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Abstract: This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newton-type method for solving nonsmooth equations. Based on advanced techniques of variational analysis and generalized differentiation, we establish the well-posedness of the algorithm, its local superlinear convergence, and its global convergence of the Kantorovich type. Our convergence results hold with no semismoothness and Lipschitzian assumptions, which is illustrated by examples. The algorithm and main results obtained in the paper are compared with well-recognized semismooth and -differentiable versions of Newton’s method for nonsmooth Lipschitzian equations. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the filtering problem for polynomial systems. By means of Lyapunov theory and matrix inequality techniques, sufficient conditions are first obtained to ensure that the filtering error system is asymptotically stable and satisfies performance constraint. Then, a sufficient condition for the existence of desired filters is established with a free matrix introduced, which will greatly facilitate the design of filter matrices. By virtue of sum-of-squares (SOS) approaches, a convergent iterative algorithm is developed to tackle the polynomial  filtering problem. Note that the approach can be efficiently implemented by means of recently developed SOS decomposition techniques, and the filter matrices can be designed explicitly. Finally, a numerical example is given to illustrate the main results of this paper. [Copyright &y& Elsevier]

Abstract: The hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) is proposed in this paper. The SA-PSO algorithm takes both of the advantages of good solution quality in simulated annealing and fast searching ability in particle swarm optimization. As stochastic optimization algorithms are sensitive to their parameters, proper procedure for parameters selection is introduced in this paper to improve solution quality. To verify the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimization functions with different dimensions. The comparative works have also been conducted among different algorithms under the criteria of quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the results, the SA-PSO could have higher efficiency, better quality and faster convergence speed than compared algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of stochastic linear complementarity problems (SLCPs) with finitely many elements. We present a smoothing Newton algorithm for solving the SLCP. Under suitable conditions, we obtain the global convergence and locally quadratic convergence of the proposed algorithm. Some numerical results are reported in this paper, which confirm the good theoretical properties of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we try to solve the semidefinite program with box constraints. Since the traditional projection method for constrained optimization with box constraints is not suitable to the semidefinite constraints, we present a new algorithm based on the feasible direction method. In the paper, we discuss two cases: the objective function in semidefinite programming is linear and nonlinear, respectively. We establish the convergence of our algorithm, and report the numerical experiments which show the effectiveness of the algorithm. [Copyright &y& Elsevier]

Abstract: Asian options are popular path-dependent financial derivatives. This paper uses lattices to price fixed-strike European-style Asian options that are discretely monitored. The algorithm proposed can also be applied to floating-strike Asian options as well because fixed-strike and floating-strike Asian options are related through an equation. The discretely monitored version is usually found in practice instead of the continuously monitored version usually encountered in the literature. This paper presents the first provably quadratic-time convergent lattice algorithm for pricing fixed-strike European-style discretely monitored Asian options. It is the most efficient lattice algorithm with convergence guarantees. The algorithm relies on the Lagrange multipliers to choose the number of states for each node of the lattice. Extensive numerical experiments and comparisons with many existing numerical methods confirm the performance claims and the competitiveness of our algorithm. This result places fixed-strike European-style discretely monitored Asian options in the same complexity class as vanilla options. [Copyright &y& Elsevier]

Abstract: In this paper, we use a projected gradient algorithm to solve a nonlinear operator equation with -norm constraint. Gradient iterations with -norm constraints have been studied recently both in the context of inverse problem and of compressed sensing. In this paper, the constrained gradient iteration is implemented via a projected operator. We establish the -norm convergence of sequence constructed by the constrained gradient iteration when . The performance of the method is testified by a numerical example. [Copyright &y& Elsevier]

Abstract: This paper proposes an enhanced cross-entropy (ECE) method to solve dynamic economic dispatch (DED) problem with valve-point effects. The cross-entropy (CE) method, originated from an adaptive variance minimization algorithm for estimating probabilities of rare events, is a generic approach to combinatorial and multi-extremal optimization. Exploration capability of CE algorithm is enhanced in this paper by using chaotic sequence and the resultant ECE is applied to DED with valve-point effects. The performance of the proposed ECE method is rigorously tested for optimality, convergence, robustness and computational efficiency on a 10-unit test system. Additional test cases with different load patterns and increased number of generators are also solved by ECE. Numerical results show that the proposed ECE approach finds high-quality solutions reliably with faster convergence. It outperforms CE and all the previous approaches. [Copyright &y& Elsevier]

