6 papers
Optimal Nonergodic Primal-Dual Complexity of Efficient Inexact Parameter-Free Augmented Lagrangian Methods
Arnesh Sujanani, Saeed Ghadimi, Henry WoÅkowicz +1
Augmented Lagrangian (AL) methods are a classical framework for constrained optimization, but for directly verifiable approximate KKT points, known first-order complexity bounds fo…
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…
Finding Maximum Determinant Principal Submatrices via Hadamard Bounds and Projection Methods
Hao Hu, Stefan Sremac, Hugo J. Woerdeman +1
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This…
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 p…
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…
A necessary condition for the guarantee of the superiorization method
Kay Barshad, Yair Censor, Walaa Moursi +2
We study a method that involves principally convex feasibility-seeking and makes secondary efforts of objective function value reduction. This is the well-known superiorization met…