caa a22 4500 475750381 CHVBK 20180406123521.0 cr unu---uuuuu 170329e20000701xx s 000 0 eng 10.1023/A:1008714607737 doi (NATIONALLICENCE)springer-10.1023/A:1008714607737 Convergence of the Gradient Projection Method for Generalized Convex Minimization [Elektronische Daten] [Changyu Wang, Naihua Xiu] This paper develops convergence theory of the gradient projection method by Calamai and Moré (Math. Programming, vol. 39, 93-116, 1987) which, for minimizing a continuously differentiable optimization problem min{f(x) : x ε Ω} where Ω is a nonempty closed convex set, generates a sequence xk+1 = P(xk − αk ∇ f(xk)) where the stepsize αk > 0 is chosen suitably. It is shown that, when f(x) is a pseudo-convex (quasi-convex) function, this method has strong convergence results: either xk → x* and x* is a minimizer (stationary point); or ‖xk‖ → ∞ arg min{f(x) : x ε Ω} = ∅, and f(xk) ↓ inf{f(x) : x ε Ω}. Kluwer Academic Publishers, 2000 generalized convex minimization nationallicence gradient projection method nationallicence global convergence nationallicence Wang Changyu aut Xiu Naihua aut Computational Optimization and Applications Kluwer Academic Publishers 16/2(2000-07-01), 111-120 0926-6003 16:2<111 2000 16 10589 https://doi.org/10.1023/A:1008714607737 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008714607737 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Changyu aut NATIONALLICENCE 700 1- Xiu Naihua aut NATIONALLICENCE 773 0- Computational Optimization and Applications Kluwer Academic Publishers 16/2(2000-07-01), 111-120 0926-6003 16:2<111 2000 16 10589 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer