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This paper presents a robust finite-time guidance (RFTG) law to a short-range interception problem. The main challenge is that the evasive strategy of the target is unpredictable because it is determined not only by the states of both the interceptor and the target, but also by external un-modeled factors. By robustly stabilizing a line-of-sight rate, this paper proposes an integrated continuous finite-time disturbance observer/bounded continuous finite-time stabilizer strategy. The design of this integrated strategy has two points: 1) effect of a target maneuver is modeled as disturbance and then is estimated by the second-order homogeneous observer; 2) the finite-time stabilizer is actively coupled with the observer. Based on homogeneity technique, the local finite-time input-to-state stability is established for the closed-loop guidance system, thus implying the proposed RFTG law can quickly render the LOS rate within a bounded error throughout intercept. Moreover, convergence properties of the LOS rate in the presence of control saturation are discussed. Numerical comparison studies demonstrate the guidance performance. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a preconditioned two-step modulus-based matrix splitting iteration method for linear complementarity problems associated with an M -matrix is proposed. The convergence analysis of the presented method is given. In particular, we provide a comparison theorem between preconditioned two-step modulus-based Gauss–Seidel (PTMGS) iteration method and two-step modulus-based Gauss–Seidel (TMGS) iteration method, which shows that PTMGS method improves the convergence rate of original TMGS method for linear complementarity problem. Numerical tested examples are used to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

Highlights • A new variational model for image retinex is proposed. • The existence of minimizer for the variational model is proved. • An efficient algorithm is derived to solve the model by adding auxiliary variables. • The convergence of the numerical algorithm is proved under some assumptions. • The proposed method can be extended to other regularization and fidelity terms. Abstract In this paper, we propose a detail preserving variational model for Retinex to simultaneously estimate the illumination and the reflectance from an observed image. Most previous models use the log-transform as pretreatment which results in loss of details in reflectance. From this observation, a detail preserving variational method is proposed for better decomposition. Different from the log-transform based models, the proposed model performs the decomposition directly in the image domain. Mathematically, we prove the existence of a solution for the proposed model. Numerically, we derive an efficient iterative algorithm by utilizing alternating direction method of multipliers (ADMM) method. Experimental results demonstrate the effectiveness of the proposed method. Compared with other closely related Retinex methods, the proposed method achieves competitive results on both subjective and objective assessments. [ABSTRACT FROM AUTHOR]

This paper is concerned with strong convergence of a tamed theta scheme for neutral stochastic differential delay equations with one-sided Lipschitz drift. Strong convergence rate is revealed under a global one-sided Lipschitz condition, while for a local one-sided Lipschitz condition, the tamed theta scheme is modified to ensure the well-posedness of implicit numerical schemes, then we show the convergence of the numerical solutions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper numerical methods for solving stochastic differential equations with Markovian switching (SDEwMSs) are developed by pathwise approximation. The proposed family of strong predictor–corrector Euler–Maruyama methods is designed to overcome the propagation of errors during the simulation of an approximate path. This paper not only shows the strong convergence of the numerical solution to the exact solution but also reveals the order of the error under some conditions on the coefficient functions. A natural analogue of the -stability criterion is studied. Numerical examples are given to illustrate the computational efficiency of the new predictor–corrector Euler–Maruyama approximation. [Copyright &y& Elsevier]

In this paper, we present a modified Newton–Traub composition with increasing order of convergence for solving systems of nonlinear equations. The idea is based on the recent development by Sharma et al. (2015). Analysis of convergence shows that the presented method has sixth order of convergence. Computational efficiency of the new method is considered and compared with some well-known existing methods. Numerical tests are performed on some problems of different nature, which confirm robust and efficient convergence behavior of the proposed method. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the numerical problems. The basins of attraction of existing methods and the presented method are given to demonstrate their performance. [ABSTRACT FROM AUTHOR]

In this paper, we suggest and analyze a unified model of two-step iterative method for solving a system of nonlinear equations. We prove that the unified model achieves fourth order convergence. Several numerical examples are given to illustrate the efficiency and the performance of the new iterative methods. From the comparison with some known methods it is observed that the present methods are of practical utility. [ABSTRACT FROM AUTHOR]

