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Abstract In this paper, we present a two-grid mixed finite element scheme for distributed optimal control problems governed by stationary Stokes equations. In order to avoid the difficulty caused by the symmetry constraint of the stress tensor, we use pseudostress to replace it. The state and co-state are approximated by the lowest order Raviart–Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We first prove that the difference between the interpolation and the numerical solution has superconvergence property for the control u with order h 2. Then, using the postprocessing technique, we derive a second-order superconvergent result for the control u . Next, we construct a two-grid mixed finite element scheme and derive a priori error estimates. Finally, a numerical experiment is presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a three-term conjugate gradient algorithm is developed for solving large-scale unconstrained optimization problems. The search direction at each iteration of the algorithm is determined by rectifying the steepest descent direction with the difference between the current iterative points and that between the gradients. It is proved that such a direction satisfies the approximate secant condition as well as the conjugacy condition. The strategies of acceleration and restart are incorporated into designing the algorithm to improve its numerical performance. Global convergence of the proposed algorithm is established under two mild assumptions. By implementing the algorithm to solve 75 benchmark test problems available in the literature, the obtained results indicate that the algorithm developed in this paper outperforms the existent similar state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes a practical formulation for the non-convex economic dispatch problem to consider multi-fuel options, ramp rate limits, valve loading effect, prohibited operating zones and spinning reserve. A new optimization algorithm based on the θ -bat algorithm ( θ -BA) is suggested to solve the problem. The θ -BA converts the Cartesian search space into the polar coordinates such that more search ability would be achieved. According to the complex, nonlinear, and constrained nature of the problem, a new self-adaptive modification method is proposed. The proposed modified θ -BA ( θ -MBA) is constructed based on the roulette wheel mechanism to effectively increase the convergence of the algorithm. The high ability and satisfying performance of the proposed optimization method is examined on IEEE 15-unit, 40-unit and 100-unit test systems. [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]

In this paper, we introduce a new algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of two finite families of demicontractive mappings. The strong convergence theorem of the proposed algorithm is established under some suitable control conditions in a real Hilbert space. Our result generalizes several recent results in the current literature. [ABSTRACT FROM AUTHOR]

In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip -like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O ( n ) in both theoretical and empirical comparisons. [ABSTRACT FROM AUTHOR]

In this paper, we establish a class of accelerated Uzawa (AU) algorithms for solving the large sparse nonsingular saddle point problems by making use of the extrapolation technique. This extrapolation technique is based on the eigenvalues of the iterative matrix. These AU algorithms involve two iteration parameters whose special choices can cover the known classical Uzawa method, as well as yield new ones. Firstly, the accelerated model for the Uzawa algorithm is established and the detail algorithm description of AU method is presented. Then the convergence analyse of the AU method is given. Moreover, theoretical analyses show that the AU algorithm converges faster than some Uzawa-type methods (the Uzawa method is also included in) when the eigenvalues of the iterative matrix and the parameter τ satisfy some conditions. Numerical experiments on a few model problems are presented to illustrate the theoretical results and examine the numerical effectiveness of the AU method. [ABSTRACT FROM AUTHOR]

Abstract: In allusion to the deficiencies of the low computational efficiency and local optimal solution of particle swarm optimization (PSO) algorithm, an improved PSO algorithm based on combining the simulated annealing (SA), co-evolution theory, quantum behavior theory and diversity-guided mutation strategy (MSCQPSO) is proposed in this paper. In the proposed MSCQPSO algorithm, the population is divided into multi-populations according to the computed fitness value. The SA and diversity-guided mutation strategy are introduced to enhance the global search ability. The quantum behavior theory is introduced into co-evolution theory to change the updating mode of the particles in order to guarantee the simplification and effectiveness. In order to prove the validity of the proposed MSCQPSO algorithm, the ten high-dimensional complex benchmark functions are selected in here. The experiment results show that the proposed MSCQPSO algorithm takes on the fast convergence, the high searching accuracy, the better robustness for solving the high-dimensional complex problems than the PSO algorithm, the CPSO algorithm and HPSO algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a subgradient extragradient method for solving multi-valued variational inequality. It is showed that the method converges globally to a solution of multi-valued variational inequality, provided the multi-valued mapping is pseudomonotone with nonempty compact convex values. Convergence rate is analyzed. Preliminary computational experience is also reported. [Copyright &y& Elsevier]

