16 research outputs found
Homogeneous Second-Order Descent Framework: A Fast Alternative to Newton-Type Methods
This paper proposes a homogeneous second-order descent framework (HSODF) for
nonconvex and convex optimization based on the generalized homogeneous model
(GHM). In comparison to the Newton steps, the GHM can be solved by extremal
symmetric eigenvalue procedures and thus grant an advantage in ill-conditioned
problems. Moreover, GHM extends the ordinary homogeneous model (OHM) to allow
adaptiveness in the construction of the aggregated matrix. Consequently, HSODF
is able to recover some well-known second-order methods, such as trust-region
methods and gradient regularized methods, while maintaining comparable
iteration complexity bounds. We also study two specific realizations of HSODF.
One is adaptive HSODM, which has a parameter-free global
complexity bound for nonconvex second-order Lipschitz continuous objective
functions. The other one is homotopy HSODM, which is proven to have a global
linear rate of convergence without strong convexity. The efficiency of our
approach to ill-conditioned and high-dimensional problems is justified by some
preliminary numerical results.Comment: improved writin
A Universal Trust-Region Method for Convex and Nonconvex Optimization
This paper presents a universal trust-region method simultaneously
incorporating quadratic regularization and the ball constraint. We introduce a
novel mechanism to set the parameters in the proposed method that unifies the
analysis for convex and nonconvex optimization. Our method exhibits an
iteration complexity of to find an approximate
second-order stationary point for nonconvex optimization. Meanwhile, the
analysis reveals that the universal method attains an
complexity bound for convex optimization and can be accelerated. These results
are complementary to the existing literature as the trust-region method was
historically conceived for nonconvex optimization. Finally, we develop an
adaptive universal method to address practical implementations. The numerical
results show the effectiveness of our method in both nonconvex and convex
problems
A Homogenization Approach for Gradient-Dominated Stochastic Optimization
Gradient dominance property is a condition weaker than strong convexity, yet
it sufficiently ensures global convergence for first-order methods even in
non-convex optimization. This property finds application in various machine
learning domains, including matrix decomposition, linear neural networks, and
policy-based reinforcement learning (RL). In this paper, we study the
stochastic homogeneous second-order descent method (SHSODM) for
gradient-dominated optimization with based on a recently
proposed homogenization approach. Theoretically, we show that SHSODM achieves a
sample complexity of for
and for . We further
provide a SHSODM with a variance reduction technique enjoying an improved
sample complexity of for . Our results match the state-of-the-art sample complexity bounds
for stochastic gradient-dominated optimization without \emph{cubic
regularization}. Since the homogenization approach only relies on solving
extremal eigenvector problems instead of Newton-type systems, our methods gain
the advantage of cheaper iterations and robustness in ill-conditioned problems.
Numerical experiments on several RL tasks demonstrate the efficiency of SHSODM
compared to other off-the-shelf methods
Trust Region Methods For Nonconvex Stochastic Optimization Beyond Lipschitz Smoothness
In many important machine learning applications, the standard assumption of
having a globally Lipschitz continuous gradient may fail to hold. This paper
delves into a more general -smoothness setting, which gains
particular significance within the realms of deep neural networks and
distributionally robust optimization (DRO). We demonstrate the significant
advantage of trust region methods for stochastic nonconvex optimization under
such generalized smoothness assumption. We show that first-order trust region
methods can recover the normalized and clipped stochastic gradient as special
cases and then provide a unified analysis to show their convergence to
first-order stationary conditions. Motivated by the important application of
DRO, we propose a generalized high-order smoothness condition, under which
second-order trust region methods can achieve a complexity of
for convergence to second-order stationary
points. By incorporating variance reduction, the second-order trust region
method obtains an even better complexity of ,
matching the optimal bound for standard smooth optimization. To our best
knowledge, this is the first work to show convergence beyond the first-order
stationary condition for generalized smooth optimization. Preliminary
experiments show that our proposed algorithms perform favorably compared with
existing methods
cuPDLP-C: A Strengthened Implementation of cuPDLP for Linear Programming by C language
A recent GPU implementation of the Restarted Primal-Dual Hybrid Gradient
Method for Linear Programming was proposed in Lu and Yang (2023). Its
computational results demonstrate the significant computational advantages of
the GPU-based first-order algorithm on certain large-scale problems. The
average performance also achieves a level close to commercial solvers for the
first time in history. However, due to limitations in experimental hardware and
the disadvantage of implementing the algorithm in Julia compared to C language,
neither the commercial solver nor cuPDLP reached their maximum efficiency.
