On the properties of positive spanning sets and positive bases

DOI10.1007/s11081-015-9286-xzbMath1364.90364OpenAlexW1692754621MaRDI QIDQ2357977

Rommel G. Regis

Publication date: 20 June 2017

Published in: Optimization and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11081-015-9286-x

zbMATH Keywords

derivative-free optimizationdirect searchpositive basispositive spanning setlinear equivalencepositive independence

Mathematics Subject Classification ID

Derivative-free methods and methods using generalized derivatives (90C56) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (13)

Learning of Structurally Unambiguous Probabilistic Grammars ⋮ On the cardinality of positively linearly independent sets ⋮ A topological approach to inferring the intrinsic dimension of convex sensing data ⋮ A discussion on variational analysis in derivative-free optimization ⋮ Using orthogonally structured positive bases for constructing positive \(k\)-spanning sets with cosine measure guarantees ⋮ A deterministic algorithm to compute the cosine measure of a finite positive spanning set ⋮ Uniform simplex of an arbitrary orientation ⋮ Nicely structured positive bases with maximal cosine measure ⋮ On the properties of the cosine measure and the uniform angle subspace ⋮ On the Convergence to Stationary Points of Deterministic and Randomized Feasible Descent Directions Methods ⋮ Derivative-free optimization methods ⋮ Positive bases with maximal cosine measure ⋮ The regularized feasible directions method for nonconvex optimization

Uses Software

• PSwarm
• IMFIL
• OrthoMADS

Cites Work

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• A short proof on the cardinality of maximal positive bases
• On the Convergence of Grid-Based Methods for Unconstrained Optimization
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• Implicit Filtering
• Reducing the Number of Function Evaluations in Mesh Adaptive Direct Search Algorithms
• PSwarm: a hybrid solver for linearly constrained global derivative-free optimization
• Using simplex gradients of nonsmooth functions in direct search methods
• OrthoMADS: A Deterministic MADS Instance with Orthogonal Directions
• Introduction to Derivative-Free Optimization
• An Algorithm for Identifying the Frame of a Pointed Finite Conical Hull
• Pattern Search Methods for User-Provided Points: Application to Molecular Geometry Problems
• Pattern Search Algorithms for Bound Constrained Minimization
• Mesh Adaptive Direct Search Algorithms for Constrained Optimization
• Unique Minimal Representations with Positive Bases
• A New Proof of the Bonnice-Klee Theorem
• Diagrams for Positive Bases
• Positive Bases for Linear Spaces
• Theory of Positive Linear Dependence
• New algorithm for the conical combination representation problem of a vector
• Positive bases in numerical optimization

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