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A family of gradient projection algorithms and their convergence properties

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Názov: A family of gradient projection algorithms and their convergence properties
Autori: Xue, Guoliang
Informácie o vydavateľovi: Chinese Academy of Sciences, Institute of Applied Mathematics, Beijing
Predmety: Convex programming, Numerical mathematical programming methods, Numerical methods based on nonlinear programming, Nonlinear programming, Methods of reduced gradient type, linearly constrained nonlinear programming, Kuhn-Tucker point, gradient projection algorithms, pseudoconvex
Popis: Summary: We provide a family of gradient projection algorithms for solving linearly constrained nonlinear programming problems and show that each accumulation point of the sequence constructed by any algorithm in the family is a Kuhn-Tucker point. Furthermore, when the objective function f(x) is pseudoconvex, it is shown that (1) \(\{\) f(x k)\(\}\downarrow \inf \{f(x)| x\in R\};\) (2) R *\(\neq \emptyset\) if and only if \(\{\) x \(k\}\) is a bounded sequence; (3) if R *\(\neq \emptyset\) then \(\{\) x \(k\}\) converges to some x *\(\in R\) *, where R and R * denote the sets of feasible points and optimal points respectively, and \(\{\) x \(k\}\) is the sequence constructed by the algorithm. Some known algorithms are shown to be special cases.
Druh dokumentu: Article
Popis súboru: application/xml
Prístupová URL adresa: https://zbmath.org/4043629
Prístupové číslo: edsair.c2b0b933574d..f99d6191bab235a8f2816a83eef09ba2
Databáza: OpenAIRE
Popis
Abstrakt:Summary: We provide a family of gradient projection algorithms for solving linearly constrained nonlinear programming problems and show that each accumulation point of the sequence constructed by any algorithm in the family is a Kuhn-Tucker point. Furthermore, when the objective function f(x) is pseudoconvex, it is shown that (1) \(\{\) f(x k)\(\}\downarrow \inf \{f(x)| x\in R\};\) (2) R *\(\neq \emptyset\) if and only if \(\{\) x \(k\}\) is a bounded sequence; (3) if R *\(\neq \emptyset\) then \(\{\) x \(k\}\) converges to some x *\(\in R\) *, where R and R * denote the sets of feasible points and optimal points respectively, and \(\{\) x \(k\}\) is the sequence constructed by the algorithm. Some known algorithms are shown to be special cases.