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- Difference-map_algorithm abstract "The difference-map algorithm is a search algorithm for general constraint satisfaction problems. It is a meta-algorithm in the sense that it is built from more basic algorithms that perform projections onto constraint sets. From a mathematical perspective, the difference-map algorithm is a dynamical system based on a mapping of Euclidean space. Solutions are encoded as fixed points of the mapping.Although originally conceived as a general method for solving the phase problem, the difference-map algorithm has been used for the boolean satisfiability problem, protein structure prediction, Ramsey numbers, diophantine equations, and Sudoku, as well as sphere- and disk-packing problems. Since these applications include NP-complete problems, the scope of the difference map is that of an incomplete algorithm. Whereas incomplete algorithms can efficiently verify solutions (once a candidate is found), they cannot prove that a solution does not exist.The difference-map algorithm is a generalization of two iterative methods: Fienup's Hybrid input output (HIO) algorithm for phase retrieval and the Douglas-Rachford algorithm for convex optimization. Iterative methods, in general, have a long history in phase retrieval and convex optimization. The use of this style of algorithm for hard, non-convex problems is a more recent development.".
- Difference-map_algorithm thumbnail Iterations_0,_100,_200,_300_and_400_in_difference-map_reconstruction_of_grayscale_image_from_Fourier_transform_modulus.png?width=300.
- Difference-map_algorithm wikiPageID "10145406".
- Difference-map_algorithm wikiPageLength "12790".
- Difference-map_algorithm wikiPageOutDegree "39".
- Difference-map_algorithm wikiPageRevisionID "684932359".
- Difference-map_algorithm wikiPageWikiLink 2-satisfiability.
- Difference-map_algorithm wikiPageWikiLink Absolute_value.
- Difference-map_algorithm wikiPageWikiLink Attractor.
- Difference-map_algorithm wikiPageWikiLink Boolean_satisfiability_problem.
- Difference-map_algorithm wikiPageWikiLink Category:Constraint_programming.
- Difference-map_algorithm wikiPageWikiLink Category:Search_algorithms.
- Difference-map_algorithm wikiPageWikiLink Chaos_theory.
- Difference-map_algorithm wikiPageWikiLink Coherence_(physics).
- Difference-map_algorithm wikiPageWikiLink Constraint_(mathematics).
- Difference-map_algorithm wikiPageWikiLink Constraint_satisfaction.
- Difference-map_algorithm wikiPageWikiLink Convex_optimization.
- Difference-map_algorithm wikiPageWikiLink Diophantine_equation.
- Difference-map_algorithm wikiPageWikiLink Discrete_Fourier_transform.
- Difference-map_algorithm wikiPageWikiLink Douglas-Rachford_algorithm.
- Difference-map_algorithm wikiPageWikiLink Dynamical_system.
- Difference-map_algorithm wikiPageWikiLink Euclidean_space.
- Difference-map_algorithm wikiPageWikiLink File:Diffraction_data.png.
- Difference-map_algorithm wikiPageWikiLink File:Iterations_0,_100,_200,_300_and_400_in_difference-map_reconstruction_of_grayscale_image_from_Fourier_transform_modulus.png.
- Difference-map_algorithm wikiPageWikiLink File:Time_series_of_norm_of_difference-map_increment_Δ,_during_solving_random_3-SAT_instance.png.
- Difference-map_algorithm wikiPageWikiLink Fixed_point_(mathematics).
- Difference-map_algorithm wikiPageWikiLink Fraunhofer_diffraction.
- Difference-map_algorithm wikiPageWikiLink Hybrid_input_output_(HIO)_algorithm_for_phase_retrieval.
- Difference-map_algorithm wikiPageWikiLink Incomplete_algorithm.
- Difference-map_algorithm wikiPageWikiLink Intersection_(set_theory).
- Difference-map_algorithm wikiPageWikiLink Iterative_method.
- Difference-map_algorithm wikiPageWikiLink Literal_(mathematical_logic).
- Difference-map_algorithm wikiPageWikiLink Local_search_(optimization).
- Difference-map_algorithm wikiPageWikiLink Map_(mathematics).
- Difference-map_algorithm wikiPageWikiLink Metaheuristic.
- Difference-map_algorithm wikiPageWikiLink NP-completeness.
- Difference-map_algorithm wikiPageWikiLink Phase_problem.
- Difference-map_algorithm wikiPageWikiLink Projection_(linear_algebra).
- Difference-map_algorithm wikiPageWikiLink Protein_structure_prediction.
- Difference-map_algorithm wikiPageWikiLink Ramseys_theorem.
- Difference-map_algorithm wikiPageWikiLink Search_algorithm.
- Difference-map_algorithm wikiPageWikiLink Sudoku.
- Difference-map_algorithm wikiPageWikiLink Support_(mathematics).
- Difference-map_algorithm wikiPageWikiLink Unitary_transformation.
- Difference-map_algorithm wikiPageWikiLinkText "Difference-map algorithm".
- Difference-map_algorithm wikiPageWikiLinkText "difference-map algorithm".
- Difference-map_algorithm wikiPageUsesTemplate Template:Reflist.
- Difference-map_algorithm subject Category:Constraint_programming.
- Difference-map_algorithm subject Category:Search_algorithms.
- Difference-map_algorithm hypernym Algorithm.
- Difference-map_algorithm type Software.
- Difference-map_algorithm type Algorithm.
- Difference-map_algorithm comment "The difference-map algorithm is a search algorithm for general constraint satisfaction problems. It is a meta-algorithm in the sense that it is built from more basic algorithms that perform projections onto constraint sets. From a mathematical perspective, the difference-map algorithm is a dynamical system based on a mapping of Euclidean space.".
- Difference-map_algorithm label "Difference-map algorithm".
- Difference-map_algorithm sameAs Q5275267.
- Difference-map_algorithm sameAs m.02q38wh.
- Difference-map_algorithm sameAs Q5275267.
- Difference-map_algorithm wasDerivedFrom Difference-map_algorithm?oldid=684932359.
- Difference-map_algorithm depiction Iterations_0,_100,_200,_300_and_400_in_difference-map_reconstruction_of_grayscale_image_from_Fourier_transform_modulus.png.
- Difference-map_algorithm isPrimaryTopicOf Difference-map_algorithm.