In this paper, we propose a partitioned PSB method for solving partially separable unconstrained optimization problems. By using a projection technique, we construct a sufficient descent direction. Under appropriate conditions, we show that the partitioned PSB method with projected direction is globally and superlinearly convergent for uniformly convex problems. In particular, the unit step length is accepted after finitely many iterations. Finally, some numerical results are presented, which show that the partitioned PSB method is effective and competitive. [ABSTRACT FROM AUTHOR]

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]

The neutron transport equation in the integral form is of difficult solution and therefore, schemes for obtaining an equivalent differential formulation are used. In this paper is used the discrete ordinates method (S N method) in order to obtain the equivalent differential formulation. Inspired in the GLS method (Galerkin least square method) a variant of the GLS (Brooks and Hughes, 1982; Ern and Guermond, 2004; Johnson, 1990) method denoted GpLS (Galerkin partial least-square) is proposed for solving this equivalent differential formulation. The convergence rates as well as the robustness of GLS method are preserved by the GpLS method that possesses computational lower cost. Simulations comparing the convergence rates of GpLS method with other methods are presented, confirming the best performance of GpLS method. The numerical experiments were made using fixed source in multiplying medium, with the objective to test the robustness of GpLS method. All the numerical experiments presented confirm the good properties of approximation of GpLS method. [ABSTRACT FROM AUTHOR]

In order to solve large sparse saddle point problems (SPP) quickly and efficiently, Wang and Zhang recently studied the preconditioned accelerated Hermitian and skew-Hermitian splitting (PAHSS) methods. Through accelerating the PAHSS iteration algorithms by using parameterized Uzawa (PU) method, a preconditioned AHSS-PU alternating splitting iterative method (PAHSS-PU method) for solving saddle point problems is proposed in this paper. The convergence results of this new method are given under some suitable conditions. Moreover, we can obtain that if the parameters are suitable selected, then the PAHSS-PU algorithm will outperform the PAHSS algorithm and some Uzawa-type methods in the same precision condition. Numerical experiments are presented to illustrate the theoretical results and examine the numerical effectiveness of the PAHSS-PU method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a discretized version of an elliptic optimal control problem which is presented by Stadler (2009). An alternating direction method is proposed to solve this problem and demonstrated as globally convergent. This class of methods is attractive due to its simplicity and thus is adequate for solving large-scale problems. The preliminary numerical results present the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we suggest and analyze the Levenberg–Marquardt method for solving system of absolute value equations A x − | x | = b , where A ∈ R n × n , b ∈ R n and x ∈ R n are unknown. We present different line search methods to convey the main idea and the significant modifications. We discuss the convergence of the proposed method. We consider numerical examples to illustrate the implementation and efficiency of the method. Results are very encouraging and may stimulate further research in this direction. [ABSTRACT FROM AUTHOR]

This paper proposes a predictor–corrector primal–dual modified log-barrier interior–exterior point method with global convergence and cubic fitting strategies for solving the Reactive Optimal Power Flow (ROPF) problem. The interior–exterior approach is a variant of the primal–dual nonlinear rescaling method, recently proposed. The application of the global convergence strategy produces only descent directions, even if the optimization problem is non-linear and non-convex. The application of a cubic fitting strategy for modified log-barrier functions preserve the continuity and also the first and second-order derivatives of the logarithm near the boundary of the feasible set. Some updating rules for the Lagrange multiplier estimates are theoretically and numerically evaluated. Numerical tests and comparisons with classical interior point methods, involving the electrical systems of 3, 9, IEEE-14, IEEE-30, IEEE-57, IEEE-118, IEEE-162 and IEEE-300 buses, are performed, which demonstrate the robustness and efficiency of the method. [ABSTRACT FROM AUTHOR]

