The convergence properties of the Fletcher-Reeves method for unconstrained optimization are further studied with the technique
of generalized line search. Two conditions are given which guarantee the global convergence of the Fletcher-Reeves method
using generalized Wolfe line searches or generalized Arjimo line searches, whereas an example is constructed showing that
the conditions cannot be relaxed in certain senses.
Project supported by the National Natural Science Foundation of China (Grant No. 19801033). 相似文献
A tetraphenylethene (TPE) derivative substituted with a sulfonyl‐based naphthalimide unit ( TPE‐Np ) was designed and synthesized. Its optical properties in solution and in the solid state were investigated. Photophysical properties indicated that the target molecule, TPE‐Np , possessed aggregation‐induced emission (AIE) behavior, although the linkage between TPE and the naphthalimide unit was nonconjugated. Additionally, it exhibited an unexpected, highly reversible mechanochromism in the solid state, which was attributed to the change in manner of aggregation between crystalline and amorphous states. On the other hand, a solution of TPE‐Np in a mixture of dimethyl sulfoxide/phosphate‐buffered saline was capable of efficiently distinguishing glutathione (GSH) from cysteine and homocysteine in the presence of cetyltrimethylammonium bromide. Furthermore, the strategy of using poly(ethylene glycol)–polyethylenimine (PEG‐PEI) nanogel as a carrier to cross‐link TPE‐Np to obtain a water‐soluble PEG‐PEI/ TPE‐Np nanoprobe greatly improved the biocompatibility, and this nanoprobe could be successfully applied in the visualization of GSH levels in living cells. 相似文献
In this paper, we address the problem of the bifurcation control of a delayed fractional-order dual model of congestion control algorithms. A fractional-order proportional–derivative (PD) feedback controller is designed to control the bifurcation generated by the delayed fractional-order congestion control model. By choosing the communication delay as the bifurcation parameter, the issues of the stability and bifurcations for the controlled fractional-order model are studied. Applying the stability theorem of fractional-order systems, we obtain some conditions for the stability of the equilibrium and the Hopf bifurcation. Additionally, the critical value of time delay is figured out, where a Hopf bifurcation occurs and a family of oscillations bifurcate from the equilibrium. It is also shown that the onset of the bifurcation can be postponed or advanced by selecting proper control parameters in the fractional-order PD controller. Finally, numerical simulations are given to validate the main results and the effectiveness of the control strategy.