Abstract: In this paper, nonlinear minimax problems with inequality constraints are discussed. Combined the norm-relaxed SQP method with the idea of strongly sub-feasible directions method, a new method of quasi-strongly sub-feasible directions (MQSSFD) with arbitrary initial point for the discussed problems is presented. At each iteration of the proposed algorithm, an improved search direction is obtained by solving a quadratic program (QP) which always has a solution, and a high-order correction direction is yielded via a system of linear equations (SLE) to avoid the Maratos effect. After finite iterations, the iteration point always get into the feasible set by introducing a new non-monotone curve search. Under some mild conditions including the weak Mangasarian–Fromovitz constraint qualification (MFCQ), the proposed algorithm possesses global convergence, and the superlinear convergence is obtained without the strict complementarity. Finally, some elementary numerical experiments are implemented and reported. [Copyright &y& Elsevier]

Abstract: The alternating direction method of multipliers (ADMM) is known to be a classic and efficient method for constrained optimization problem with two blocks of variables, and its empirical efficiency has been well illustrated in various fields. Specially, for improving its speed performance, Ye and Yuan suggested to do an additional extension with an optimal step size on the variables after each iteration of the primary ADMM. Indeed, the numerical experiments indicate that this modified ADMM improves the speed performance of the ADMM by around 40% without changing the algorithmic framework much. Recently, the convergence rate of the primary ADMM is established. Inspired by its idea, in this paper, we show that this improved ADMM also has convergence rate. The reason that larger γ yields better speed performance is also investigated and explained. [Copyright &y& Elsevier]

Abstract: In this paper we study two solution methods for finding the largest eigenvalue (singular value) of general square (rectangular) nonnegative tensors. For a positive tensor, one can find the largest eigenvalue (singular value) based on the properties of the positive tensor and the power-type method. While for a general nonnegative tensor, we use a series of decreasing positive perturbations of the original tensor and repeatedly recall power-type method for finding the largest eigenvalue (singular value) of a positive tensor with an inexact strategy. We prove the convergence of the method for the general nonnegative tensor. Under a certain assumption, the computing complexity of the method is established. Motivated by the interior-point method for the convex optimization, we put forward a one-step inner iteration power-type method, whose convergence is also established under certain assumption. Additionally, by using embedding technique, we show the relationship between the singular values of the rectangular tensor and the eigenvalues of related square tensor, which suggests another way for finding the largest singular value of nonnegative rectangular tensor besides direct power-type method for this problem. Finally, numerical examples of our algorithms are reported, which demonstrate the convergence behaviors of our methods and show that the algorithms presented are promising. [Copyright &y& Elsevier]

Abstract: The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The shape of the cost function, and hence the difficulty in solving the optimization problem, depends directly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. Therefore, it seems plausible to improve the convergence to the global minimum by properly choosing the spectrum of the input; in this paper, we address this problem. We present a condition for convergence to the global minimum of the cost function and propose its inclusion in the input design. We present the application of the proposed approach to case studies where the algorithms tend to get trapped in nonglobal minima. [Copyright &y& Elsevier]

Abstract: In this paper, the steepest descent algorithm without line search is proposed for p-Laplacian. Its search direction is the weighted preconditioned steepest descent one, and step length is estimated by a formula except the first iteration. Continuation method is applied for solving the p-Laplacian with very large p. Lots of numerical experiments are carried out on these algorithms. All numerical results show the algorithm without line search can cut down some computational time. Fast convergence of these new algorithms is displayed by their step length figures. These figures show that if search direction is the steepest descent one, exact step lengths can be substituted properly with step lengths obtained by the formula. [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: In this paper, we propose a new partial splitting augmented Lagrangian method for solving the separable constrained convex programming problem where the objective function is the sum of three separable convex functions and the constraint set is also separable into three parts. The proposed algorithm combines the alternating direction method (ADM) and parallel splitting augmented Lagrangian method (PSALM), where two operators are handled by a parallel method, while the third operator and the former two are dealt with by an alternating manner. Under mild conditions, we prove the global convergence of the new method. We also report some preliminary numerical results on constrained matrix optimization problem, illustrating the advantage of the new algorithm over the most recently PADALM of Peng and Wu (2010) [12]. [Copyright &y& Elsevier]

Abstract: In this paper, a new algorithm is proposed to solve the nonlinear constrained optimization problems. Unlike sequential quadratic programming (SQP) type methods, this algorithm does not involve solutions of quadratic programs. It is merely necessary to solve systems of linear equations with small scale to obtain a direction. The scheme is based on an idea of -effective active set strategies. The theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions. [Copyright &y& Elsevier]