In this paper, we first present a shift-splitting preconditioner for saddle point problems. The preconditioner is based on a shift-splitting of the saddle point matrix, resulting in an unconditional convergent fixed-point iteration. Based on the idea of the splitting, we further propose a local shift-splitting preconditioner. Some properties of the local shift-splitting preconditioned matrix are studied. These preconditioners extend those studied by Bai, Yin and Su for solving non-Hermitian positive definite linear systems (Bai et al., 2006). Finally, numerical experiments of a model Stokes problem are presented to show the effectiveness of the proposed preconditioners. [ABSTRACT FROM AUTHOR]

The paper deals with the numerical solution of a nonstandard Sturm-Liouville boundary value problem on the half line where the coefficients of the differential terms depend on the unknown function by means of a scalar integral operator. By using a finite difference discretization, a truncated quadrature rule and an iterative procedure, we construct a numerical method, whose convergence is proved. The order of convergence and the truncation at infinity are also discussed. Finally, some numerical tests are given to show the performance of the method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical approximation of elliptic interface problems via isoparametric finite element methods. First, a convergence analysis is carried which asserts that optimal rates of convergence are recovered in both the energy and the L 2 –norms. Subsequently, the efficiency of isoparametric finite elements for the problem at hand is also assessed via numerical experiments. Results both with smooth and piecewise regular interfaces are presented and discussed. The numerical predictions corroborate the theoretical results and they also indicate that second-order convergence is achieved in the L ∞ -norm. Comparisons between isoparametric finite elements, Lagrangian finite elements and the Immersed Interface Method are also performed. [ABSTRACT FROM AUTHOR]

The definition of weighted statistical convergence was first introduced by Karakaya & Chishti (2009) and later on Mursaleen et al. (2012) modified the definition of this concept. Using the modified definition, Edely et al. (2013) had researched further in approximation theory for periodic functions and Belen & Mohiuddine (2013) had further extended to the new-definition of weighted λ -statistical convergence. But some problems are still there, so the definition of weighted λ -statistical convergence is needed to modify. In this paper, we will introduce some new constraints which will make the definition of weighted λ -statistical convergence is more useful by using the definition of αβ -statistical convergence. Using it and independently, some newly developed concepts of the convergence of a sequence of random variables in probability, namely, weighted modulus αβ -statistical convergence of order γ , weighted modulus αβ -strong Cesáro convergence of order γ , weighted modulus S α β -convergence of order γ , and weighted modulus N α β -convergence of order γ , have been introduced and their basic interrelations also have been investigated. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new hybrid conjugate gradient method for solving unconstrained optimization problems. The proposed method can be viewed as a convex combination of Liu–Storey method and Dai–Yuan method. An remarkable property is that the search direction of this method not only satisfies the famous D–L conjugacy condition, but also accords with the Newton direction with suitable condition. Furthermore, this property is not dependent on any line searches. Under the strong Wolfe line searches, the global convergence of the proposed method is established. Preliminary numerical results also show that our method is robust and effective. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide a-priori error estimates for problems involving curved interfaces and solved with the linear or quadratic extended finite-element method (X-FEM), with particular emphasis on the influence of the geometry representation and the quadrature. We focus on strong discontinuity problems, which covers the case of holes in a material or cracks not subjected to contact as the main applications. The well-known approximation of the curved geometry based on the interpolated level-set function and straight linear or curved quadratic subcells is used, whose accuracy is quantified by means of an appropriate error measure. A priori error estimates are then derived, which depend upon the interpolation order of the displacement, and foremost upon the above error measure and the quadrature scheme in the subcells. The theoretical predictions are successfully compared with numerical experiments. [ABSTRACT FROM AUTHOR]

Abstract: The numerical method proposed in this paper is an improvement of the ADI method by Li and Mayo (1994). The proposed method is unconditionally stable for both two and three-dimensional heat conduction interface problems, while Li’s ADI method is only stable for two-dimensional problems. The method is a modification of a Locally One-Dimensional (LOD) difference scheme, with correction term added to the right-hand side of the standard LOD difference scheme at irregular points. The correction term is determined so that the local truncation error is of order at irregular points. Then the method is two-order convergent in both time and space directions. Numerical examples show good agreement with exact solutions and confirm the order of convergence and stability. [Copyright &y& Elsevier]

