A new family of eighth-order derivative-freemethods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight. These new methods are derivative-free and only use four evaluations of the function per iteration. In fact, we have obtained the optimal order of convergence which supports the Kung and Traub conjecture. Kung and Traub conjectured...

We consider the problem of minimizing a continuously differentiable function of several variables subject to smooth nonlinear constraints. We assume that the first order derivatives of the objective function and of the constraints can be neither calculated nor approximated explicitly. Hence, every minimization procedure must use only a suitable sampling of the problem functions. These problems ...

In this review paper we summarise several nonparametric methods recently applied to the pricing of financial options. After a short introduction to martingale-based option pricing theory, we focus on two possible fields of application for nonparametric methods: the estimation of risk-neutral probabilities and the estimation of the dynamics of the underlying instruments in order to construct an ...

From position and velocity coordinates for several given instants, it is possible to determine orbital elements for the preliminary orbit. This theoretical trajectory, also known as keplerian orbit, is defined taking only into account mutual gravitational attraction forces between both bodies, the Earth and the satellite. Nevertheless it should be refined with later observations from ground sta...

Exponentially growing melanoma cells of the line FME were incubated with hematoporphyrin derivative (HpD) for 1 and 18 h and subsequently exposed to light in the presence of HpD. Quantitative changes in the expression of the melanoma-associated surface antigen p250 recognized by the monoclonal antibody 9.2.27 were studied by flow cytometry. Treatment with HpD and light resulted in no immediate ...

Second derivative general linear methods (SGLMs) as an extension of general linear methods (GLMs) have been introduced to improve the stability and accuracy properties of GLMs. The coefficients of SGLMs are given by six matrices, instead of four matrices for GLMs, which are obtained by solving nonlinear systems of order and usually Runge–Kutta stability conditions. In this paper, we introduce a...

Production optimization involves the determination of optimum well controls to maximize an objective function such as cumulative oil production or net present value. In practice, this problem additionally requires the satisfaction of physical and economic constraints. Thus the overall problem represents a challenging nonlinearly constrained optimization. This work entails a comparative study of...

In this survey article we give the basic description of the interpolation based derivative free optimization methods and their variants. We review the recent contributions dealing with the maintaining the geometry of the interpolation set, the management of the trust region radius and the stopping criteria. Derivative free algorithms developed for problems with some structure like for partially...

In control of distributed parameter systems the piezoelectric actuators are of common use. The topology optimization of a multiphysic model in piezoelectricity is considered. The topological derivative of a tracking-type shape functional is derived in its closed form for the purpose of shape optimization of piezoelectric actuators. The optimum design procedure is applied to a micromechanism whi...

We present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dial grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points xi. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that sp...