no code implementations • 2 Sep 2020 • Alfonso Landeros, Oscar Hernan Madrid Padilla, Hua Zhou, Kenneth Lange

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.

1 code implementation • NeurIPS 2020 • Zhiyue Zhang, Kenneth Lange, Jason Xu

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.

1 code implementation • 8 Nov 2018 • Joong-Ho Won, Hua Zhou, Kenneth Lange

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

no code implementations • NeurIPS 2017 • Jason Xu, Eric C. Chi, Kenneth Lange

Estimation in generalized linear models (GLM) is complicated by the presence of constraints.

no code implementations • 16 Dec 2016 • Jason Xu, Eric C. Chi, Meng Yang, Kenneth Lange

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.

1 code implementation • 4 Aug 2016 • Kevin L. Keys, Gary K. Chen, Kenneth Lange

This paper introduces the iterative hard thresholding (IHT) algorithm to the GWAS analysis of continuous traits.

1 code implementation • 19 Apr 2016 • Kevin L. Keys, Hua Zhou, Kenneth Lange

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

1 code implementation • 27 Jul 2015 • Kenneth Lange, Kevin L. Keys

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

no code implementations • 1 Apr 2013 • Eric C. Chi, Kenneth Lange

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.

no code implementations • 16 Nov 2012 • Eric C. Chi, Hua Zhou, Kenneth Lange

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics.

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