Abstract: The main contribution of this paper is an algorithm to solve an extended version of the quantized consensus problem over networks represented by Hamiltonian graphs, i.e., graphs containing a Hamiltonian cycle, which we assume to be known in advance. Given a network of agents, we assume that a certain number of tokens should be assigned to the agents, so that the total number of tokens weighted by their sizes is the same for all the agents. The algorithm is proved to converge almost surely to a finite set containing the optimal solution. A worst case study of the expected convergence time is carried out, thus proving the efficiency of the algorithm with respect to other solutions recently presented in the literature. Moreover, the algorithm has a decentralized stop criterion once the convergence set is reached. [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: In this paper, we study the identification of parametric Hammerstein systems with FIR linear parts. By a proper normalization and a clever characterization, it is shown that the average squared error cost function for identification can be expressed in terms of the inner product between the true but unknown parameter vector and its estimate. Further, the cost function is concave in the inner product and linear in the inner product square. Therefore, the identification of parametric Hammerstein systems with FIR linear parts is a globally convergent problem and has one and only one (local and global) minimum. This implies that the identification of such systems is a linear problem in terms of the inner product square and any local search based identification algorithm converges globally. [Copyright &y& Elsevier]

Abstract: This paper presents an augmented Lagrangian methodology with a stochastic population based algorithm for solving nonlinear constrained global optimization problems. The method approximately solves a sequence of simple bound global optimization subproblems using a fish swarm intelligent algorithm. A stochastic convergence analysis of the fish swarm iterative process is included. Numerical results with a benchmark set of problems are shown, including a comparison with other stochastic-type algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, the system of mixed variational inequalities is introduced and considered in Banach spaces, which includes some known systems of variational inequalities and the classical variational inequalities as special cases. Using the projection operator technique, we suggest some iterative algorithms for solving the system of mixed variational inequalities and prove the convergence of the proposed iterative methods under suitable conditions. Our theorems generalize some known results shown recently. [Copyright &y& Elsevier]

Abstract: A comprehensive and systematic strategy for evaluating the performances of several trilinear second-order calibration algorithms is presented in this paper, in particular with a view of practical applications. Several trilinear second-order calibration methods such as PARAFAC, ATLD, SWATLD and APTLD, which have the “second-order advantage” and are gaining widespread acceptance in the field of chemometrics, were compared. Based on different input parameters including noise level, initial value, number of estimated components and collinearity in simulated and real data, the performances of these methods were evaluated in terms of predicting ability, consistency of resolved and real profiles, fitness obtained by selected components and speed of convergence. The obtained results give a reevaluation of the position and role of these trilinear second-order calibration methods in chemometrics and provide a guidance in practical applications for solving complicated quantitative analysis problems in analytical chemistry. It is useful and helpful to choose, for example, which algorithm would be more suitable for predicting the concentration of the analyte(s) of interest even in the presence of unknown interferents in complex systems. [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: In this paper, we prove strong convergence theorems by the hybrid method for a family of hemi-relatively nonexpansive mappings in a Banach space. Our results improve and extend the corresponding results given by Qin et al. [Xiaolong Qin, Yeol Je Cho, Shin Min Kang, Haiyun Zhou, Convergence of a modified Halpern-type iteration algorithm for quasi--nonexpansive mappings, Appl. Math. Lett. 22 (2009) 1051–1055], and at the same time, our iteration algorithm is different from the Kimura and Takahashi algorithm, which is a modified Mann-type iteration algorithm [Yasunori Kimura, Wataru Takahashi, On a hybrid method for a family of relatively nonexpansive mappings in Banach space, J. Math. Anal. Appl. 357 (2009) 356–363]. In addition, we succeed in applying our algorithm to systems of equilibrium problems which contain a family of equilibrium problems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we suggest and analyze two projection methods (one implicit and one explicit) for finding a particular solution of a mixed equilibrium problem in a real Hilbert space. Furthermore, we prove that the proposed projection methods converge strongly to a particular solution of the mixed equilibrium problem. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a new composite iteration approximating to common fixed points for a finite family of nonexpansive mappings in Banach spaces which have a uniformly Gâteaux differentiable norm. Utilizing the iterative algorithm, we obtain the strong convergence theorems for a finite family of nonexpansive mappings. Furthermore, the problem of image recovery is considered in the above result. Our results extend and improve the corresponding results. [Copyright &y& Elsevier]

Abstract: 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 -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 -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 -strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 70 (2009) 1902–1911] and other authors. [Copyright &y& Elsevier]

This paper concerns an adaptive finite element method for the Stefan one-phase problem. We derive a parabolic variational inequality using the Duvaut transformation. In each time-step we consider an adaptive algorithm based on a combination of the Uzawa method associated with the corresponding multivalued operator and a convergent adaptive method for the linear problem. We justify the convergence of the method. As an application we model an endoglacial conduit in which a phase change phenomenon takes place. [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]