ADMM for monotone operators: convergence analysis and rates
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DOI: 10.1007/s10444-018-9619-3
Abstract: We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We show… read more here.
Keywords: admm monotone; monotone operators; monotone; convergence analysis ... See more keywords
Symbolic Computation with Monotone Operators
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DOI: 10.1007/s11228-017-0418-7
Abstract: We consider a class of monotone operators which are appropriate for symbolic representation and manipulation within a computer algebra system. Various structural properties of the class (e.g., closure under taking inverses, resolvents) are investigated as… read more here.
Keywords: symbolic computation; computation; class; monotone operators ... See more keywords
Existence and uniqueness of fixed points for monotone operators in partially ordered Banach spaces and applications
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DOI: 10.1007/s11784-021-00853-5
Abstract: In this paper, we employ partial order method, cone theory, and the techniques of measure of weak noncompactness to prove several new theorems on the existence and the uniqueness of fixed points or coupled fixed… read more here.
Keywords: points monotone; fixed points; monotone operators; uniqueness fixed ... See more keywords
Forward–backward splitting algorithm for fixed point problems and zeros of the sum of monotone operators
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DOI: 10.1007/s40065-018-0236-2
Abstract: In this paper, we construct a forward–backward splitting algorithm for approximating a zero of the sum of an $$\alpha $$ α -inverse strongly monotone operator and a maximal monotone operator. The strong convergence theorem is… read more here.
Keywords: forward backward; monotone; backward splitting; monotone operators ... See more keywords
Strong convergence theorems by hybrid and shrinking projection methods for sums of two monotone operators
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DOI: 10.1186/s13660-017-1338-7
Abstract: In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong… read more here.
Keywords: two monotone; shrinking projection; monotone operators; monotone ... See more keywords