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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Primal Dual Alternating Proximal Gradient Algorithms for Nonsmooth Nonconvex Minimax Problems with Coupled Linear Constraints
耦合 线性约束 非光滑 非凸极小问题 基本对偶交替 近端梯度算法
2023/4/14
Nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose a primal dual alternating proximal grad...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stochastic approximation methods for nonconvex constrained optimization
非凸 约束优化 随机逼近方法
2023/4/14
Nonconvex constrained optimization (NCO) has been one of the important research fields in optimization community. It has widely appeared in many application fields. However, challenges for solving NCO...
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...
A PDE approach to large-time asymptotics for boundary-value problems for nonconvex Hamilton-Jacobi Equations
Large-time Behavior Hamilton-Jacobi Equations Initial-Boundary Value Problem
2011/1/18
We investigate the large-time behavior of three types of initial-boundary value problems for Hamilton-Jacobi Equations with nonconvex Hamiltonians.
Restricted p-isometry property and its application for nonconvex compressive sensing
Compressed sensing lp minimization instance optimality stability
2018/4/19
Compressed sensing is a new scheme which shows the ability to recover sparse signal from fewer measurements, using l1 minimization. Recently, Chartrand and Staneva shown in [7] that the lp minimizatio...
Limiting Convex Examples for Nonconvex Subdifferential Calculus
Nonsmooth analysis subdifferentials coderivatives extremal principle open mapping theorem metric regularity multiplier rules compactly Lipschitzian conditions
2009/1/23
We show, largely using convex examples, that most of the core results for limiting subdifferential calculus fail without additional restrictions in infinite dimensional Banach spaces.
Nonexistence of Solutions in Nonconvex Multidimensional Variational Problems
Gradient Young measures extreme points Cantor sets integration factors Bauer principle nonattainment
2009/1/19
In the scalar n-dimensional situation, the extreme points in the set of certain gradient Lp-Young measures
are studied. For n = 1, such Young measures must be composed from Diracs, while for n µ...
An Iterative Method for Nonconvex Equilibrium Problems
Uniform prox-regularity Uniform regularity over sets Strong monotonicity
2008/7/3
Using some recent results from nonsmooth analysis, we prove the convergence of a new iterative scheme to a solution of a nonconvex equilibrium problem.
Iterative Schemes to Solve Nonconvex Variational Problems
Prox-regularity Normal cone Variational inequality
2008/6/30
In this paper, we present several algorithms of the projection type to solve a class of nonconvex variational problems.
The Global Convergence of Self-scale BFGS Algorithm with Nonmonotone Line Search for Unconstrained Nonconvex Optimization Problems
nonmonotone line search self-scaling BFGS method global convergence
2007/12/11
The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenva...