Projected gradient methods for linearly constrained problems
Mathematical Programming: Series A and B
On the identification of active constraints
SIAM Journal on Numerical Analysis
On identification of active constraints II: the nonconvex case
SIAM Journal on Numerical Analysis
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
On the Accurate Identification of Active Constraints
SIAM Journal on Optimization
Pattern Search Methods for Linearly Constrained Minimization
SIAM Journal on Optimization
Double Description Method Revisited
Selected papers from the 8th Franco-Japanese and 4th Franco-Chinese Conference on Combinatorics and Computer Science
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
Active Set Identification in Nonlinear Programming
SIAM Journal on Optimization
Stationarity Results for Generating Set Search for Linearly Constrained Optimization
SIAM Journal on Optimization
Implementing Generating Set Search Methods for Linearly Constrained Minimization
SIAM Journal on Scientific Computing
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We consider active set identification for linearly constrained optimization problems in the absence of explicit information about the derivative of the objective function. We begin by presenting some general results on active set identification that are not tied to any particular algorithm. These general results are sufficiently strong that, given a sequence of iterates converging to a Karush-Kuhn-Tucker point, it is possible to identify binding constraints for which there are nonzero multipliers. We then focus on generating set search methods, a class of derivative-free direct search methods. We discuss why these general results, which are posed in terms of the direction of steepest descent, apply to generating set search, even though these methods do not have explicit recourse to derivatives. Nevertheless, there is a clearly identifiable subsequence of iterations at which we can reliably estimate the set of constraints that are binding at a solution. We discuss how active set estimation can be used to accelerate generating set search methods and illustrate the appreciable improvement that can result using several examples from the CUTEr test suite. We also introduce two algorithmic refinements for generating set search methods. The first expands the subsequence of iterations at which we can make inferences about stationarity. The second is a more flexible step acceptance criterion.