Therefore, in this report, we have re-implemented and optimized cuPDLP in C
language. Utilizing state-of-the-art CPU and GPU hardware, we extensively
compare cuPDLP with the best commercial solvers. The experiments further
highlight its substantial computational advantages and potential for solving
large-scale linear programming problems. We also discuss the profound impact
this breakthrough may have on mathematical programming research and the entire
operations research community.Comment: fix typos, update numerical result
An Enhanced ADMM-based Interior Point Method for Linear and Conic Optimization
The ADMM-based interior point (ABIP, Lin et al. 2021) method is a hybrid
algorithm that effectively combines interior point method (IPM) and first-order
methods to achieve a performance boost in large-scale linear optimization.
Different from traditional IPM that relies on computationally intensive Newton
steps, the ABIP method applies the alternating direction method of multipliers
(ADMM) to approximately solve the barrier penalized problem. However, similar
to other first-order methods, this technique remains sensitive to condition
number and inverse precision. In this paper, we provide an enhanced ABIP method
with multiple improvements. Firstly, we develop an ABIP method to solve the
general linear conic optimization and establish the associated iteration
complexity. Secondly, inspired by some existing methods, we develop different
implementation strategies for ABIP method, which substantially improve its
performance in linear optimization. Finally, we conduct extensive numerical
experiments in both synthetic and real-world datasets to demonstrate the
empirical advantage of our developments. In particular, the enhanced ABIP
method achieves a 5.8x reduction in the geometric mean of run time on
selected LP instances from Netlib, and it exhibits advantages in certain
structured problems such as SVM and PageRank. However, the enhanced ABIP method
still falls behind commercial solvers in many benchmarks, especially when high
accuracy is desired. We posit that it can serve as a complementary tool
alongside well-established solvers
Diversity of Trichoderma species associated with the black rot disease of Gastrodia elata, including four new species
IntroductionTrichoderma species establish symbiotic relationships with plants through both parasitic and mutualistic mechanisms. While some Trichoderma species act as plant pathogenic fungi, others utilize various strategies to protect and enhance plant growth.MethodsPhylogenetic positions of new species of Trichoderma were determined through multi-gene analysis relying on the internal transcribed spacer (ITS) regions of the ribosomal DNA, the translation elongation factor 1-Ī± (tef1-Ī±) gene, and the RNA polymerase II (rpb2) gene. Additionally, pathogenicity experiments were conducted, and the aggressiveness of each isolate was evaluated based on the area of the cross-section of the infected site.ResultsIn this study, 13 Trichoderma species, including 9 known species and 4 new species, namely, T. delicatum, T. robustum, T. perfasciculatum, and T. subulatum were isolated from the diseased tubers of Gastrodia elata in Yunnan, China. Among the known species, T. hamatum had the highest frequency. T. delicatum belonged to the Koningii clade. T. robustum and T. perfasciculatum were assigned to the Virens clade. T. subulatum emerged as a new member of the Spirale clade. Pathogenicity experiments were conducted on the new species T. robustum, T. delicatum, and T. perfasciculatum, as well as the known species T. hamatum, T. atroviride, and T. harzianum. The infective abilities of different Trichoderma species on G. elata varied, indicating that Trichoderma was a pathogenic fungus causing black rot disease in G. elata.DiscussionThis study provided the morphological characteristics of new species and discussed the morphological differences with phylogenetically proximate species, laying the foundation for research aimed at preventing and managing diseases that affect G. elata
Analyses of a chromosome-scale genome assembly reveal the origin and evolution of cultivated chrysanthemum
DATA AVAILABILITY : The raw sequencing data generated in this study have been deposited
in the NCBI under accession PRJNA796762 and PRJNA895586 The
chloroplast andmitochondrial genome were also available at GenBank
under the accession number OP104251 and OP104742 respectively.
