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In this paper, we present a feasible predictor-corrector interior-point method for symmetric cone optimization problem in the large neighbourhood of the central path. The method is generalization of Ai-Zhang's predictor-corrector algorithm to the symmetric cone optimization problem. Starting with a feasible point in given large neighbourhood of the central path, the algorithm still terminates in at most iterations. This matches the best known iteration bound that is usually achieved by short-step methods, thereby, closing the complexity gap between long- and short-step interior-point methods for symmetric cone optimization. The preliminary numerical results on a selected set of NETLIB problems show advantage of the method in comparison with the version of the algorithm that is not based on the predictor-corrector scheme. [ABSTRACT FROM AUTHOR]

In this paper, iterative algorithm for strong vector equilibrium problem (SVEP) is studied. Firstly, an auxiliary problem for SVEP is introduced and the relationships between these two problems are discussed. Then, based on the auxiliary problem, a projection iterative algorithm for SVEP is proposed. Moreover, analysis of convergence of this iterative algorithm is investigated under suitable conditions of continuity and convexity. The main result obtained in this paper generalizes and improves the corresponding ones of Iusem and Sosa [Iusem AN, Sosa W. Iterative algorithms for equilibrium problems. Optimization. 2003;52(3):301–316.] and Cheng and Liu [Cheng B, Liu SY. An iterative algorithm for vector equilibrium problems. J. Lanzhou Univ. (Nat. Sci.). 2009;45(5):105–109.]. [ABSTRACT FROM AUTHOR]

This paper presents a method for determining the optimum number, impedance, and locations of fault current limiter (FCL) to reduce the negative impact of distributed generations presence in the power systems such as increasing the short circuit current levels and improve the system reliability. In the considered method, we have modeled the FCL placement as an optimization problem while the objectives are; bus fault current difference, reliability, the number and impedance of FCLs. Moreover, to solve the proposed problem, a new multi-objective optimization algorithm based on firework algorithm namely multi-objective firework algorithm has been implemented. In the new algorithm, several iterations have been considered, and the non-dominated solutions are extracted and stored in an external repository in the iterations. Finally, a fuzzy clustering technique is used to control the size of the repository during the algorithm evolution. The proposed approach is tested on two different systems, namely, Roy Billinton Test System (RBTS) 2 and RBTS 4 test system. The obtained results demonstrate the effectiveness and feasibility of the new method. [ABSTRACT FROM PUBLISHER]

In this paper, an iterative algorithm for solving the strong vector equilibrium problem with variable domination structure (VSVEP) is considered. First, an auxiliary problem for the VSVEP is introduced and the relationships between the auxiliary problem and VSVEP are discussed. Then, using the auxiliary principle technique, a projection iterative algorithm to compute the approximate solutions of the VSVEP is proposed and analysed. Furthermore, convergence of the iterative sequences generated by this algorithm is investigated under suitable conditions of continuity and convexity. These results extend and improve some recent works in this field. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following minimization problem:where,,,andare given. An efficient inequality relaxation technique is presented to relax the matrix inequality constraint so that there is an optimal solution which is(R,S)-symmetric that minimize, and also satisfies the corrected matrix inequality constraint. A hybrid algorithm with convergence analysis is given to solve this problem. Numerical examples show that the algorithm requires less CPU times when compared with some other methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose hybrid implicit and explicit viscosity iterative algorithms for solving general hierarchical fixed-point problems for a countable family of non-expansive mappings in uniformly smooth Banach spaces. These hybrid viscosity algorithms are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under suitable conditions. Our results extend, improve, supplement and develop the recent results in the literature. [ABSTRACT FROM PUBLISHER]

We propose an iterative scheme for finding a common element of fixed points set of a nonexpansive mapping and the solutions set of a generalized variational inequality problem in Euclidean space. Under some mild conditions, we establish the convergence theorem for the proposed algorithm. We also give a suitable condition to ensure the intersection of fixed points set of a nonexpansive mapping and the solutions set of a generalized variational inequality problem to be nonempty. In addition, under certain error bound conditions, we prove the convergence rate of the iterative sequence. Preliminary computational experience is also reported. [ABSTRACT FROM AUTHOR]

We propose a trust-region algorithm for constrained optimization problems in which the derivatives of the objective function are not available. In each iteration, the objective function is approximated by a model obtained by quadratic interpolation, which is then minimized within the intersection of the feasible set with the trust region. Since the constraints are handled in the trust-region subproblems, all the iterates are feasible even if some interpolation points are not. The rules for constructing and updating the quadratic model and the interpolation set use ideas from theBOBYQAsoftware, a largely used algorithm for box-constrained problems. The subproblems are solved byALGENCAN, a competitive implementation of an Augmented Lagrangian approach for general-constrained problems. Some numerical results for the Hock–Schittkowski collection are presented, followed by a performance comparison between our proposal and three derivative-free algorithms found in the literature. [ABSTRACT FROM AUTHOR]

We develop a novel yet simple iterative algorithm to solve a mixed-type inverse heat conduction problem, which is a combination of the Cauchy problem, the backward heat conduction problem (BHCP) and a heat source recovery problem. First, we transform the heat conduction equation into a new one, including a spring term and a damping term, which can raise the accuracy of numerical solution. Second, we use the differential quadrature method to semi-discretize the differential term, and then the group-preserving scheme leads to an accurate solution of the mixing Cauchy and BHCP. Third, with the aid of an overspecified right-end boundary condition, an iterative Lie-group adaptive method is developed to recover the space-dependent heat source function through a few iterations. The heat source term recovered is quite smooth, even the input data are polluted by a random noise, being large up to. The accuracy and efficiency of the new methods are assessed by comparing the estimated results with exact solutions from several numerical examples. [ABSTRACT FROM AUTHOR]

In the iterative solution of an ill-posed linear system, how to select a fast and easily established descent directionto reduce the residualis an important issue. A mathematical procedure to find a double optimal descent directionin, without inverting, is developed in an-dimensional Krylov subspace. The novelty is that we expandin an affine Krylov subspace with undetermined coefficients, and then two optimization techniques are used to determine these coefficients in closed form, which can greatly accelerate the convergence speed in solving the ill-posed linear problems. The double optimal descent algorithm is proven to be absolutely convergent very fast, accurate and robust against noise, which is confirmed by numerical tests of several linear inverse problems, including the heat source identification problem, the backward heat conduction problem, the inverse Cauchy problem and the external force identification problem. [ABSTRACT FROM AUTHOR]