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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: 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]

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, 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: 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: 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: 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 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: 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 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]

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, an active set limited BFGS algorithm is proposed for bound constrained optimization. The global convergence will be established under some suitable conditions. Numerical results show that the given method is effective. [Copyright &y& Elsevier]

Abstract: There has been great interest in deciding whether a combinatorial structure satisfies some property, or in estimating the value of some numerical function associated with this combinatorial structure, by considering only a randomly chosen substructure of sufficiently large, but constant size. These problems are called property testing and parameter testing, where a property or parameter is said to be testable if it can be estimated accurately in this way. The algorithmic appeal is evident, as, conditional on sampling, this leads to reliable constant-time randomized estimators. Our paper addresses property testing and parameter testing for permutations in a subpermutation perspective; more precisely, we investigate permutation properties and parameters that can be well approximated based on a randomly chosen subpermutation of much smaller size. In this context, we use a theory of convergence of permutation sequences developed by the present authors [C. Hoppen, Y. Kohayakawa, C.G. Moreira, R.M. Sampaio, Limits of permutation sequences through permutation regularity, Manuscript, 2010, 34pp.] to characterize testable permutation parameters along the lines of the work of Borgs et al. [C. Borgs, J. Chayes, L. Lovász, V.T. Sós, B. Szegedy, K. Vesztergombi, Graph limits and parameter testing, in: STOC’06: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, ACM, New York, 2006, pp. 261–270.] in the case of graphs. Moreover, we obtain a permutation result in the direction of a famous result of Alon and Shapira [N. Alon, A. Shapira, A characterization of the (natural) graph properties testable with one-sided error, SIAM J. Comput. 37 (6) (2008) 1703–1727.] stating that every hereditary graph property is testable. [Copyright &y& Elsevier]

Abstract: This paper presents selective regeneration particle swarm optimization (SRPSO), a novel algorithm developed based on particle swarm optimization (PSO). It contains two new features, unbalanced parameter setting and particle regeneration operation. The unbalanced parameter setting enables fast convergence of the algorithm and the particle regeneration operation allows the search to escape from local optima and explore for better solutions. This algorithm is applied to data clustering problems for performance evaluation and a hybrid algorithm (KSRPSO) of K-means clustering method and SRPSO is developed. In the conducted numerical experiments, SRPSO and KSRPSO are compared to the original PSO algorithm, K-means, as well as, other methods proposed by other studies. The results demonstrate that SRPSO and KSRPSO are efficient, accurate, and robust methods for data clustering problems. [Copyright &y& Elsevier]

Abstract: We introduce in this paper a new direction splitting algorithm for solving the incompressible Navier–Stokes equations. The main originality of the method consists of using the operator (I − ∂ xx )(I − ∂ yy )(I − ∂ zz ) for approximating the pressure correction instead of the Poisson operator as done in all the contemporary projection methods. The complexity of the proposed algorithm is significantly lower than that of projection methods, and it is shown the have the same stability properties as the Poisson-based pressure-correction techniques, either in standard or rotational form. The first-order (in time) version of the method is proved to have the same convergence properties as the classical first-order projection techniques. Numerical tests reveal that the second-order version of the method has the same convergence rate as its second-order projection counterpart as well. The method is suitable for parallel implementation and preliminary tests show excellent parallel performance on a distributed memory cluster of up to 1024 processors. The method has been validated on the three-dimensional lid-driven cavity flow using grids composed of up to 2×109 points. [Copyright &y& Elsevier]

Abstract: The max-bisection problem is an NP-hard combinatorial optimization problem. In this paper, a new Lagrangian net algorithm is proposed to solve max-bisection problems. First, we relax the bisection constraints to the objective function by introducing the penalty function method. Second, a bisection solution is calculated by a discrete Hopfield neural network (DHNN). The increasing penalty factor can help the DHNN to escape from the local minimum and to get a satisfying bisection. The convergence analysis of the proposed algorithm is also presented. Finally, numerical results of large-scale G-set problems show that the proposed method can find a better optimal solutions. [Copyright &y& Elsevier]