Abstract: In traditional load flow calculation, only three types of buses, PQ, PV, and Vθ, are generally specified. To accommodate the integration of new kinds of power equipment and flexible load flow control facilities, extra bus types are needed in load flow model. The load flow model incorporated with all possible bus types is named as bus-type extended load flow (BELF) for short in this paper. Both Newton–Raphson and decoupled BELF solutions are developed. An important problem for BELF is its solvability, which is carefully studied and topology-based criteria are proposed to ascertain BELF’s solvability. Numerical tests are carried out to verify the convergence of the BELF solution and the correctness of the proposed solvability criteria. [Copyright &y& Elsevier]

Abstract: Methods like the Chebyshev and the Halley method are well known methods for solving nonlinear systems of equations. They are members in the Halley class of methods and all members in this class have local and third order rate of convergence. They are single point iterative methods using the first and second derivatives. Schröderʼs method is another single point method using the first and second derivatives. However, this method is only quadratically convergent. In this paper we derive a unified framework for these methods and show their local convergence and rate of convergence. We also use the same approach to derive inexact methods. The methods in the Halley class require solution of two linear systems of equations for each iteration. However, in the Chebyshev method the coefficient matrices will be the same. Using the unified framework we show how to extend this to all methods in the class. We will illustrate these results with some numerical experiments. [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: This paper presents a numerical method for solving a class of fractional variational problems (FVPs) with multiple dependent variables, multi order fractional derivatives and a group of boundary conditions. The fractional derivative in the problem is in the Caputo sense. In the presented method, the given optimization problem reduces to a system of algebraic equations using polynomial basis functions. An approximate solution for the FVP is achieved by solving the system. The choice of polynomial basis functions provides the method with such a flexibility that initial and boundary conditions can be easily imposed. We extensively discuss the convergence of the method and finally present illustrative examples to demonstrate validity and applicability of the new technique. [Copyright &y& Elsevier]

Abstract: In this paper we propose a distributed dual averaging method for solving the constrained multi-agent optimization problem, in which multiple agents try to cooperatively optimize the sum of their local convex objective functions subject to a global convex constraint set over a network. We consider two cases: (i) The communications among agents are perfect, and (ii) The communications among agents are deterministically or probabilistically quantized. In the first case, we provide a way to control the convergence performance of the proposed method through adjusting the number of consensus iterations we run in the subgradient step. In the second case, we consider two kinds of quantizers, and provide bounds on their convergence rates to highlight the dependence on the quantization resolutions respectively. Finally, we provide a numerical example to show the effectiveness of the proposed methods. [Copyright &y& Elsevier]

Abstract: This paper presents a novel heuristic algorithm for solving economic dispatch (ED) problems, by employing iteration particle swarm optimization with time varying acceleration coefficients (IPSO-TVAC) method. Due to the effect of valve-points and prohibited operation zones (POZs) in the generating units’ cost functions, ED problem is a non-linear and non-convex optimization problem. The problem even may be more complicated if transmission losses are taken into account. The effectiveness of the proposed method is examined and validated by carrying out extensive tests on three different test systems. Valve-point effects, POZs, ramp-rate constraints and transmission losses are modeled. Numerical results show that the IPSO-TVAC method has a good convergence property. Furthermore, the generation costs of the IPSO-TVAC method are lower than other optimization algorithms reported in recent literature. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new approach for solving second kind Fredholm integral equation system. The method is based on the minimization of a suitable functional in a certain Sobolev space. We study the convergence of the method and we present some numerical examples in order to show the validity of the proposed method. [Copyright &y& Elsevier]

