APPLICATION OF PROJECTION ALGORITHMS TO DIFFERENTIAL EQUATIONS: BOUNDARY VALUE PROBLEMS

DOI10.1017/S1446181118000391zbMath1410.65269arXiv1705.11032OpenAlexW2619563255MaRDI QIDQ3122033

Bishnu P. Lamichhane, Brailey Sims, Scott B. Lindstrom

Publication date: 20 March 2019

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.11032

zbMATH Keywords

Newton's methodhypersurfaceboundary value problemDouglas-Rachford method

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Monotone operators and generalizations (47H05) Nonlinear boundary value problems for ordinary differential equations (34B15) Programming in abstract spaces (90C48) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (7)

Circumcentering reflection methods for nonconvex feasibility problems ⋮ A product space reformulation with reduced dimension for splitting algorithms ⋮ Computable centering methods for spiraling algorithms and their duals, with motivations from the theory of Lyapunov functions ⋮ The Douglas-Rachford algorithm for convex and nonconvex feasibility problems ⋮ The Douglas-Rachford algorithm for a hyperplane and a doubleton ⋮ Comparing Averaged Relaxed Cutters and Projection Methods: Theory and Examples ⋮ SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD

Cites Work

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• The Douglas-Rachford algorithm for the case of the sphere and the line
• Local linear convergence for alternating and averaged nonconvex projections
• Solving graph coloring problems with the Douglas-Rachford algorithm
• Dynamics of the Douglas-Rachford method for ellipses and \(p\)-spheres
• A cyclic Douglas-Rachford iteration scheme
• Global convergence of a non-convex Douglas-Rachford iteration
• Linear convergence of the Douglas–Rachford method for two closed sets
• The Douglas–Rachford Algorithm in the Absence of Convexity
• DOUGLAS–RACHFORD FEASIBILITY METHODS FOR MATRIX COMPLETION PROBLEMS
• On Weak Convergence of the Douglas–Rachford Method
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Decomposition through formalization in a product space
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD
• Linear Convergence of Projection Algorithms
• Searching with iterated maps
• Convex analysis and monotone operator theory in Hilbert spaces

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