For the improved two-sided projected quasi-Newton algorithms, which were presented in PartI, we prove in this paper that they are locally one-step or two-step superlinearly convergent. Numerical tests are reported the...For the improved two-sided projected quasi-Newton algorithms, which were presented in PartI, we prove in this paper that they are locally one-step or two-step superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selectedfrom literature have demonstrated the extreme importance of these modifications in making Nocedal& Overton's original methon practical. Furthermore, these results show that the improved algoritnmsare very competitive in comparison with some highly praised sequential quadratic programmingmethods.展开更多
In this paper we improve the two versions of the two-sided projected quasi-Newton method-onewas proposed by Nocedal & Overton in [1] and the other was discussed in our previous paper, byintroducing three different...In this paper we improve the two versions of the two-sided projected quasi-Newton method-onewas proposed by Nocedal & Overton in [1] and the other was discussed in our previous paper, byintroducing three different merit functions to make inexact one-dimensional searches. It is shown that these improved quasi-Newton algorithms have gained global convergence propertywhich is not possessed by the original two algorithms.展开更多
The recently proposed random-phase-free method enables holographic reconstructions with very low noise,which allows fine projections without time integration of sub-holograms. Here, we describe the additional advantag...The recently proposed random-phase-free method enables holographic reconstructions with very low noise,which allows fine projections without time integration of sub-holograms. Here, we describe the additional advantage of this method, namely, the extended depth of sharp imaging. It can be attributed to a lower effective aperture of the hologram section forming a given image point at the projection screen. We experimentally compare the depth of focus and imaging resolution for various defocusing parameters in the cases of the random-phase method and the random-phase-free method. Moreover, we discuss the influence of the effective aperture in the presence of local obstacles in the hologram＇s plane.展开更多
基金This research was supported in part by the National Natural Science Foundation of china
文摘For the improved two-sided projected quasi-Newton algorithms, which were presented in PartI, we prove in this paper that they are locally one-step or two-step superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selectedfrom literature have demonstrated the extreme importance of these modifications in making Nocedal& Overton's original methon practical. Furthermore, these results show that the improved algoritnmsare very competitive in comparison with some highly praised sequential quadratic programmingmethods.
基金This research was supported in part by tbe National Natural Science Foundation of China
文摘In this paper we improve the two versions of the two-sided projected quasi-Newton method-onewas proposed by Nocedal & Overton in [1] and the other was discussed in our previous paper, byintroducing three different merit functions to make inexact one-dimensional searches. It is shown that these improved quasi-Newton algorithms have gained global convergence propertywhich is not possessed by the original two algorithms.
基金funded by the Polish National Centre for Research and Development(No.LIDER/013/469/L-4/12/NCBR/2013)the Polish National Science Centre(No.2015/17/B/ST7/03754)
文摘The recently proposed random-phase-free method enables holographic reconstructions with very low noise,which allows fine projections without time integration of sub-holograms. Here, we describe the additional advantage of this method, namely, the extended depth of sharp imaging. It can be attributed to a lower effective aperture of the hologram section forming a given image point at the projection screen. We experimentally compare the depth of focus and imaging resolution for various defocusing parameters in the cases of the random-phase method and the random-phase-free method. Moreover, we discuss the influence of the effective aperture in the presence of local obstacles in the hologram＇s plane.
