Quadratic approximations to the objective function provide a way of estimating first and second derivatives in iterative algorithms for unconstrained minimization. Therefore we address the construction of suitable quadratic models Q by interpolating values of the objective function F . On a typical iteration, the objective function is calculated at the point that minimizes the current quadratic...

UOBYQA is a new algorithm for general unconstrained optimization calculations, that takes account of the curvature of the objective function, F say, by forming quadratic models by interpolation. Therefore, because no rst derivatives are required, each model is deened by 1 2 (n+1)(n+2) values of F, where n is the number of variables, and the interpolation points must have the property that no no...

This paper studies the H1 Sobolev seminorm of quadratic functions. The research is motivated by the least-norm interpolation that is widely used in derivative-free optimization. We express the H1 seminorm of a quadratic function explicitly in terms of the Hessian and the gradient when the underlying domain is a ball. The seminorm gives new insights into least-norm interpolation. It clarifies th...

Some highly successful algorithms for unconstrained minimization without derivatives construct changes to the variables by applying trust region methods to quadratic approximations to the objective function F (x), x∈R. A quadratic model has (n+1)(n+2)/2 independent parameters, but each new model may interpolate only 2n+1 values of F , for instance. The symmetric Broyden method takes up the rema...

Some highly successful algorithms for unconstrained minimization without derivatives construct changes to the variables by applying trust region methods to quadratic approximations to the objective function F (x), x∈R. A quadratic model has (n+1)(n+2)/2 independent parameters, but each new model may interpolate only 2n+1 values of F , for instance. The symmetric Broyden method takes up the rema...

This paper proposes an optimized LSB matching steganography based on Fisher Information. The embedding algorithm is designed to solve the optimization problem, in which Fisher information is the objective function and embedding transferring probabilities are variables to be optimized. Fisher information is the quadratic function of the embedding transferring probabilities, and the coefficients ...

We suggest a branch and bound algorithm for solving continuous optimization problems where a (generally nonconvex) objective function is to be minimized under nonconvex inequality constraints which satisfy some specific solvability assumptions. The assumptions hold for some special cases of nonconvex quadratic optimization problems. We show how the algorithm can be applied to the problem of min...

A direct approach for the design of 2-D nonseparable diamond-shaped filter banks is proposed. The design goal is achieved by formulating the problem as an iterative quadratic programming problem in which the perfect reconstruction condition is incorporated in a weighted quadratic objective function. Satisfactory stopband attenuation is assured by imposing a set of constraints on the amplitude r...

This paper studies forecasts when the forecast loss function is asymmetric, using Australian unemployment rates as an example. We focus on simple univariate models including autoregressive models and self-exciting threshold autoregressive models and we employ the same asymmetric quadratic loss function that is used for forecast evaluation at the model selection, model estimation and forecast co...

In this paper, a new method for gray-scale image and color zooming algorithm based on their local information is offered. In the proposed method, the unknown values of the new pixels on the image are computed by Moving Least Square (MLS) approximation based on both the quadratic spline and Gaussian-type weight functions. The numerical results showed that this method is more preferable to biline...