Geometry of interpolation sets in derivative free optimization

Geometry of interpolation sets in derivative free optimization

We consider derivative free methods based on sampling approaches for nonlinear optimization problems where derivatives of the objective function are not available and cannot be directly approximated. We show how the bounds on the error between an interpolating polynomial and the true function can be used in the convergence theory of derivative free sampling methods. These bounds involve a const...

Geometry of Sample Sets in Derivative-free Optimization: Polynomial Regression and Underdetermined Interpolation

In recent years, there has been a considerable amount of work on the development of numerical methods for derivative-free optimization problems. Some of this work relies on the management of the geometry of sets of sampling points for function evaluation and model building. In this paper, we continue the work developed in [8] for complete or determined interpolation models (when the number of i...

Derivative Free Optimization

Derivative-Free Optimization

In many engineering applications it is common to find optimization problems where the cost function and/or constraints require complex simulations. Though it is often, but not always, theoretically possible in these cases to extract derivative information efficiently, the associated implementation procedures are typically non-trivial and time-consuming (e.g., adjoint-based methodologies). Deriv...

Derivative free optimization method

Derivative free optimization (DFO) methods are typically designed to solve optimization problems whose objective function is computed by a “black box”; hence, the gradient computation is unavailable. Each call to the “black box” is often expensive, so estimating derivatives by finite differences may be prohibitively costly. Finally, the objective function value may be computed with some noise, ...