7 papers
Optimal Diagonal Preconditioning Beyond Worst-Case Conditioning: Theory and Practice of Omega Scaling
Saeed Ghadimi, Woosuk L. Jung, Arnesh Sujanani +2
We study optimal diagonal preconditioning using the classical worst-case -condition number and the averaging-based -condition number. For the -optimal preconditioning prob…
On the local and global minimizers of the smooth stress function in Euclidean Distance Matrix problems
Mengmeng Song, Douglas Goncalves, Woosuk L. Jung +3
We consider the nonconvex minimization problem, with quartic objective function, that arises in the exact recovery of a configuration matrix of points when a Euc…
Projection, Degeneracy, and Singularity Degree for Spectrahedra
Haesol Im, Woosuk L. Jung, David Torregrosa-Belén +1
Facial reduction, FR, is a regularization technique for convex programs where the strict feasibility constraint qualification, CQ, fails.Though this CQ holds generically, failure i…
Single Element Error Correction/ in a Euclidean Distance Matrix
Abdo Alfakih, Woosuk L. Jung, Henry Wolkowicz +1
We consider the \emph{exact} error correction of a noisy Euclidean distance matrix, EDM, where the elements are the squared distances between points in . For our problem w…
Exact Solutions for the NP-hard Wasserstein Barycenter Problem using a Doubly Nonnegative Relaxation and a Splitting Method
Woosuk L. Jung, Henry Wolkowicz
The so-called \emph{simplified} Wasserstein barycenter problem, also known as the cheapest hub problem, consists in selecting one point from each of given sets, each set consis…
The -Condition Number: Applications to Optimal Preconditioning and Low Rank Generalized Jacobian Updating
Woosuk L. Jung, David Torregrosa-Belén, Henry Wolkowicz
Preconditioning is essential in iterative methods for solving linear systems. It is also the implicit objective in updating approximations of Jacobians in optimization methods, e.g…
Role of Subgradients in Variational Analysis of Polyhedral Functions
N. T. V. Hang, W. Jung, M. E. Sarabi
Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of important classes of functions in var…