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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long-time asymptotics of soliton equations via the nonlinear steepest descent method
非线性 最速下降法 孤立子方程 长时间渐近性
2023/11/13
Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
Regularization Paths for Cox’s Proportional Hazards Model via Coordinate Descent
survival Cox model lasso elastic net
2015/8/21
We introduce a pathwise algorithm for the Cox proportional hazards model, regularized by convex combinations of `1 and `2 penalties (elastic net). Our algorithm fits via cyclical coordinate descent, a...
SparseNet:Coordinate Descent with Non-Convex Penalties
Sparse Regression Regularization Surface Non-convex Optimization Coordinate Descent Degrees of Freedom Variable Selection LASSO
2015/8/21
We address the problem of sparse selection in linear models. A number of non-convex penalties have been proposed in the literature for this purpose, along with a variety of convex-relaxation algorithm...
THE PEAK ALGEBRA AND THE DESCENT ALGEBRAS OF TYPES B AND D
peak algebra signed permutations Coxeter groups
2015/8/14
We show the existence of a unital subalgebra Pn of the symmetric group
algebra linearly spanned by sums of permutations with a common peak set, which we
call the peak algebra. We show that Pn is the...
Structured Stable Homotopy Theory and the Descent Problem for the Algebraic K-theory of Fields
Structured Stable Homotopy Theory Algebraic K-theory
2015/7/7
his is a relative result which asserts that the K-theory spectra of any two
algebraically closed fields of a given characteristic are equivalent to each other
after completion at a prime not e...
In the theory of schemes, faithfully
at descent is a very powerful tool. One wants a descent theory
not only for quasi-coherent sheaves and morphisms of schemes (which is rather elementary), but al...
Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors
Group descent algorithms nonconvex penalized linear model logistic regression model grouped predictors
2012/11/22
Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not indi...
Learning Model-Based Sparsity via Projected Gradient Descent
Model-Based Sparsity Projected Gradient Descent
2012/11/22
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization paramete...
On the Quiver Presentation of the Descent Algebra of the Symmetric Group
Descent algebra symmetric group quiver presentation
2012/6/15
We describe a presentation for the descent algebra of the symmetric group $\sym{n}$ as a quiver with relations. This presentation arises from a new construction of the descent algebra as a homomorphic...
Explicit n-descent on elliptic curves. III. Algorithms
Explicit n-descent elliptic curves Algorithms Number Theory
2011/9/14
Abstract: This is the third in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as genus one normal curves of degree n. The metho...
Iteration Complexity of Randomized Block-Coordinate Descent Methods for Minimizing a Composite Function
Block coordinate descent iteration complexity composite minimization coordinate relaxation alternating minimization
2011/9/6
Abstract: In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $...
We extend the descent theory of Colliot-Th´el`ene and Sansuc to arbi-trary smooth algebraic varieties by removing the condition that every invertible regular function is constant. This links the...
In the local, unramified case the determinantal functions associated to the group-ring of a finite group satisfy Galois descent. This note examines the obstructions to Galois determinantal descent in ...
We give a self-contained exposition of the proof of faithfully flat descent for projectivity of modules. This fills a gap in the proof given in the literature.
Unconstrained steepest descent method for multicriteria optimization on Riemmanian manifolds
Steepestdescent Paretooptimality Vectoroptimization
2010/11/8
In this paper we present a steepest descent method with Armijo's rule for multicriteria optimization in the Riemannian context. The well definedness of the sequence generated by the method is guarant...