Generalized Pattern Search methods for a class of nonsmooth optimization problems with structure
Journal of Computational and Applied Mathematics
Active Set Identification for Linearly Constrained Minimization Without Explicit Derivatives
SIAM Journal on Optimization
A Low-rate Data Transfer Technique for Compressed Voice Channels
Journal of Signal Processing Systems
Controlling variability in split-merge systems
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
| Hi-index | 0.00 |
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. In the hard case, the calculation of the search directions corresponds to finding the extreme rays of a cone with a degenerate vertex at the origin, a difficult problem. We discuss here how state-of-the-art computational geometry methods make it tractable to solve this problem in connection with generating set search. We also discuss a number of other practical issues of implementation, such as the careful treatment of equality constraints and the desirability of augmenting the set of search directions beyond the theoretically minimal set. We illustrate the behavior of the implementation on several problems from the CUTEr test suite. We have found it to be successful on problems with several hundred variables and linear constraints.