A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set

DOI10.1007/s10898-017-0510-4zbMath1377.65067OpenAlexW2594099471MaRDI QIDQ1675572

Rudolf Scitovski

Publication date: 2 November 2017

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10898-017-0510-4

zbMATH Keywords

DIRECTglobal optimizationsymmetric functionnumerical experimentimage segmentationcenter-based clusteringLipschitz continuous functionDISIMPLSymDIRECT

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Nonconvex programming, global optimization (90C26) Derivative-free methods and methods using generalized derivatives (90C56) Symmetric functions and generalizations (05E05) Combinatorial optimization (90C27) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (4)

Application of the \texttt{DIRECT} algorithm to searching for an optimal \(k\)-partition of the set \(\mathcal {A}\subset \mathbb {R}^n\) and its application to the multiple circle detection problem ⋮ Searching for an Optimal Partition of Incomplete Data with Application in Modeling Energy Efficiency of Public Buildings ⋮ Incremental method for multiple line detection problem -- iterative reweighted approach ⋮ The adaptation of the \(k\)-means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm.

Uses Software

• LGO
• DIRECT
• flexclust
• SymDIRECT
• PRMLT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A modification of the \texttt{DIRECT} method for Lipschitz global optimization for a symmetric function
• Lipschitz global optimization methods in control problems
• Lipschitz gradients for global optimization in a one-point-based partitioning scheme
• Univariate geometric Lipschitz global optimization algorithms
• An approach to cluster separability in a partition
• A modified DIviding RECTangles algorithm for a problem in astrophysics
• The big cube small cube solution method for multidimensional facility location problems
• Global optimization. Scientific and engineering case studies
• A review of recent advances in global optimization
• Additive scaling and the \texttt{DIRECT} algorithm
• A generalized Weiszfeld method for the multi-facility location problem
• A toolbox for \(K\)-centroids cluster analysis
• A univariate global search working with a set of Lipschitz constants for the first derivative
• Lipschitzian optimization without the Lipschitz constant
• Global optimization with non-convex constraints. Sequential and parallel algorithms
• Index branch-and-bound algorithm for Lipschitz univariate global optimization with multiextremal constraints
• Global optimization in action. Continuous and Lipschitz optimization: algorithms, implementations and applications
• One-dimensional center-based l 1-clustering method
• Simplicial Lipschitz optimization without the Lipschitz constant
• Globally-biased disimpl algorithm for expensive global optimization
• Simplicial Global Optimization
• Multiple ellipse fitting by center-based clustering
• Unsupervised Classification
• Complete search in continuous global optimization and constraint satisfaction
• An algorithm for minimizing clustering functions
• Global Search Based on Efficient Diagonal Partitions and a Set of Lipschitz Constants
• Computer vision. Algorithms and applications
• Advantages of simplicial partitioning for Lipschitz optimization problems with linear constraints

This page was built for publication: A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set