Abstract: Equations with box constraints are applied in many fields, for example the complementarity problem. After studying the existing methods, we find that quadratic convergence of majority algorithms is based on the solvability of the equations. But whether the equations are solvable is previously unknown. So, it is necessary to design an algorithm which has fast quadratic convergence. The quadratic convergence does not depend on the solvability of the equations. In this paper, we propose a new method for solving equations. The global and local quadratic convergence of the proposed algorithm are established under some suitable assumptions. We apply the proposed algorithm to a class of stochastic linear complementarity problems. Numerical results show that our method is valid. [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: In this paper, we propose a trust region method for unconstrained optimization that can be regarded as a combination of conic model, nonmonotone and line search techniques. Unlike in traditional trust region methods, the subproblem of our algorithm is the conic minimization subproblem; moreover, our algorithm performs a nonmonotone line search to find the next iteration point when a trial step is not accepted, instead of resolving the subproblem. The global and superlinear convergence results for the algorithm are established under reasonable assumptions. Numerical results show that the new method is efficient for unconstrained optimization problems. [ABSTRACT FROM AUTHOR]

Abstract: Total variation minimisation is a well-established method for digital image restoration. Its implicit preservation of edges permits the derivation of anisotropic models for a qualitative improvement at corners. This paper is a synopsis of anisotropic models with state-of-the-art insights into the numerics of isotropic models. We generalise two representative models from both branches of research. This formulation leads to a general convergent algorithm and a general highly efficient algorithm which apply for both cases. A transfer of the discretisation from the anisotropic model to the isotropic setting results in an improvement of rotational invariance. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce and analyze Uzawa algorithms for non-symmetric saddle point systems. Convergence for the algorithms is established based on new spectral results about Schur complements. A new Uzawa type algorithm with optimal relaxation parameters at each new iteration is introduced and analyzed in a general framework. Numerical results supporting the efficiency of the algorithms are presented for finite element discretization of steady state Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

Abstract: The Arnoldi-type algorithm proposed by Golub and Greif [G. Golub, C. Greif, An Arnoldi-type algorithm for computing PageRank, BIT 46 (2006) 759–771] is a restarted Krylov subspace method for computing PageRank. However, this algorithm may not be efficient when the damping factor is high and the dimension of the search subspace is small. In this paper, we first develop an extrapolation method based on Ritz values. We then consider how to periodically knit this extrapolation method together with the Arnoldi-type algorithm. The resulting algorithm is the Arnoldi-Extrapolation algorithm. The convergence of the new algorithm is analyzed. Numerical experiments demonstrate the numerical behavior of this algorithm. [Copyright &y& Elsevier]

Abstract: In this paper a new approach combining the features of the homotopy concept with an efficient computational algorithm which provides a simple and rigorous procedure to control the convergence of the solution is proposed to find accurate analytical explicit solutions for some oscillators with discontinuities and a fractional power restoring force which is proportional to . A very fast convergence to the exact solution was proved, since the second-order approximation lead to very accurate results. Comparisons with numerical results are presented to show the effectiveness of this method. Four numerical applications prove the accuracy of the method, which works very well for the whole range of initial amplitudes. The obtained results prove the validity and efficiency of the method, which can be easily extended to other strongly nonlinear problems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a new iterative method (successive projection iterative method) to solve matrix equation , where is a symmetric positive definite (SPD) matrix. Based on this method an algorithm is proposed and proved to be convergent. In addition, analysis of the algorithm and numerical experiments are also given to show the efficiency of the method. [Copyright &y& Elsevier]