Abstract: Many physical phenomena are modelled by nonclassical parabolic boundary value problems with nonlocal boundary conditions. Many different papers studied the second-order parabolic equation, particularly the heat equation subject to the specifications of mass. In this paper, we provide a whole family of new algorithms that improve the CPU time and accuracy of Crandall''s formula shown in [J. Martin-Vaquero, J. Vigo-Aguiar, A note on efficient techniques for the second-order parabolic equation subject to non-local conditions, Appl. Numer. Math. 59 (6) (2009) 1258–1264] (and this algorithm improved the results obtained with BTCS, FTCS or Dufort–Frankel three-level techniques previously used in other works, see [M. Dehghan, Efficient techniques for the second-order parabolic equation subject to nonlocal specifications, Appl. Numer. Math. 52 (2005) 39–62]) with this kind of problems. Other methods got second or fourth order only when , while the new codes got nth order for ; therefore, the new schemes require a smaller storage and CPU time employed than other algorithms. We will study the convergence of the new algorithms and finally we will compare the efficiency of the new methods with some well-known numerical examples. [Copyright &y& Elsevier]

Abstract: In this paper, a heuristic algorithm, different from the Frank–Wolfe and its modified methods, is introduced for network equilibration. By using the column generation technique and the network equilibrium conditions, the new method need not enumerate initially all feasible paths for all origin/destination (O/D) pairs, but can give all paths used between each O/D pair and the path flows accordingly while the new algorithm obtains an optimal traffic assignment. Some convergence issues of the new method is discussed in this paper. Numerical experiments show that the new method is efficient and robust. [Copyright &y& Elsevier]

A trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper. In the current iteration, the trial step providing sufficient descent is generated by solving a corresponding trust-region subproblem. Then, the step size is decided by backtracking line search together with filter technique to obtain the next iteration point. The advantage of this method is that resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be avoided and hence the expensive computation can be lessened. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect. Convergence analysis shows that fast local convergence can be achieved under some mild assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

Vibro-acoustic analysis of a rail vehicle cabin is presented in this paper. Vehicle is modeled by an air cavity coupled to a flexible floor panel. Analytical procedure is employed to predict the structural-borne noise in the vehicle model generated by random excitation of the panel. In this study, natural frequencies of the coupled system are obtained and then the sound pressure field inside the cavity is analytically determined. In order to find dynamic responses of the coupled system in the time domain, Durbin's numerical Laplace transform inversion algorithm is employed. Convergence of the algorithm is verified and eventually a parametric study is carried out to investigate the effects of rail irregularity and vehicle speed on the time and frequency responses. [ABSTRACT FROM AUTHOR]

In the CQ-like algorithms for the split feasibility problem, in order to get the step-size, one has to compute the largest eigenvalue of the related matrix or use some line search scheme. Our contribution in this short note is to give a simple CQ-like algorithm in which the step-size is directly computed. The algorithm presented in this paper not only need not to compute the largest eigenvalue of the related matrix but also need not to use any line search scheme. The theoretical convergence and numerical results are also given. [ABSTRACT FROM AUTHOR]

In this paper we deal with the numerical analysis of an adsorption dynamic model arising in a surfactant solution at the air–water interface; the diffusion model is considered together with the so-called Langmuir isotherm. An existence and uniqueness result is stated. Then, fully discrete approximations are introduced by using a finite element method and a hybrid combination of backward and forward Euler schemes. Error estimates are proved from which, under adequate additional regularity conditions, the linear convergence of the algorithm is derived assuming a dependence between both spatial and time discretization parameters. Finally, some numerical simulations are presented in order to demonstrate the accuracy of the algorithm and the behaviour of the solution for two commercially available surfactants. [ABSTRACT FROM AUTHOR]

