Projection onto the capped simplex

快速投影到带帽单纯形及其在生物信息学稀疏回归中的应用

Fast Projection onto the Capped Simplex with Applications to Sparse Regression in Bioinformatics

本文提出一种基于牛顿法的O(n)复杂度快速投影算法，用于k-带帽单纯形投影，在生物信息学大规模稀疏回归中显著加速PQN方法，较现有方法快3-8倍。

Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application

We provide an elementary proof of a simple, efficient algorithm for computing the Euclidean projection of a point onto the probability simplex. We also show an application in Laplacian K-modes clustering.

Sparse projections onto the simplex

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the $\ell_1$-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank and sparsity constraints. In this setting, we derive efficient sparse projections onto the simplex and its extension, and illustrate how to use them to solve high-dimensional learning problems in quantum tomography, sparse density estimation and portfolio selection with non-convex…

考虑协方差的简单投影用于具有约束的组合优化

Covariance-Aware Simplex Projection for Cardinality-Constrained Portfolio Optimization

本文提出CASP，一种考虑协方差的简单形投影方法，用于解决具有约束的投资组合优化问题，通过波动性标准化选择和协方差意识的几何投影降低投资组合方差，提升夏普比率。

NewVEM：一类约束自和谐最小化问题的牛顿顶点交换方法

NewVEM: A Newton Vertex Exchange Method for a Class of Constrained Self-Concordant Minimization Problems

提出NewVEM算法，结合投影牛顿与顶点交换方法，高效求解广义单纯形约束下的自和谐最小化问题，并辅以半光滑牛顿投影方法，实验验证其高效性与可扩展性。

Fresh-CL：持续学习中通过超球面上专家实现的特征重对齐

Fresh-CL: Feature Realignment through Experts on Hypersphere in Continual Learning

针对持续学习中新任务引入导致的特征纠缠问题，提出结合超球面单纯形ETF与动态MoE扩展的Fresh-CL方法，11个数据集实验显示较最强基线准确率提升2%，有效增强特征区分度。