In this paper, we develop a new hybrid conjugate gradient method that inherits the features of the Liu and Storey (LS), Hestenes and Stiefel (HS), Dai and Yuan (DY) and Conjugate Descent (CD) conjugate gradient methods. The new method generates a descent direction independently of any line search and possesses good convergence properties under the strong Wolfe line search conditions. Numerical results show that the proposed method is robust and efficient.
We consider digital input-constrained adaptive and non-adaptive output feedback control for a class of nonlinear systems which arise as models for controlled exothermic chemical reactors. Our objective is set-point control of the temperature of the reaction, with pre-specified asymptotic tracking accuracy set by the designer. Our approach is based on -tracking controllers, but in a context of piecewise constant sampled-data output feedbacks and possibly adapted sampling periods. The approach does not require any knowledge of the systems parameters, does not invoke an internal model, is simple in its design, copes with noise corrupted output measurements, and requires only a feasibility assumption in terms of the reference temperature and the input constraints.
This article presents a modified quadratic hybridization of the Polak–Ribiere–Polyak and Fletcher–Reeves conjugate gradient method for solving unconstrained optimization problems. Global convergence, with the strong Wolfe line search conditions, of the proposed quadratic hybrid conjugate gradient method is established. We also report some numerical results to show the competitiveness of the new hybrid method.
Let C be a nonempty closed convex subset of a real Hilbert space H and $$T: C\rightarrow CB(H)$$
T
:
C
→
C
B
(
H
)
be a multi-valued Lipschitz pseudocontractive nonself mapping. A Halpern–Ishikawa type iterative scheme is constructed and a strong convergence result of this scheme to a fixed point of T is proved under appropriate conditions. Moreover, an iterative method for approximating a fixed point of a k-strictly pseudocontractive mapping $$T: C\rightarrow Prox(H)$$
T
:
C
→
P
r
o
x
(
H
)
is constructed and a strong convergence of the method is obtained without end point condition. The results obtained in this paper improve and extend known results in the literature.
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