In this paper we present a new trust-region SQP algorithm for nonlinear programming. This method avoids using a penalty function, nor a filter, and instead establishes a new step acceptance mechanism. Under some reasonable assumptions, the method can be proved to be globally convergent to a KT point. Preliminary numerical experiments are presented that show the potential efficiency of the new approach. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a family of fixed point algorithms for the numerical resolution of some systems of nonlinear equations is designed and analyzed. The family introduced here generalizes the Petviashvili method and can be applied to the numerical generation of traveling waves in some nonlinear dispersive systems. Conditions for the local convergence are derived and numerical comparisons between different elements of the family are carried out. [Copyright &y& Elsevier]

In this paper, a two-level defect-correction Oseen iterative finite element method is presented for the stationary conduction–convection equations based on local Gauss integration. The method combines the defect-correction method, the two-level strategy, and the locally stabilized method. The stability and convergence of the proposed method are deduced. Finally, numerical examples verify the theoretical results of the proposed algorithm and show that it is highly efficient and reliable for the considered problem. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, based on a symmetrically perturbed smoothing Fischer–Burmeister function, a non-interior continuation method is proposed for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. Under monotonicity, it is shown that our algorithm is globally and locally superlinearly convergent without requiring strict complementarity assumption at the SOCCP solution. Furthermore, the proposed algorithm has local quadratic convergence under mild conditions. Some numerical results are reported which indicate the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: This paper studies the identification of finite impulse response (FIR) systems with binary-valued observations. Combining with the stochastic gradient algorithm and statistical property of the system noise, a recursive projection algorithm is proposed to estimate the unknown system parameters. Under some mild conditions on the a priori knowledge of the unknown parameters and inputs, the algorithm is proved to be convergent in the almost sure and mean square sense. Furthermore, the almost sure and mean square convergence rates of estimation errors are also obtained. A numerical example is given to demonstrate the effectiveness of the algorithm and the main results obtained. [Copyright &y& Elsevier]

Abstract: This paper deals with the null controllability of an initial-boundary value problem for a parabolic coupled system with nonlinear terms of local and nonlocal kinds. The control is distributed in space and time and is exerted through one scalar function whose support can be arbitrarily small. We first prove that, if the initial data are sufficiently small and the linearized system at zero satisfies an appropriate coupling condition, the equations can be driven exactly to zero. We also present an iterative algorithm of the quasi-Newton kind for the computation of the control and we prove a convergence result. The behavior of this algorithm is illustrated with some numerical experiments. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the convergence of the double-shift and multi-shift QR algorithms for symmetric tridiagonal matrices. We analyze how to choose multi-shifts by comparing the relationships between the number of iterations, CPU time and the number of multi-shifts. Numerical tests and figures are performed. [Copyright &y& Elsevier]

Abstract: DIRECT is a sample-based global optimisation method for Lipschitz continuous functions defined over compact multidimensional domains. This paper adapts the DIRECT method with a modified termination criterion for global extremum seeking control of multivariable dynamical plants. Finite-time semi-global practical convergence is established based on a periodic sampled-data control law, whose sampling period is a parameter which determines the region and accuracy of convergence. A crucial part of the development is dedicated to a robustness analysis of the DIRECT method against bounded additive perturbations on the objective function. Extremum seeking involving multiple units is also considered within the same context as a means to increase the speed of convergence. Numerical examples of global extremum seeking based on DIRECT are presented at the end. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new unit commitment model that captures the sub-hourly variability of wind power. Scenarios are included in the stochastic unit commitment formulation to represent the uncertainty and intermittency of wind power output. A modified Benders decomposition method is used to improve the convergence of the algorithm. The numerical results show that the proposed model based on finer granularity outperforms the conventional model of hourly resolution. [Copyright &y& Elsevier]

Abstract: In this paper, a trust-region sequential quadratic programming algorithm with a modified filter acceptance mechanism is proposed for nonlinear equality constrained optimization. The most important advantage of the proposed algorithm is its avoidance of any feasibility restoration phase, a necessity in traditional filter methods. We solve quadratic programming subproblems based on the well-known Byrd–Omojokun trust-region method. Inexact solutions to these subproblems are allowed. Under some standard assumptions, global convergence of the proposed algorithm is established. Numerical results show our approach is potentially useful. [Copyright &y& Elsevier]

Abstract: A deflated restarting Krylov subspace method for approximating a function of a matrix times a vector is proposed. In contrast to other Krylov subspace methods, the performance of the method in this paper is better. We further show that the deflating algorithm inherits the superlinear convergence property of its unrestarted counterpart for the entire function and present the results of numerical experiments. [Copyright &y& Elsevier]

