Nonlinearly Constrained Optimization Using Heuristic Penalty Methods and Asynchronous Parallel Generating Set Search

Asynchronous Parallel Generating Set Search for Linearly Constrained Optimization

We describe an asynchronous parallel derivative-free algorithm for linearly constrained optimization. Generating set search (GSS) is the basis of our method. At each iteration, a GSS algorithm computes a set of search directions and corresponding trial points and then evaluates the objective function value at each trial point. Asynchronous versions of the algorithm have been developed in the un...

Stationarity Results for Generating Set Search for Linearly Constrained Optimization

We derive new stationarity results for derivative-free, generating set search methods for linearly constrained optimization. We show that a particular measure of stationarity is of the same order as the step length at an identifiable subset of the iterations. Thus, even in the absence of explicit knowledge of the derivatives of the objective function, we still have information about stationarit...

Implementing Generating Set Search Methods for Linearly Constrained Minimization

We discuss an implementation of a derivative-free generating set search method for linearly constrained minimization with no assumption of nondegeneracy placed on the constraints. The convergence guarantees for generating set search methods require that the set of search directions possesses certain geometrical properties that allow it to approximate the feasible region near the current iterate...

Penalty and Barrier Methods for Constrained Optimization

Asynchronous Parallel Pattern Search for Nonlinear Optimization

We introduce a new asynchronous parallel pattern search (APPS). Parallel pattern search can be quite useful for engineering optimization problems characterized by a small number of variables (say, fifty or less) and by objective functions that are expensive to evaluate, such as those defined by complex simulations that can take anywhere from a few seconds to many hours to run. The target platfo...