with a momentum term we show that this algorithm can learn an unknown margin halfspace over n dimensions using n poly 1 processors and running in time o 1 o log n in contrast naive parallel algorithms that learn a margin halfspace in time that depends polylogarithmically on n have an inverse quadratic running time dependence on the margin parameter our negative result deals with boosting which is a standard approach to learning large margin halfspaces we prove that in the original pac framework in which a weak learning algorithm is provided as an oracle that is called by the booster boosting cannot be parallelized more precisely we show that if the algorithm is allowed to call the weak learner multiple times in parallel within a single boosting stage this ability does not reduce the overall number of successive stages of boosting needed for learning by even a single stage our proof is information theoretic and does not rely on unproven assumptions

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

a deterministic poly log log n time n processor algorithm for linear programming in fixed dimension it is shown that for any fixed number of variables linear programming problems with n linear inequalities can be solved deterministically by n parallel processors in sublogarithmic time the parallel time bound counting only the arithmetic operations is o log log n d where d is the number of variables in the one dimensional case this bound is optimal if we take into account the operations needed for processor allocation the time bound is o log log n d c where c is an absolute constant

strong convergence theorem of an iterative method for variational inequalities and fixed point problems in hilbert spaces in this paper we introduce a new iteration method based on the hybrid method in mathematical programming and the descent like method for finding a common element of the set of solutions for a variational inequality and the set of fixed points for a nonexpansive mapping in hilbert spaces our method modifies and improves some methods in literature

new monotone hybrid algorithm for hemi relatively nonexpansive mappings and maximal monotone operators the purpose of this article is to prove the strong convergence theorems for hemi relatively nonexpansive mappings in banach spaces in order to get the strong convergence theorems for hemi relatively nonexpansive mappings a new monotone hybrid iteration algorithm is presented and is used to approximate the fixed point of hemi relatively nonexpansive mappings noting that the general hybrid iteration algorithm can be used for relatively nonexpansive mappings but it can not be used for hemi relatively nonexpansive mappings however this new monotone hybrid algorithm can be used for hemi relatively nonexpansive mappings in addition a new method of proof has been used in this article that is by using this new monotone hybrid algorithm we firstly claim that the iterative sequence is a cauchy sequence the results of this paper modify and improve the results of matsushita and takahashi and some others

on a multidimensional search technique and its application to the euclidean one centre problem the paper is divided into two main sections the first deals with a multidimensional search technique of megiddo j assoc comput mach 31 1984 pp 114 127 and suggests an improvement the second gives an application of the technique to the euclidean one centre problem in mathbb r d an algorithm of time complexity o 3 d 2 2 n is derived for this problem this improves the best previous bound even in the case d 2

asymptotically strict pseudocontractive mappings in the intermediate sense abstract it is proved that the modified mann iteration process x n 1 1 n x n n t n x n n n where n is a sequence in 0 1 with n 1 for some 0 1 converges weakly to a fixed point of an asymptotically strict pseudocontractive mapping t in the intermediate sense which is not necessarily lipschitzian we also develop cq method for this modified mann iteration process which generates a strongly convergent sequence

a modified frequency domain condition for the physical realizability of linear quantum stochastic systems this paper is concerned with a modified version of the frequency domain physical realizability pr condition for linear quantum systems we consider open quantum systems whose dynamic variables satisfy the canonical commutation relations of an open quantum harmonic oscillator and are governed by linear quantum stochastic differential equations qsdes in order to correspond to physical quantum systems these qsdes must satisfy pr conditions we provide a relatively simple proof that the pr condition is equivalent to the frequency domain j j unitarity of the input output transfer function and orthogonality of the feedthrough matrix of the system without the technical spectral assumptions required in previous work we also show that the poles and transmission zeros associated with the transfer function of pr linear quantum systems are the mirror reflections of each other about the imaginary axis an example is provided to illustrate the results

strong convergence for a countable family of strict pseudocontractions in q uniformly smooth banach spaces we introduce a new iterative algorithm for finding a common fixed point of a countable family of strict pseudocontractions in q uniformly smooth and uniformly convex banach spaces we then prove that the sequence generated by the proposed algorithm converges strongly to a common fixed point of an infinite family of strict pseudocontractions our results mainly improve and extend the results announced by yao et al y yao y c liou g marino strong convergence of two iterative algorithms for nonexpansive mappings in hilbert spaces fixed point theory appl 2009 2009 7 pages doi 10 1155 2009 279058 art id 279058

h infty control of linear quantum stochastic systems the purpose of this paper is to formulate and solve a h infin controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology the paper includes results on the class of such systems for which the quantum commutation relations are preserved such a requirement must be satisfied in a physical quantum system a quantum version of standard classical dissipativity results are presented and from this a quantum version of the strict bounded real lemma is derived this enables a quantum version of the two riccati solution to the h infin control problem to be presented this result leads to controllers which may be realized using purely quantum purely classical or a mixture of quantum and classical elements this issue of physical realizability of the controller is examined in detail and necessary and sufficient conditions are given our results are constructive in the sense that we provide explicit formulas for the hamiltonian function and coupling operator corresponding to the controller