Abstract: An adaptive parameter tuning of particle swarm optimization based on velocity information (APSO-VI) algorithm is proposed. In this paper the velocity convergence of particles is first analyzed and the relationship between the velocity of particle and the search failures is pointed out, which reveals the reasons why PSO has relative poor global searching ability. Then this algorithm introduces the velocity information which is defined as the average absolute value of velocity of all the particles. A new strategy is presented that the inertia weight is dynamically adjusted according to average absolute value of velocity which follows a given nonlinear ideal velocity by feedback control, which can avoid the velocity closed to zero at the early stage. Under the guide of the nonlinear ideal velocity, APSO-VI can maintain appropriate swarm diversity and alleviate the premature convergence validly. Numerical experiments are conducted to compare the proposed algorithm with different variants of PSO on some benchmark functions. Experimental results show that the proposed algorithm remarkably improves the ability of PSO to jump out of the local optima and significantly enhance the convergence speed and precision. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a compact alternating direction implicit (ADI) scheme for solving the two-dimensional parabolic equation. The maximum norm convergence is proven, and the convergence rate is second-order in time and fourth-order in space. We develop a Richardson extrapolation algorithm to increase the accuracy to sixth-order both in time and space. Numerical experiments show the effectiveness of the method. [Copyright &y& Elsevier]

Abstract: The split feasibility problem is to find with , if such points exist, where A is a given real matrix, C and Q are nonempty closed convex sets in and , respectively. Byrne (2002) [2] proposed a well-known CQ algorithm for solving this problem. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively, and performs an additional projection step onto some simple closed convex set in each iteration. We further give a relaxation scheme for this modification to make it more easily implemented. Convergence results of both algorithms are analyzed, and preliminary numerical results are reported. We also extend these modified algorithms to solve the multiple-sets split feasibility problem, which is to find a point closest to the intersection of a family of closed convex sets in one space such that its image under a linear transformation will be closest to the intersection of another family of closed convex sets in the image space. [Copyright &y& Elsevier]

Abstract: In this paper, we consider numerical simulation to a class of constrained dynamic problems where the overall dynamics are determined by the interactions between two sub-systems. We present an iterative algorithm that naturally decouples the computation of the two sub-systems and that ensures an accurate and efficient solution procedure. We conduct rigorous error analysis for the convergence of the iterative algorithm, and verify the analytical results through careful numerical tests. [Copyright &y& Elsevier]

Abstract: Integrated layout optimization of multi-component structures under static loads and random excitations is studied in this paper. Dynamic responses are obtained by using the mode superposition method, and the prestress effect introduced by the static loads is taken into account in the analyses of dynamic responses. Locations of embedded components and pseudo-densities related to supporting structure are chosen as design variables. Design sensitivities of the dynamic responses with respect to the pseudo-densities are analytically derived. The optimization algorithm GCMMA (Global Convergent Method of Moving Asymptotes algorithm) is used to minimize simultaneously the static strain energy and dynamic responses. Three numerical examples are presented to show the validity of the optimization procedure and its potential application in practical designs. [Copyright &y& Elsevier]

Abstract: The momentum method is a commonly used method to accelerate the learning of neural networks. In this paper, a new adaptive momentum algorithm is proposed for split-complex recurrent neural networks training. Different from other momentum methods, this new algorithm uses a variable gain factor and a variable learning rate to speed up the convergence and smooth the weight trace. The global convergence of the new algorithm is proved under mild conditions. Numerical results show that the algorithm is efficient for the given test problems. [Copyright &y& Elsevier]

Abstract: In this paper, an inexact secant algorithm in association with nonmonotone technique and filter is proposed for solving the large scale nonlinear systems of equalities and inequalities. The systems are transformed into a continuous constrained optimization solved by inexact secant algorithm. Global convergence of the proposed algorithm is established under the reasonable conditions. Numerical results validate the effectiveness of our approach. [Copyright &y& Elsevier]