Abstract: Gorman’s Superposition method is known as one of the most efficient methods to solve the eigenvalue problems of plates because of its excellent convergence rate. However, there are few published results available that provide sufficient information on its boundedness. Here we have considered the nature of convergence of the eigenvalues for rectangular plates with the following sets of boundary conditions, completely free, fully clamped and cantilever. This paper shows numerically, the boundedness of the Superposition method for undamped vibration problems of rectangular isotropic plates subjected to different boundary conditions. The Superposition method gives upper bound results for eigenvalues of plates if the building blocks used in the Superposition method are subjected to stiffer boundary conditions than those of the original system being modelled. In contrast, the Superposition method yields lower bound results if the boundary conditions of building blocks are more flexible than those of the original system. The results would be useful to estimate the maximum possible error if the other bound can be obtained by another method. [Copyright &y& Elsevier]

Abstract: In this paper, we study an abstract constrained optimization problem which subsumes a common model for the optimal control of linear partial differential equations. Our emphasis is the case when the ordering cone for the optimization problem has an empty interior. To circumvent this difficulty, we propose a new regularization approach which is based on the decoupling of the ordering cone by using certain half-spaces. The approach results in a family of regular optimization problems having a simpler structure than the original optimization problem. Existence theorems, convergence analysis, and optimality conditions are given for the regularized problems. We present two numerical examples and the results are quite encouraging, showing the potential of the proposed approach. [Copyright &y& Elsevier]

Abstract: We present a numerical analysis to solve a parameter identification problem. We identify the demographical parameters of a multistage population dynamics model (Ainseba et al., 2011 ). Our nonlinear optimization problem with constraints is solved by a Quasi-Newton method. The convergence proof of this numerical method is performed here. Some numerical applications of it are also given at the end of the paper. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze a FEM and two-grid FEM decoupling algorithms for elliptic problems on disjoint domains. First, we study the rate of convergence of the FEM and, in particular, we obtain a superconvergence result. Then with proposed algorithms, the solution of the multi-component domain problem (simple example — two disjoint rectangles) on a fine grid is reduced to the solution of the original problem on a much coarser grid together with solution of several problems (each on a single-component domain) on fine meshes. The advantage is the computational cost although the resulting solution still achieves asymptotically optimal accuracy. Numerical experiments demonstrate the efficiency of the algorithms. [Copyright &y& Elsevier]

Abstract: The discrete mollification method is a convolution-based filtering procedure suitable for the regularization of ill-posed problems. Combined with explicit space-marching finite difference schemes, it provides stability and convergence for a variety of coefficient identification problems in linear parabolic equations. In this paper, we extend such a technique to identify some nonlinear diffusion coefficients depending on an unknown space dependent function in one dimensional parabolic models. For the coefficient recovery process, we present detailed error estimates and to illustrate the performance of the algorithms, several numerical examples are included. [Copyright &y& Elsevier]

Abstract: In this paper, a kind of Center Based Genetic Algorithm (CBGA) is proposed to overcome the premature convergence and to solve the stiffness equivalence problem. With the information of population center, central chaotic mutation and space shrinking strategy are designed to guide the evolutionary searching process. Meanwhile, the rank value based roulette selection and a new Cauchy preferential crossover operator are collaboratively used with the mutation operators in the CBGA. To avoid the loss of the best solution, the elitist strategy is employed as well. In addition, local search is embedded in the CBGA after the main evolutionary search process to enhance the exploitation ability by further improving the elite solution. Numerical simulation and comparison based on a set of benchmark functions show that, the proposed CBGA is superior to the hybrid genetic algorithm from the literature in terms of searching efficiency, solution quality, robustness and success ratio. Finally, CBGA is applied to successfully solve the stiffness equivalence problem of the small-aspect-ratio aircraft wing to tapered beam. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with solving the Cauchy problem for an elliptic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to adapted stopping criteria for the minimization process depending on the noise rate. Numerical examples involving smooth and singular data are presented. [Copyright &y& Elsevier]

Abstract: In this paper, we propose an interval version of the generalized accelerated overrelaxation methods, which we refer to as IGAOR, for solving the linear complementarity problems, LCP (M, q), and develop a class of multisplitting IGAOR methods which can be easily implemented in parallel. In addition, in regards to the H-matrix with positive diagonal elements, we prove the convergence of these algorithms and illustrate their efficiency through our numerical results. [Copyright &y& Elsevier]