The assembled genome sequences and annotations are available at
Figshare [https://doi.org/10.6084/m9.figshare.21655364.v2]. The Arabidopsis
ABCE and chrysanthemum CYC2 genes were used as query
sequences for gene family identification, which are available at Figshare
[https://doi.org/10.6084/m9.figshare.21610305]. Source data are
provided with this paper.Chrysanthemum (Chrysanthemum morifolium Ramat.) is a globally important
ornamental plant with great economic, cultural, and symbolic value. However,
research on chrysanthemum is challenging due to its complex genetic background.
Here, we report a near-complete assembly and annotation for
C. morifolium comprising 27 pseudochromosomes (8.15 Gb; scaffold N50 of
303.69Mb). Comparative and evolutionary analyses reveal a whole-genome
triplication (WGT) event shared by Chrysanthemum species approximately 6
million years ago (Mya) and the possible lineage-specific polyploidization of
C. morifolium approximately 3 Mya. Multilevel evidence suggests that
C. morifolium is likely a segmental allopolyploid. Furthermore, a combination
of genomics and transcriptomics approaches demonstrate the C. morifolium
genome can be used to identify genes underlying key ornamental traits. Phylogenetic
analysis of CmCCD4a traces the flower colour breeding history of
cultivated chrysanthemum. Genomic resources generated from this study
could help to accelerate chrysanthemum genetic improvement.The National Natural Science Foundation of China, the Natural Science Fund of Jiangsu Province, China Agriculture Research System, the National Key Research and Development Program of China, the āJBGSā Project of Seed Industry Revitalisation in Jiangsu Province, the European Unionās Horizon 2020 research and innovation program from European Research Council, the Methusalem funding from Ghent University, and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institution.https://www.nature.com/ncomms/am2024BiochemistryGeneticsMicrobiology and Plant PathologySDG-15:Life on lan
ļ»æTwo new Trichoderma species (Hypocreales, Hypocreaceae) isolated from decaying tubers of Gastrodia elate
Species of Trichoderma are widely distributed around the world. In this study, two new species in Trichoderma, named as T. albidum and T. variegatum, were introduced and illustrated. These species were isolated from diseased tubers of Gastrodia elata in China and identified based on morphological characteristics and multi-gene sequence analyses of three loci that is the internal transcribed spacer regions of the ribosomal DNA (ITS), the translation elongation factor 1-Ī± encoding gene (tef1-Ī±) and the gene encoding the second largest nuclear RNA polymerase subunit (rpb2). Distinctions between the new species and their close relatives were discussed. According to results of the phylogenetic analyses, T. albidum belonged to the Harzianum clade and T. variegatum are grouped with species of the Spirale clade. The expansion of two clades provided research foundations for the prevention and control of tuber diseases in G. elata
Oral Delivery of a Nanocrystal Formulation of Schisantherin A with Improved Bioavailability and Brain Delivery for the Treatment of Parkinsonās Disease
Schisantherin A (SA)
is a promising anti-Parkinsonism Chinese herbal
medicine but with poor water solubility and challenges to be delivered
to the brain. We formulated SA as nanocrystals (SA-NC), aiming to
improve its solubility and pharmacokinetic profile and thus provide
a potential therapeutic agent for the treatment of Parkinsonās
disease (PD). The rod-shaped SA-NC had a particle size of ā¼160
nm with 33.3% drug loading, and the nanocrystals exhibited a fast
dissolution rate <i>in vitro</i>. The intact drug nanocrystals
could be internalized into Madin-Darby canine kidney (MDCK) cells,
which were followed by rapid intracellular release, and most of the
drug was transported to the basolateral side in its soluble form.
Following oral administration of the SA-NC or an SA suspension, the
accumulated concentration of the SA-NC in the plasma and brain was
considerably higher than that observed for the SA suspension, but
the drug targeting efficiency was similar. The SA-NC significantly
reversed the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP)-induced
dopaminergic (DA) neuronal loss and locomotion deficiency in zebrafish,
as well as the 1-methyl-4-phenylpyridinium ion (MPP<sup>+</sup>)-induced
damage of neuronal cell culture model. Further Western blot analysis
demonstrated that the stronger neuroprotective effect of SA-NC may
be partially mediated by the activation of the protein kinase B (Akt)/glycogen
synthase kinase-3Ī² (Gsk3Ī²) pathway. Taken together, these
data provide solid evidence that the nanocrystal formulation has the
potential to improve the bioavailability and brain concentration of
this Biopharmaceutics Classification System (BCS) class II compound,
SA, for the treatment of PD