Abstract: The Thick Level Set (TLS) model is a damage model containing a non-local treatment that prevents from spurious localization issues. It also offers an automatic transition from damage to fracture. The TLS approach to model damage growth was first presented in Möes et al. with a first numerical implementation for a time-dependent damage evolution law. In this paper, we propose some improvements in terms of discretization and explicit damage growth algorithms to obtain a robust, efficient and easy-to-implement model. These improvements include a simple and efficient variational formulation for computing the non-local quantities as well as the introduction of a so-called ramped Heaviside enrichment function to properly take into account the transition to cracks in fully damaged zones. We consider here a simple explicit formulation for quasi-static loadings, decoupling the elastic computation and the damage growth. The method is validated through standard benchmarks and compared to the Griffith’s fracture theory. The convergence of energy and displacement errors is observed. More complex computations including damage initiations are eventually performed. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new penalty-free-type method for nonlinear equality constrained problems. The new algorithm uses trust region framework and feasibility safeguarding technique. Moreover, it has no choice of penalty parameter and penalty function as a merit function, and it does not use the filter technique to avoid the penalty function either. We analyze the global convergence of the main algorithm under the standard assumptions. The preliminary numerical tests are reported. [Copyright &y& Elsevier]

Abstract: In FEM simulations contact in conjunction with plastic material behaviour leads to highly nonlinear equations in the FEM algorithms. This causes problems in numerical convergence. FEM-software providers handle this problem by automatic contact damping or similar algorithms. In this paper a benchmark between four FEM-solvers is performed based on a model for ring compression tests. For all simulations identical physical as well as numerical influence parameters are used. The simulations have shown a significant divergence in the results depending on the used FEM-software. [Copyright &y& Elsevier]

Abstract: This paper considers Nyström type methods for solving a generalized aerofoil equation with weakly singular kernel. Based on sigmoidal transformations and Nyström method, we obtain new algorithms for solving this equation. Convergence analysis for this methods are given. Finally, numerical examples complete this work. [Copyright &y& Elsevier]

Abstract: In this paper, a new line search filter algorithm for equality constrained optimization is presented. The approach belongs to the class of inexact Newton-like methods. It can also be regarded as an inexact version of generic sequential quadratic programming (SQP) methods. The trial step is obtained by truncatedly solving the primal–dual system based on any robust and efficient linear system solver. Practical termination tests for the linear system solver are established to ensure global convergence. Preliminary numerical results demonstrate the approach is potentially useful. [Copyright &y& Elsevier]

Abstract: In this paper, an in-depth analysis of the implementation issues of sine-fitting algorithms in systems with 32-bit floating point representation is presented. The results obtained in 32-bit systems are compared with the ones obtained in 64-bit floating point representation systems. The four-parameter sine-fitting is an iterative algorithm and the criterion used to detect convergence is even more crucial in 32-bit systems. A modification of the traditional implementation is used to, in some situations, reduce the number of iterations required to converge without compromising the final accuracy or precision of the estimated parameters. It is shown that, as the number of samples increases, the limitations of the 32-bit systems clearly limit the use of the sine-fitting algorithms. Nevertheless, the number of samples at which this effect is detected is much higher than the number of samples usually used so far in stand-alone instrumentation systems. [Copyright &y& Elsevier]

Abstract: In this paper the problem of performing external validation of the semantic coherence of topic models is considered. The Fowlkes–Mallows index, a known clustering validation metric, is generalized for the case of overlapping partitions and multi-labeled collections, thus making it suitable for validating topic modeling algorithms. In addition, we propose new probabilistic metrics inspired by the concepts of recall and precision. The proposed metrics also have clear probabilistic interpretations and can be applied to validate and compare other soft and overlapping clustering algorithms. The approach is exemplified by using the Reuters-21578 multi-labeled collection to validate LDA models, then using Monte Carlo simulations to show the convergence to the correct results. Additional statistical evidence is provided to better understand the relation of the metrics presented. [Copyright &y& Elsevier]

Abstract: In this paper, we present an enhanced version of the minimax algorithm of Chen, Ni, and Zhou that offers the additional guarantee that the solution found is a fix-point of a projector on a cone. Positivity, negativity, and monotonicity can be expressed in this way. The convergence of the algorithm is proved by means of a “computational deformation lemma” instead of the usual deformation lemma used in the calculus of variations. [Copyright &y& Elsevier]

