The 1669-1670 Newton-Raphson’s method is still used to solve equations systems and unconstrained optimization problems. Since this method, some other algorithms inspired by Newton’s have been proposed: in 1839 Chebyshev developped a high order cubical convergence algorithm, and in 1967 Shamanskii proposed an acceleration of Newton’s method. By considering a Newton-type methods as displacement d...

Modifications that introduce parallelization of standard cuckoo search algorithm are proposed in this paper. Basic form of the cuckoo search algorithm has already shown great potential for optimization problems, especially when applied to unconstrained continuous functions. In this paper two aspects of parallelization are proposed. The first one addresses the performance issue, while the second...

Various techniques have been proposed for incorporating constraints in interval branch and bound algorithms for global optimization. However, few reports of practical experience with these techniques have appeared to date. Such experimental results appear here. The underlying implementation includes use of an approximate optimizer combined with a careful tesselation process and rigorous veriica...

A well-known technique for the solution of quasi-variational inequalities (QVIs) consists in the reformulation of QVIs as a constrained or unconstrained optimization problem by means of so-called gap functions. In contrast to standard variational inequalities, however, these gap functions turn out to be nonsmooth in general. Here it is shown that one can obtain an unconstrained optimization ref...

In this paper, we incorporate a nonmonotone technique with the new proposed adaptive trust region radius (Shi and Guo, 2008) [4] in order to propose a new nonmonotone trust region method with an adaptive radius for unconstrained optimization. Both the nonmonotone techniques and adaptive trust region radius strategies can improve the trust region methods in the sense of global convergence. The g...

A challenge in hybrid evolutionary algorithms is to define efficient strategies to cover all search space, applying local search only in actually promising search areas. This paper proposes a way of detecting promising search areas based on clustering. In this approach, an iterative clustering works simultaneously to an evolutionary algorithm accounting the activity (selections or updatings) in...

Multi-start algorithms are a common and effective tool for metaheuristic searches. In this paper we amplify multi-start capabilities by employing the parallel processing power of the graphics processer unit (GPU) to quickly generate a diverse starting set of solutions for the Unconstrained Binary Quadratic Optimization Problem which are evaluated and used to implement screening methods to selec...

Our interest lies in solving large-scale unconstrained polynomial optimization problems. Because interior-point methods for solving these problems are severely limited by the large-scale, we are motivated to explore efficient implementations of an accelerated first-order method to solve this class of problems. By exploiting special structural properties of this problem class, we greatly reduce ...

In this paper we address the problem of using quaternions in unconstrained nonlinear optimization of 3-D rotations. Quaternions representing rotations have four elements but only three degrees of freedom, since they must be of norm one. This constraint has to be taken into account when applying e. g. the Levenberg-Marquardt algorithm, a method for unconstrained nonlinear optimization widely use...