A Class of Accelerated Subspace Minimization Conjugate Gradient Methods

Journal of Optimization Theory and Applications - The subspace minimization conjugate gradient methods based on Barzilai–Borwein method (SMCG_BB) and regularization model (SMCG_PR), which...     

New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization

In this paper, two new subspace minimization conjugate gradient methods based on p-regularization models are proposed, where a special scaled norm in p-regularization model is analyzed. Different choices of special scaled norm lead to different solutions to the p-regularized subproblem. Based on the analyses of the solutions in a two-dimensional subspace, we derive new directions satisfying the sufficient descent condition. With a modified nonmonotone line search, we establish the global convergence of the proposed methods under mild assumptions. R-linear convergence of the proposed methods is also analyzed. Numerical results show that, for the CUTEr library, the proposed methods are superior to four conjugate gradient methods, which were proposed by Hager and Zhang (SIAM J. Optim. 16(1):170–192, 2005), Dai and Kou (SIAM J. Optim. 23(1):296–320, 2013), Liu and Liu (J. Optim. Theory. Appl. 180(3):879–906, 2019) and Li et al. (Comput. Appl. Math. 38(1):2019), respectively.

     

A new adaptive Barzilai and Borwein method for unconstrained optimization

In this paper we view the Barzilai and Borwein (BB) method from a new angle, and present a new adaptive Barzilai and Borwein (NABB) method with a nonmonotone line search for general unconstrained optimization. In the proposed method, the scalar approximation to the Hessian matrix is updated by the Broyden class formula to generate an adaptive stepsize. It is remarkable that the new stepsize is chosen adaptively in the interval which contains the two well-known BB stepsizes. Moreover, for the negative curvature direction, a strategy for the choice of the stepsize is designed to accelerate the convergence rate of the NABB method. Furthermore, we apply the NABB method without any line search to strictly convex quadratic minimization. The numerical experiments show the NABB method is very promising.     

Computational analysis of phosphoproteomics: progresses and perspectives

Phosphorylation is one of the most essential post-translational modifications (PTMs) of proteins, regulates a variety of cellular signaling pathways, and at least partially determines the biological diversity. Recent progresses in phosphoproteomics have identified more than 100,000 phosphorylation sites, while this number will easily exceed one million in the next decade. In this regard, how to extract useful information from flood of phosphoproteomics data has emerged as a great challenge. In this review, we summarized the leading edges on computational analysis of phosphoproteomics, including discovery of phosphorylation motifs from phosphoproteomics data, systematic modeling of phosphorylation network, analysis of genetic variation that influences phosphorylation, and phosphorylation evolution. Based on existed knowledge, we also raised several perspectives for further studies. We believe that integration of experimental and computational analyses will propel the phosphoproteomics research into a new phase.     

Radical Addition Enables 1,2‐Aryl Migration from a Vinyl‐Substituted All‐Carbon Quaternary Center

An efficient method for photocatalytic perfluoroalkylation of vinyl‐substituted all‐carbon quaternary centers involving 1,2‐aryl migration has been developed. The rearrangement reactions use fac‐Ir(ppy)₃, visible light and commercially available fluoroalkyl halides and can generate valuable multisubstituted perfluoroalkylated compounds in a single step that would be challenging to prepare by other methods. Mechanistically, the photoinduced alkyl radical addition to an alkene leads to the migration of a vicinal aryl substituent from its adjacent all‐carbon quaternary center with the concomitant generation of a C‐radical bearing two electron‐withdrawing groups that is further reduced by a hydrogen donor to complete the domino sequence.     

A new subspace minimization conjugate gradient method with nonmonotone line search for unconstrained optimization

A new subspace minimization conjugate gradient algorithm with a nonmonotone Wolfe line search is proposed and analyzed. In the scheme, we propose two choices of the search direction by minimizing a quadratic approximation of the objective function in special subspaces, and state criterions on how to choose the direction. Under given conditions, we obtain the significant conclusion that each choice of the direction satisfies the sufficient descent property. Based on the idea on how the function is close to a quadratic function, a new strategy for choosing the initial stepsize is presented for the line search. With the used nonmonotone Wolfe line search, we prove the global convergence of the proposed method for general nonlinear functions under mild assumptions. Numerical comparisons are given with well-known CGOPT and CG_DESCENT and show that the proposed algorithm is very promising.     

An efficient gradient method with approximate optimal stepsize for the strictly convex quadratic minimization problem

In this paper, a new type of stepsize, approximate optimal stepsize, for gradient method is introduced to interpret the Barzilai–Borwein (BB) method, and an efficient gradient method with an approximate optimal stepsize for the strictly convex quadratic minimization problem is presented. Based on a multi-step quasi-Newton condition, we construct a new quadratic approximation model to generate an approximate optimal stepsize. We then use the two well-known BB stepsizes to truncate it for improving numerical effects and treat the resulted approximate optimal stepsize as the new stepsize for gradient method. We establish the global convergence and R-linear convergence of the proposed method. Numerical results show that the proposed method outperforms some well-known gradient methods.     

An Olefinic 1,2‐Boryl‐Migration Enabled by Radical Addition: Construction of gem‐Bis(boryl)alkanes

A series of in situ formed alkenyl diboronate complexes from alkenyl Grignard reagents (commercially available or prepared from alkenyl bromides and Mg) with B₂Pin₂ (bis(pinacolato)diboron) react with diverse alkyl halides by a Ru photocatalyst to give various gem‐bis(boryl)alkanes. Alkyl radicals add efficiently to the alkenyl diboronate complexes, and the adduct radical anions undergo radical‐polar crossover, specifically, a 1,2‐boryl‐anion shift from boron to the α‐carbon sp² center. This transformation shows good functional‐group compatibility and can serve as a powerful synthetic tool for late‐stage functionalization in complex compounds. Measurements of the quantum yield reveal that a radical‐chain mechanism is operative in which the alkenyl diboronates acts as reductive quencher for the excited state of the photocatalyst.     

Some modified fast iterative shrinkage thresholding algorithms with a new adaptive non-monotone stepsize strategy for nonsmooth and convex minimization problems

Computational Optimization and Applications - The “ fast iterative shrinkage-thresholding algorithm " (FISTA) is one of the most famous first order optimization schemes, and the...     

在线测量低能离子束电荷态和能量的新型探测器

基于加速器装置的离子与物质相互作用过程研究,在原子物理、材料、生物等诸多领域具有重要的科学意义和应用价值。本工作设计并研发了一种新型磁谱仪离子探测器,主要由高稳定性偏转磁铁、大面积位置灵敏探测器、空间匹配的散射腔室构成,可以准确在线测量不同离子的电荷态分布以及对应的能谱信息。基于HIRFL加速器装置,完成了该探测器装置的在线标定工作,获得了探测器位置信号与离子能谱之间的定量关系,给出了定标实验条件下该探测系统的最佳能谱精度和能量分辨率分别为0.1%及0.8%。