a hybrid iterative scheme for equilibrium problems and fixed point problems of asymptotically k strict pseudo contractions in this paper we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of asymptotically k strict pseudo contractions in the setting of real hilbert spaces by using our proposed scheme we get a weak convergence theorem for a finite family of asymptotically k strict pseudo contractions and then we modify these algorithm to have strong convergence theorem by using the two hybrid methods in the mathematical programming our results improve and extend the recent ones announced by ceng et al s result l c ceng al homidan q h ansari and j c yao an iterative scheme for equilibrium problems and fixed point problems of strict pseudo contraction mappings j comput appl math 223 2009 967 974 qin cho kang and shang x qin y j cho s m kang and m shang a hybrid iterative scheme for asymptotically k strict pseudo contractions in hilbert spaces nonlinear anal 70 2009 1902 1911 and other authors

strong convergence of a proximal type algorithm in a banach space in this paper we study strong convergence of the proximal point algorithm it is known that the proximal point algorithm converges weakly to a solution of a maximal monotone operator but it fails to converge strongly then in math program 87 2000 pp 189 202 solodov and svaiter introduced the new proximal type algorithm to generate a strongly convergent sequence and established a convergence property for it in hilbert spaces our purpose is to extend solodov and svaiter s result to more general banach spaces using this we consider the problem of finding a minimizer of a convex function

iterative methods for strict pseudo contractions in hilbert spaces abstract let t i i 1 n be n strict pseudo contractions defined on a closed convex subset c of a real hilbert space h consider the problem of finding a common fixed point of these mappings and consider the parallel and cyclic algorithms for solving this problem we will prove the weak convergence of these algorithms moreover by applying additional projections we further prove that these algorithms can be modified to have strong convergence

hybrid ishikawa iterative methods for a nonexpansive semigroup in hilbert space in this paper on the base of the ishikawa iteration method and the hybrid method in mathematical programming we give two new strong convergence methods for finding a point in the common fixed point set of a nonexpansive semigroup in hilbert space

direct and indirect couplings in coherent feedback control of linear quantum systems the purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems a general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented fundamental properties of stability dissipation passivity and gain for this class of linear quantum models are presented and characterized using complex lyapunov equations and linear matrix inequalities lmis coherent h and lqg synthesis methods are extended to accommodate direct couplings using multistep optimization examples are given to illustrate the results

strong convergence theorem for pseudo contractive mappings in hilbert spaces abstract the purpose of this paper is to construct an ishikawa type of hybrid algorithm for pseudo contractive mappings in hilbert spaces our results extend the recent ones announced by yao et al y h yao y c liou g marino a hybrid algorithm for pseudo contractive mappings nonlinear anal 71 2009 4997 5002 and many others

strong convergence theorems for a common fixed point of two hemi relatively nonexpansive mappings abstract the purpose of this article is to prove strong convergence theorems for common fixed points of two closed hemi relatively nonexpansive mappings in banach spaces in order to get the strong convergence theorems the monotone hybrid algorithms are presented and are used to approximate the common fixed points finally a new simplified hybrid algorithm has been proposed and relative convergence theorem has been proved by using the new method for proofs the results of this article modify and improve the results of matsushita takahashi s matsushita w takahashi a strong convergence theorem for relatively nonexpansive mappings in a banach space j approx theory 134 2005 257 266 and the results of plubtieng ungchittrakool s plubtieng k ungchittrakool strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a banach space j approx theory 149 2007 103 115 and many others

a weak to strong convergence principle for feje monotone methods in hilbert spaces we consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly exploiting an idea originally proposed by haugazeau we present a simple modification of these methods that makes them strongly convergent without additional assumptions several applications are discussed

projection algorithms for solving nonmonotone equilibrium problems in hilbert space we propose two projection algorithms for solving an equilibrium problem where the bifunction is not required to be satisfied any monotone property under assumptions on the continuity convexity of the bifunction and the nonemptyness of the solution set of the minty equilibrium problem we show that the sequences generated by the proposed algorithms converge weakly and strongly to a solution of the primal equilibrium problem respectively

strong convergence theorems for a finite family of nonexpansive mappings and semigroups via the hybrid method strong convergence theorems are obtained for a finite family of nonexpansive mappings and semigroups by the hybrid method 2009 elsevier ltd all rights reserved

on some algorithms in banach spaces finding fixed points of nonlinear mappings abstract by using a modification of the hybrid method in mathematical programming we give some new algorithm to find out a fixed point of mappings which are in some sense non expansive our results hold in reflexive strictly convex smooth banach spaces with the kadec klee property