Abstract: Parabolic equations with nonlocal boundary conditions have been given considerable attention in recent years. In this paper new high-order algorithms for the linear diffusion–reaction problem are derived. The convergence of the new schemes is studied and numerical examples are given to show the efficiency of the new methods to solve linear and nonlinear diffusion–reaction equations with these non classical conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate uniform convergence of the improper Hubbell radiation rectangular source (HRS) integral H(a,b). We prove that HRS integral is uniform convergent in the domain for any positive finite number A. Then we give an accurate and efficient computation algorithm for the HRS integral. [Copyright &y& Elsevier]

Abstract: This paper presents an efficient algorithm based on a monotone method for the solution of a class of nonlinear integro-differential equations of second order. This method is applied to derive two monotone sequences of upper and lower solutions which are uniformly convergent. Theorems which list the conditions for the existence of such sequences are presented. The numerical results demonstrate reliability and efficiency of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper it is presented a compensated de Casteljau algorithm to accurately evaluate a bivariate polynomial in Bernstein–Bézier form. The principle is to apply error-free transformations to improve the traditional de Casteljau algorithm. A forward error and a running error analysis are performed. Finally, some numerical experiments illustrate the accuracy of the proposed algorithm in ill-conditioned problems. [Copyright &y& Elsevier]

Abstract: This paper describes a numerical approximation to the solution of Volterra integral equations of the second kind. This algorithm combines trapezoidal and Simpson rules. We prove the convergence of the method. Numerical examples are provided to illustrate the accuracy of the method. [Copyright &y& Elsevier]

Abstract: In this paper, we present a new sequential quadratically constrained quadratic programming (SQCQP) algorithm, in which a simple updating strategy of the penalty parameter is adopted. This strategy generates nonmonotone penalty parameters at early iterations and only uses the multiplier corresponding to the bound constraint of the quadratically constrained quadratic programming (QCQP) subproblem instead of the multipliers of the quadratic constraints, which will bring some numerical advantages. Furthermore, by using the working set technique, we remove the constraints of the QCQP subproblem that are locally irrelevant, and thus the computational cost could be reduced. Without assuming the convexity of the objective function or the constraints, the algorithm is proved to be globally, superlinearly and quadratically convergent. Preliminary numerical results show that the proposed algorithm is very promising when compared with the tested SQP algorithms. [Copyright &y& Elsevier]

Abstract: This paper proposes a novel hybrid immune algorithm (HIA) that can overcome the typical drawback of the artificial immune algorithm (AIA), which runs slowly and experiences slow convergence. The HIA combines the adaptive AIA based on the steepest descent algorithm. The HIA fully displays global search ability and the global convergence of the immune algorithm. At the same time, it inserts a quasi-descent operator to strengthen its local search ability. A good convergence of the HIA with the quasi-descent idea is shown as well. Numerical experiment results show that the HIA successfully improves running speed and convergence performance. [Copyright &y& Elsevier]

Abstract: The work of Hundal [H. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal. 57 (1) (2004) 35–61] has revealed that the sequence generated by the method of alternating projections converges weakly, but not strongly in general. In this paper, we present several algorithms based on alternating resolvents of two maximal monotone operators, and , that can be used to approximate common zeros of and . In particular, we prove that the sequences generated by our algorithms converge strongly. A particular case of such algorithms enables one to approximate minimum values of certain convex functionals. [Copyright &y& Elsevier]

Abstract: This paper is concerned with repetitive control of Hamiltonian systems, which is based on iterative learning control utilizing the variational symmetry of those systems. Variational symmetry allows us to obtain an algorithm to solve a certain class of optimal control problems in a repetitive control framework. Therefore, the proposed method can deal with not only trajectory tracking control problems but also optimal trajectory generation problems, never before considered in a repetitive control framework. A convergence analysis of this algorithm is also discussed. Furthermore, some numerical simulations demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper presents a non-homogeneous age-usage semi-Markov model with a measurable state space. Several probability functions useful to assess the system’s reliability are investigated. They satisfy the same family of equations we call indexed Markov renewal equations. Sufficient conditions to assure the existence and uniqueness of their solutions are provided. The numerical analysis of these equations is executed through the construction of a process discrete in time and space, which is shown to converge to the continuous one in the Skorohod topology. An algorithm useful for solving the discretized system of equations is presented by using a matrix representation. [Copyright &y& Elsevier]