Abstract: Artificial bee colony (ABC) is the one of the newest nature inspired heuristics for optimization problem. Like the chaos in real bee colony behavior, this paper proposes new ABC algorithms that use chaotic maps for parameter adaptation in order to improve the convergence characteristics and to prevent the ABC to get stuck on local solutions. This has been done by using of chaotic number generators each time a random number is needed by the classical ABC algorithm. Seven new chaotic ABC algorithms have been proposed and different chaotic maps have been analyzed in the benchmark functions. It has been detected that coupling emergent results in different areas, like those of ABC and complex dynamics, can improve the quality of results in some optimization problems. It has been also shown that, the proposed methods have somewhat increased the solution quality, that is in some cases they improved the global searching capability by escaping the local solutions. [Copyright &y& Elsevier]

Abstract: In this paper, a new feasible primal–dual interior point algorithm for solving inequality constrained optimization problems is presented. At each iteration, the algorithm solves only two or three reduced systems of linear equations with the same coefficient matrix. The searching direction is feasible and the object function is monotone decreasing. The proposed algorithm is proved to possess global and superlinear convergence under mild conditions. Finally, some numerical experiments with the algorithm are reported. [Copyright &y& Elsevier]

Abstract: A new norm-relaxed sequential quadratic programming algorithm with global convergence for inequality constrained problem is presented in this paper, and the quadratic programming subproblem can be solved at each iteration. Without the boundedness assumptions on any of the iterative sequences, the global convergence can be guaranteed by line search with penalty function and under some mild assumptions. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate a smoothing-type algorithm with a nonmonotone line search for solving a system of equalities and inequalities. We prove that the nonmonotone algorithm is globally and locally superlinearly convergent under suitable assumptions. The preliminary numerical results are reported. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a BFGS trust-region method for solving symmetric nonlinear equations. The global convergence and the superlinear convergence of the presented method will be established under favorable conditions. Numerical results show that the new algorithm is effective. [Copyright &y& Elsevier]

Abstract: This paper discusses nonlinear complementarity problems; its goal is to present a globally and superlinearly convergent algorithm for the discussed problems. Filter methods are extensively studied to handle nonlinear complementarity problem. Because of good numerical results, filter techniques are attached. By means of a filter strategy, we present a new trust region method based on a conic model for nonlinear complementarity problems. Under a proper condition, the superlinear convergence of the algorithm is established without the strict complementarity condition. [Copyright &y& Elsevier]

Abstract: In this paper we consider a conic trust-region method for unconstrained optimization problems and analyze its convergence properties. We propose a convenient curvilinear search method to approximately solve the arising conic trust-region subproblem. Note that this approximate method preserves the strong convergence properties of the exact solution methods and is easy to implement. Both the linear and superlinear convergence of the method are established under commonly used conditions. Numerical experiments are conducted to show the efficiency of the new method. [Copyright &y& Elsevier]

Abstract: In this paper a globally convergent first-order training algorithm is proposed that uses sign-based information of the batch error measure in the framework of the nonlinear Jacobi process. This approach allows us to equip the recently proposed Jacobi–Rprop method with the global convergence property, i.e. convergence to a local minimizer from any initial starting point. We also propose a strategy that ensures the search direction of the globally convergent Jacobi–Rprop is a descent one. The behaviour of the algorithm is empirically investigated in eight benchmark problems. Simulation results verify that there are indeed improvements on the convergence success of the algorithm. [Copyright &y& Elsevier]

In this paper, a new gradient-related algorithm for solving large-scale unconstrained optimization problems is proposed. The new algorithm is a kind of line search method. The basic idea is to choose a combination of the current gradient and some previous search directions as a new search direction and to find a step-size by using various inexact line searches. Using more information at the current iterative step may improve the performance of the algorithm. This motivates us to find some new gradient algorithms which may be more effective than standard conjugate gradient methods. Uniformly gradient-related conception is useful and it can be used to analyze global convergence of the new algorithm. The global convergence and linear convergence rate of the new algorithm are investigated under diverse weak conditions. Numerical experiments show that the new algorithm seems to converge more stably and is superior to other similar methods in many situations. [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]