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Found 10 papers, 5 papers with code
Extensions to the Proximal Distance Method of Constrained Optimization
The current paper studies the problem of minimizing a loss $f(\boldsymbol{x})$ subject to constraints of the form $\boldsymbol{D}\boldsymbol{x} \in S$, where $S$ is a closed set, convex or not, and $\boldsymbol{D}$ is a matrix that fuses parameters.
Simple and Scalable Sparse k-means Clustering via Feature Ranking
In this paper, we propose a novel framework for sparse k-means clustering that is intuitive, simple to implement, and competitive with state-of-the-art algorithms.
Orthogonal Trace-Sum Maximization: Applications, Local Algorithms, and Global Optimality
Through a close inspection of Ky Fan's classical result (1949) on the variational formulation of the sum of largest eigenvalues of a symmetric matrix, and a semidefinite programming (SDP) relaxation of the latter, we first provide a simple method to certify global optimality of a given stationary point of OTSM.
Optimization and Control Computation
Generalized Linear Model Regression under Distance-to-set Penalties
Estimation in generalized linear models (GLM) is complicated by the presence of constraints.
An MM Algorithm for Split Feasibility Problems
Furthermore, we show that the Euclidean norm appearing in the proximity function of the non-linear split feasibility problem can be replaced by arbitrary Bregman divergences.
Iterative Hard Thresholding for Model Selection in Genome-Wide Association Studies
This paper introduces the iterative hard thresholding (IHT) algorithm to the GWAS analysis of continuous traits.
Proximal Distance Algorithms: Theory and Examples
If $f(\boldsymbol{x})$ is the loss function, and $C$ is the constraint set in a constrained minimization problem, then the proximal distance principle mandates minimizing the penalized loss $f(\boldsymbol{x})+\frac{\rho}{2}\mathop{dist}(x, C)^2$ and following the solution $\boldsymbol{x}_{\rho}$ to its limit as $\rho$ tends to $\infty$.
Optimization and Control 90C59, 90C26, 65K05
The proximal distance algorithm
For convex programming subject to nonsmooth constraints, one can combine an exact penalty method with distance majorization to create versatile algorithms that are effective even in discrete optimization.
Optimization and Control Data Structures and Algorithms
Splitting Methods for Convex Clustering
In contrast to previously considered algorithms, our ADMM and AMA formulations provide simple and unified frameworks for solving the convex clustering problem under the previously studied norms and open the door to potentially novel norms.
Distance Majorization and Its Applications
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics.
