A modeling language for mathematical programming
Management Science
Lipschitzian optimization without the Lipschitz constant
Journal of Optimization Theory and Applications
Genetic algorithms + data structures = evolution programs (3rd ed.)
Genetic algorithms + data structures = evolution programs (3rd ed.)
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
An updated set of basic linear algebra subprograms (BLAS)
ACM Transactions on Mathematical Software (TOMS)
Pattern Search Methods for Linearly Constrained Minimization
SIAM Journal on Optimization
On Numerical Solution of the Maximum Volume Ellipsoid Problem
SIAM Journal on Optimization
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
A Study of Global Optimization Using Particle Swarms
Journal of Global Optimization
Linearly Constrained Global Optimization and Stochastic Differential Equations
Journal of Global Optimization
A particle swarm pattern search method for bound constrained global optimization
Journal of Global Optimization
Stationarity Results for Generating Set Search for Linearly Constrained Optimization
SIAM Journal on Optimization
Pattern search in the presence of degenerate linear constraints
Optimization Methods & Software
Introduction to Derivative-Free Optimization
Introduction to Derivative-Free Optimization
Benchmarking Derivative-Free Optimization Algorithms
SIAM Journal on Optimization
A study of particle swarm optimization particle trajectories
Information Sciences: an International Journal
Stochastic ranking for constrained evolutionary optimization
IEEE Transactions on Evolutionary Computation
Optimization Methods & Software - GLOBAL OPTIMIZATION
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PSwarm was developed originally for the global optimization of functions without derivatives and where the variables are within upper and lower bounds. The underlying algorithm used is a pattern search method, or more specifically, a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the (optional) search step of coordinate search, the algorithm incorporates a particle swarm scheme for dissemination of points in the feasible region, equipping the overall method with the capability of finding a global minimizer. Our extensive numerical experiments showed that the resulting algorithm is highly competitive with other global optimization methods based only on function values. PSwarm is extended in this paper to handle general linear constraints. The poll step now incorporates positive generators for the tangent cone of the approximated active constraints, including a provision for the degenerate case. The search step has also been adapted accordingly. In particular, the initial population for particle swarm used in the search step is computed by first inscribing an ellipsoid of maximum volume to the feasible set. We have again compared PSwarm with other solvers (including some designed for global optimization) and the results confirm its competitiveness in terms of efficiency and robustness.