`` Direct Search'' Solution of Numerical and Statistical Problems
Journal of the ACM (JACM)
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Frame based methods for unconstrained optimization
Journal of Optimization Theory and Applications
On the Convergence of Grid-Based Methods for Unconstrained Optimization
SIAM Journal on Optimization
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
Pattern Search Algorithms for Bound Constrained Minimization
SIAM Journal on Optimization
Pattern Search Methods for Linearly Constrained Minimization
SIAM Journal on Optimization
Positive Bases in Numerical Optimization
Computational Optimization and Applications
Analysis of Generalized Pattern Searches
SIAM Journal on Optimization
RANK ORDERING AND POSITIVE BASES IN PATTERN SEARCH ALGORITHMS
RANK ORDERING AND POSITIVE BASES IN PATTERN SEARCH ALGORITHMS
Mesh Adaptive Direct Search Algorithms for Constrained Optimization
SIAM Journal on Optimization
Stationarity Results for Generating Set Search for Linearly Constrained Optimization
SIAM Journal on Optimization
Using Sampling and Simplex Derivatives in Pattern Search Methods
SIAM Journal on Optimization
Implementing Generating Set Search Methods for Linearly Constrained Minimization
SIAM Journal on Scientific Computing
Benchmarking Derivative-Free Optimization Algorithms
SIAM Journal on Optimization
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Positive basis is an important concept in direct search methods. Although any positive basis can ensure the convergence in theory, the maximum positive bases are often used to construct direct search algorithms. In this paper, two direct search methods for computational expensive functions are proposed based on the minimal positive bases. The Coope---Price's frame-based direct search framework is employed to insure convergence. PRP+ method and a recently developed descent conjugate gradient method are employed respectively to accelerate convergence. The data profiles and the performance profiles of the numerical experiments show that the proposed methods are effective for computational expensive functions.