We consider the problem of minimizing a continuously di erentiable function of several variables subject to simple bound and general nonlinear inequality constraints, where some of the variables are restricted to take integer values. We assume that the rst order derivatives of the objective and constraint functions can be neither calculated nor approximated explicitly. This class … Read more
Many derivative-free methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty-like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated by the difficulties of improving feasibility. … Read more
We analyze globally convergent derivative-free trust region algorithms relying on radial basis function interpolation models. Our results extend the recent work of Conn, Scheinberg, and Vicente to fully linear models that have a nonlinear term. We characterize the types of radial basis functions that fit in our analysis and thus show global convergence to first-order … Read more
Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from less points than there are basis components. Often, in practical applications, the contribution of the problem variables to the objective function is such that many pairwise correlations … Read more
Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from less points than there are basis components. Often, in practical applications, the contribution of the problem variables to the objective function is such that many pairwise correlations … Read more
We propose a derivative-free algorithm for optimizing computationally expensive functions with computational error. The algorithm is based on the trust region regression method by Conn, Scheinberg, and Vicente [4], but uses weighted regression to obtain more accurate model functions at each trust region iteration. A heuristic weighting scheme is proposed which simultaneously handles i) differing … Read more
We consider iterative trust region algorithms for the unconstrained minimization of an objective function F(x) of n variables, when F is differentiable but no derivatives are available, and when each model of F is a linear or quadratic polynomial. The models interpolate F at n+1 points, which defines them uniquely when they are linear polynomials. … Read more
We consider the problem of minimizing a continuously differentiable function of several variables subject to simple bound constraints where some of the variables are restricted to take integer values. We assume that the first order derivatives of the objective function can be neither calculated nor approximated explicitly. This class of mixed integer nonlinear optimization problems … Read more
The (optimal) function/gradient evaluations worst-case complexity analysis available for the Adaptive Regularizations algorithms with Cubics (ARC) for nonconvex smooth unconstrained optimization is extended to finite-difference versions of this algorithm, yielding complexity bounds for first-order and derivative free methods applied on the same problem class. A comparison with the results obtained for derivative-free methods by Vicente … Read more
Research in optimization algorithm design is often accompanied by benchmarking a new al- gorithm. Some benchmarking is done as a proof-of-concept, by demonstrating the new algorithm works on a small number of dicult test problems. Alternately, some benchmarking is done in order to demonstrate that the new algorithm in someway out-performs previous methods. In this … Read more