Abstract: Many real life problems can be stated as a minimax optimization problem, such as the problems in economics, finance, management, engineering and other fields. In this paper, we present an algorithm with nonmonotone strategy and second-order correction technique for minimax optimization problems. Using this scheme, the new algorithm can overcome the difficulties of the Maratos effect occurred in the nonsmooth optimization, and the global and superlinear convergence of the algorithm can be achieved accordingly. Numerical experiments indicate some advantages of this scheme. [Copyright &y& Elsevier]

Abstract: An improved version of rectangular method (IRM) is introduced in this paper to numerically solve the stochastic Volterra equation (SVE). We focus on studying the order of error between the numerical and exact solutions, which is improved to . Furthermore, an explicit form of the IRM scheme is introduced and its convergence is established. A numerical example has also been presented to show the feasibility of the methods. [ABSTRACT FROM AUTHOR]

Abstract: The coupling of cell-centered finite volume method with primal discontinuous Galerkin method is introduced in this paper for elliptic problems. Convergence of the method with respect to the mesh size is proved. Numerical examples confirm the theoretical rates of convergence. Advantages of the coupled scheme are shown for problems with discontinuous coefficients or anisotropic diffusion matrix. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates a class of minimax problems, in which the cost functions are nonsmooth. A generalized neural network for solving the minimax problems was proposed, and its convergence was proven based on the nonsmooth analysis. The rate of convergence was discussed by virtue of the łojasiewicz inequality. Two numerical examples were given to illustrate the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a new nonmonotone trust-region method of conic model for solving unconstrained optimization problems. Both the local and global convergence properties are analyzed under reasonable assumptions. Numerical experiments are conducted to compare this method with some existed ones which indicate that the new method is efficient. [Copyright &y& Elsevier]

Abstract: In this paper, based on a simple model of the trust region subproblem, we propose a new self-adaptive trust region method with a line search technique for solving unconstrained optimization problems. By use of the simple subproblem model, the new method needs less memory capacitance and computational complexity. And the trust region radius is adjusted with a new self-adaptive adjustment strategy which makes full use of the information at the current point. When the trial step results in an increase in the objective function, the method does not resolve the subproblem, but it performs a line search technique from the failed point. Convergence properties of the method are proved under certain conditions. Numerical experiments show that the new method is effective and attractive for large-scale optimization problems. [Copyright &y& Elsevier]

Abstract: In this paper, a new trust region algorithm is proposed for solving unconstrained optimization problems. This method can be regarded as a combination of trust region technique, fixed step-length and ODE-based methods. A feature of this proposed method is that at each iteration, only a system of linear equations is solved to obtain a trial step. Another is that when a trial step is not accepted, the method generates an iterative point whose step-length is defined by a formula. Under some standard assumptions, it is proven that the algorithm is globally convergent and locally superlinear convergent. Preliminary numerical results are reported. [Copyright &y& Elsevier]

Abstract: We consider the employment of numerical optimization and state regulation to solve the extremum seeking control (ESC) problem, which does not assume the time scale separation between the plant dynamics and the extremum seeking loop. Extremum seeking is realized via a state regulator that drives the state traveling along a convergent set point sequence generated by a numerical optimization algorithm. In this paper, we propose a novel design of an asymptotic state regulator via output tracking for state feedback linearizable systems, where we trade off finite time state regulation to obtain flexibility in designing a robust extremum seeking controller. Existing techniques such as nonlinear damping and nonlinear adaptive control are then used to deal with input disturbance and unmodeled plant dynamics. Simulation examples illustrate the effectiveness of the basic and robust extremum seeking schemes, and some design guidelines are provided for engineering applications. [Copyright &y& Elsevier]

Abstract: This paper proves the convergence of some generalized Schwarz algorithms for solvingthe obstacle problems with a T-monotone operator. Numerical results show that the generalized Schwarz algorithms converge faster than the classical Schwarz algorithms. [Copyright &y& Elsevier]